Add SIKE software
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Patrick Longa
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15
README.md
15
README.md
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@ -26,19 +26,24 @@ relative to AES and SHA-3.
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- - -
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## File Organization
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- `platform/AC701/` contains hardware development files targeting the Artix-7 AC701 XC7A200TFBG676 FPGA.
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- `platforms/AC701/` contains hardware development files targeting the Artix-7 AC701 XC7A200TFBG676 FPGA.
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- `platforms/Murax/` contains the scala source code for generating the Murax SoC.
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- `platforms/rtl` contains the APB bridge modules developed for the communication between the software and hardware.
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- `src/hardware` contains hardware accelerators source code.
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- `Python_script` contains the Python3 script for the security estimation of SIKE relative to AES and SHA-3.
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- `src/murax` contains Murax library files.
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- `SIKE_sw` contains the software implementation of SIKE, including the new parameter sets SIKEp377, SIKEp546 and SIKEp697.
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- `src/ref_c` contains the software implementation of vOW on SIKE, which is based on [3] and the [vOW4SIKE library](https://github.com/microsoft/vOW4SIKE).
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- `SIKE_vOW_hw-sw/hardware` contains the hardware accelerators source code.
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- `src/ref_c_riscv` contains the software libraries for calling the hardware accelerators and RISC-V testing files.
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- `SIKE_vOW_hw-sw/murax` contains the Murax library files.
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- `SIKE_vOW_hw-sw/ref_c` contains the software implementation of vOW on SIKE, which is based on [3] and the [vOW4SIKE library](https://github.com/microsoft/vOW4SIKE).
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- `SIKE_vOW_hw-sw/ref_c_riscv` contains the hardware/software co-design of vOW on SIKE.
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It contains the software libraries for calling the hardware accelerators and RISC-V testing files.
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- `LICENSE` MIT license covering all the implementations, except for the files that are labeled as created by third parties.
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@ -0,0 +1,263 @@
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#### Makefile for compilation on Linux ####
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OPT=-O3 # Optimization option by default
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CC=clang
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ifeq "$(CC)" "gcc"
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COMPILER=gcc
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else ifeq "$(CC)" "clang"
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COMPILER=clang
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endif
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ARCHITECTURE=_AMD64_
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USE_OPT_LEVEL=_FAST_
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ifeq "$(ARCH)" "x64"
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ARCHITECTURE=_AMD64_
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USE_OPT_LEVEL=_FAST_
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else ifeq "$(ARCH)" "x86"
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ARCHITECTURE=_X86_
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USE_OPT_LEVEL=_GENERIC_
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endif
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ifeq "$(OPT_LEVEL)" "GENERIC"
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USE_OPT_LEVEL=_GENERIC_
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endif
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ifeq "$(ARCHITECTURE)" "_AMD64_"
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ifeq "$(USE_OPT_LEVEL)" "_FAST_"
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MULX=-D _MULX_
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ifeq "$(USE_MULX)" "FALSE"
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MULX=
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else
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ADX=-D _ADX_
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ifeq "$(USE_ADX)" "FALSE"
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ADX=
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endif
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endif
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endif
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endif
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ifeq "$(SET)" "EXTENDED"
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ADDITIONAL_SETTINGS=-fwrapv -fomit-frame-pointer -march=native
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endif
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AR=ar rcs
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RANLIB=ranlib
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CFLAGS=$(OPT) $(ADDITIONAL_SETTINGS) -D $(ARCHITECTURE) -D __LINUX__ -D $(USE_OPT_LEVEL) $(MULX) $(ADX) -fPIE
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LDFLAGS=-lm
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ifeq "$(ARCHITECTURE)" "_AMD64_"
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ifeq "$(USE_OPT_LEVEL)" "_FAST_"
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CFLAGS += -mavx2 -maes -msse2
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endif
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endif
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ifeq "$(USE_OPT_LEVEL)" "_GENERIC_"
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EXTRA_OBJECTS_377=objs377/fp_generic.o
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EXTRA_OBJECTS_434=objs434/fp_generic.o
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EXTRA_OBJECTS_503=objs503/fp_generic.o
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EXTRA_OBJECTS_546=objs546/fp_generic.o
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EXTRA_OBJECTS_610=objs610/fp_generic.o
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EXTRA_OBJECTS_697=objs697/fp_generic.o
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EXTRA_OBJECTS_751=objs751/fp_generic.o
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else ifeq "$(USE_OPT_LEVEL)" "_FAST_"
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ifeq "$(ARCHITECTURE)" "_AMD64_"
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EXTRA_OBJECTS_377=objs377/fp_x64.o objs377/fp_x64_asm.o
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EXTRA_OBJECTS_434=objs434/fp_x64.o objs434/fp_x64_asm.o
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EXTRA_OBJECTS_503=objs503/fp_x64.o objs503/fp_x64_asm.o
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EXTRA_OBJECTS_546=objs546/fp_x64.o objs546/fp_x64_asm.o
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EXTRA_OBJECTS_610=objs610/fp_x64.o objs610/fp_x64_asm.o
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EXTRA_OBJECTS_697=objs697/fp_x64.o objs697/fp_x64_asm.o
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EXTRA_OBJECTS_751=objs751/fp_x64.o objs751/fp_x64_asm.o
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CFLAGS+= -fPIC
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endif
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endif
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OBJECTS_377=objs377/P377.o $(EXTRA_OBJECTS_377) objs/random.o objs/fips202.o
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OBJECTS_434=objs434/P434.o $(EXTRA_OBJECTS_434) objs/random.o objs/fips202.o
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OBJECTS_503=objs503/P503.o $(EXTRA_OBJECTS_503) objs/random.o objs/fips202.o
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OBJECTS_546=objs546/P546.o $(EXTRA_OBJECTS_546) objs/random.o objs/fips202.o
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OBJECTS_610=objs610/P610.o $(EXTRA_OBJECTS_610) objs/random.o objs/fips202.o
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OBJECTS_697=objs697/P697.o $(EXTRA_OBJECTS_697) objs/random.o objs/fips202.o
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OBJECTS_751=objs751/P751.o $(EXTRA_OBJECTS_751) objs/random.o objs/fips202.o
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all: lib377 lib434 lib503 lib546 lib610 lib697 lib751 tests tests_sike
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objs377/%.o: src/P377/%.c
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@mkdir -p $(@D)
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$(CC) -c $(CFLAGS) $< -o $@
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objs434/%.o: src/P434/%.c
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@mkdir -p $(@D)
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$(CC) -c $(CFLAGS) $< -o $@
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objs503/%.o: src/P503/%.c
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@mkdir -p $(@D)
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$(CC) -c $(CFLAGS) $< -o $@
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objs546/%.o: src/P546/%.c
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@mkdir -p $(@D)
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$(CC) -c $(CFLAGS) $< -o $@
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objs610/%.o: src/P610/%.c
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@mkdir -p $(@D)
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$(CC) -c $(CFLAGS) $< -o $@
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objs697/%.o: src/P697/%.c
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@mkdir -p $(@D)
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$(CC) -c $(CFLAGS) $< -o $@
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objs751/%.o: src/P751/%.c
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@mkdir -p $(@D)
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$(CC) -c $(CFLAGS) $< -o $@
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ifeq "$(USE_OPT_LEVEL)" "_GENERIC_"
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objs377/fp_generic.o: src/P377/generic/fp_generic.c
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$(CC) -c $(CFLAGS) src/P377/generic/fp_generic.c -o objs377/fp_generic.o
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objs434/fp_generic.o: src/P434/generic/fp_generic.c
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$(CC) -c $(CFLAGS) src/P434/generic/fp_generic.c -o objs434/fp_generic.o
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objs503/fp_generic.o: src/P503/generic/fp_generic.c
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$(CC) -c $(CFLAGS) src/P503/generic/fp_generic.c -o objs503/fp_generic.o
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objs546/fp_generic.o: src/P546/generic/fp_generic.c
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$(CC) -c $(CFLAGS) src/P546/generic/fp_generic.c -o objs546/fp_generic.o
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objs610/fp_generic.o: src/P610/generic/fp_generic.c
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$(CC) -c $(CFLAGS) src/P610/generic/fp_generic.c -o objs610/fp_generic.o
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objs697/fp_generic.o: src/P697/generic/fp_generic.c
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$(CC) -c $(CFLAGS) src/P697/generic/fp_generic.c -o objs697/fp_generic.o
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objs751/fp_generic.o: src/P751/generic/fp_generic.c
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$(CC) -c $(CFLAGS) src/P751/generic/fp_generic.c -o objs751/fp_generic.o
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else ifeq "$(USE_OPT_LEVEL)" "_FAST_"
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ifeq "$(ARCHITECTURE)" "_AMD64_"
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objs377/fp_x64.o: src/P377/AMD64/fp_x64.c
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$(CC) -c $(CFLAGS) src/P377/AMD64/fp_x64.c -o objs377/fp_x64.o
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objs377/fp_x64_asm.o: src/P377/AMD64/fp_x64_asm.S
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$(CC) -c $(CFLAGS) src/P377/AMD64/fp_x64_asm.S -o objs377/fp_x64_asm.o
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objs434/fp_x64.o: src/P434/AMD64/fp_x64.c
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$(CC) -c $(CFLAGS) src/P434/AMD64/fp_x64.c -o objs434/fp_x64.o
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objs434/fp_x64_asm.o: src/P434/AMD64/fp_x64_asm.S
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$(CC) -c $(CFLAGS) src/P434/AMD64/fp_x64_asm.S -o objs434/fp_x64_asm.o
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objs503/fp_x64.o: src/P503/AMD64/fp_x64.c
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$(CC) -c $(CFLAGS) src/P503/AMD64/fp_x64.c -o objs503/fp_x64.o
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objs503/fp_x64_asm.o: src/P503/AMD64/fp_x64_asm.S
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$(CC) -c $(CFLAGS) src/P503/AMD64/fp_x64_asm.S -o objs503/fp_x64_asm.o
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objs546/fp_x64.o: src/P546/AMD64/fp_x64.c
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$(CC) -c $(CFLAGS) src/P546/AMD64/fp_x64.c -o objs546/fp_x64.o
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objs546/fp_x64_asm.o: src/P546/AMD64/fp_x64_asm.S
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$(CC) -c $(CFLAGS) src/P546/AMD64/fp_x64_asm.S -o objs546/fp_x64_asm.o
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objs610/fp_x64.o: src/P610/AMD64/fp_x64.c
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$(CC) -c $(CFLAGS) src/P610/AMD64/fp_x64.c -o objs610/fp_x64.o
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objs610/fp_x64_asm.o: src/P610/AMD64/fp_x64_asm.S
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$(CC) -c $(CFLAGS) src/P610/AMD64/fp_x64_asm.S -o objs610/fp_x64_asm.o
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objs697/fp_x64.o: src/P697/AMD64/fp_x64.c
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$(CC) -c $(CFLAGS) src/P697/AMD64/fp_x64.c -o objs697/fp_x64.o
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objs697/fp_x64_asm.o: src/P697/AMD64/fp_x64_asm.S
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$(CC) -c $(CFLAGS) src/P697/AMD64/fp_x64_asm.S -o objs697/fp_x64_asm.o
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objs751/fp_x64.o: src/P751/AMD64/fp_x64.c
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$(CC) -c $(CFLAGS) src/P751/AMD64/fp_x64.c -o objs751/fp_x64.o
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objs751/fp_x64_asm.o: src/P751/AMD64/fp_x64_asm.S
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$(CC) -c $(CFLAGS) src/P751/AMD64/fp_x64_asm.S -o objs751/fp_x64_asm.o
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endif
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endif
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INDEPENDENT_OBJS=objs/random.o objs/fips202.o
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objs/random.o: src/random/random.c
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objs/fips202.o: src/sha3/fips202.c
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$(INDEPENDENT_OBJS):
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@mkdir -p $(@D)
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$(CC) -c $(CFLAGS) $< -o $@
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lib377: $(OBJECTS_377)
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rm -rf lib377 sike377
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mkdir lib377 sike377
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$(AR) lib377/libsidh.a $^
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$(RANLIB) lib377/libsidh.a
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lib434: $(OBJECTS_434)
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rm -rf lib434 sike434
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mkdir lib434 sike434
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$(AR) lib434/libsidh.a $^
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$(RANLIB) lib434/libsidh.a
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lib503: $(OBJECTS_503)
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rm -rf lib503 sike503
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mkdir lib503 sike503
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$(AR) lib503/libsidh.a $^
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$(RANLIB) lib503/libsidh.a
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lib546: $(OBJECTS_546)
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rm -rf lib546 sike546
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mkdir lib546 sike546
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$(AR) lib546/libsidh.a $^
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$(RANLIB) lib546/libsidh.a
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lib610: $(OBJECTS_610)
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rm -rf lib610 sike610
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mkdir lib610 sike610
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$(AR) lib610/libsidh.a $^
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$(RANLIB) lib610/libsidh.a
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lib697: $(OBJECTS_697)
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rm -rf lib697 sike697
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mkdir lib697 sike697
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$(AR) lib697/libsidh.a $^
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$(RANLIB) lib697/libsidh.a
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lib751: $(OBJECTS_751)
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rm -rf lib751 sike751
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mkdir lib751 sike751
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$(AR) lib751/libsidh.a $^
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$(RANLIB) lib751/libsidh.a
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tests: lib377 lib434 lib503 lib546 lib610 lib697 lib751
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$(CC) $(CFLAGS) -L./lib377 tests/arith_tests-p377.c tests/test_extras.c -lsidh $(LDFLAGS) -o arith_tests-p377 $(ARM_SETTING)
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$(CC) $(CFLAGS) -L./lib434 tests/arith_tests-p434.c tests/test_extras.c -lsidh $(LDFLAGS) -o arith_tests-p434 $(ARM_SETTING)
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$(CC) $(CFLAGS) -L./lib503 tests/arith_tests-p503.c tests/test_extras.c -lsidh $(LDFLAGS) -o arith_tests-p503 $(ARM_SETTING)
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$(CC) $(CFLAGS) -L./lib546 tests/arith_tests-p546.c tests/test_extras.c -lsidh $(LDFLAGS) -o arith_tests-p546 $(ARM_SETTING)
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$(CC) $(CFLAGS) -L./lib610 tests/arith_tests-p610.c tests/test_extras.c -lsidh $(LDFLAGS) -o arith_tests-p610 $(ARM_SETTING)
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$(CC) $(CFLAGS) -L./lib697 tests/arith_tests-p697.c tests/test_extras.c -lsidh $(LDFLAGS) -o arith_tests-p697 $(ARM_SETTING)
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$(CC) $(CFLAGS) -L./lib751 tests/arith_tests-p751.c tests/test_extras.c -lsidh $(LDFLAGS) -o arith_tests-p751 $(ARM_SETTING)
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tests_sike377: lib377
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$(CC) $(CFLAGS) -L./lib377 tests/test_SIKEp377.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike377/test_SIKE $(ARM_SETTING)
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tests_sike434: lib434
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$(CC) $(CFLAGS) -L./lib434 tests/test_SIKEp434.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike434/test_SIKE $(ARM_SETTING)
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tests_sike503: lib503
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$(CC) $(CFLAGS) -L./lib503 tests/test_SIKEp503.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike503/test_SIKE $(ARM_SETTING)
|
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tests_sike546: lib546
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$(CC) $(CFLAGS) -L./lib546 tests/test_SIKEp546.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike546/test_SIKE $(ARM_SETTING)
|
||||
tests_sike610: lib610
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$(CC) $(CFLAGS) -L./lib610 tests/test_SIKEp610.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike610/test_SIKE $(ARM_SETTING)
|
||||
tests_sike697: lib697
|
||||
$(CC) $(CFLAGS) -L./lib697 tests/test_SIKEp697.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike697/test_SIKE $(ARM_SETTING)
|
||||
tests_sike751: lib751
|
||||
$(CC) $(CFLAGS) -L./lib751 tests/test_SIKEp751.c tests/test_extras.c -lsidh $(LDFLAGS) -o sike751/test_SIKE $(ARM_SETTING)
|
||||
|
||||
tests_sike: tests_sike377 tests_sike434 tests_sike503 tests_sike546 tests_sike610 tests_sike697 tests_sike751
|
||||
|
||||
check: tests tests_sike
|
||||
|
||||
.PHONY: clean
|
||||
|
||||
clean:
|
||||
rm -rf *.req objs* lib* sike* arith_tests-*
|
||||
|
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@ -0,0 +1,57 @@
|
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# Software implementation of SIKE
|
||||
# Paper "The Cost to Break SIKE: A Comparative Hardware-Based Analysis with AES and SHA-3"
|
||||
|
||||
This library contains efficient C implementations of the CCA-secure key encapsulation mechanism "SIKE".
|
||||
This scheme is conjectured to be secure against quantum computer attacks.
|
||||
The software is based on the SIDH library version 3.3 (https://github.com/microsoft/PQCrypto-SIDH).
|
||||
|
||||
This library includes the following KEM schemes:
|
||||
|
||||
* SIKEp377: matching the post-quantum security of AES128 (NEW, level 1).
|
||||
* SIKEp434: matching the post-quantum security of AES128 (level 1).
|
||||
* SIKEp503: matching the post-quantum security of SHA3-256 (level 2).
|
||||
* SIKEp546: matching the post-quantum security of AES192 (NEW, level 3).
|
||||
* SIKEp610: matching the post-quantum security of AES192 (level 3).
|
||||
* SIKEp697: matching the post-quantum security of AES256 (NEW, level 5).
|
||||
* SIKEp751: matching the post-quantum security of AES256 (level 5).
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||||
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||||
## Contents
|
||||
|
||||
In the remainder, pXXX is one of {p377,p434,p503,p546,p610,p697,p751}.
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||||
|
||||
* [`src folder`](src/): C and header files. Public APIs can be found in src/PXXX/PXXX_api.h.
|
||||
* Optimized x64 implementation for pXXX (src/PXXX/AMD64/): optimized implementation of the field arithmetic over the prime pXXX for x64 platforms.
|
||||
* Generic implementation for pXXX (src/PXXX/generic/): implementation of the field arithmetic over the prime pXXX in portable C.
|
||||
* [`random folder`](src/random/): randombytes function using the system random number generator.
|
||||
* [`sha3 folder`](src/sha3/): SHAKE256 implementation.
|
||||
* [`Test folder`](tests/): test files.
|
||||
* [`Visual Studio folder`](Visual%20Studio/): Visual Studio 2015 files for compilation in Windows.
|
||||
* [`Makefile`](Makefile): Makefile for compilation using the GNU GCC or clang compilers on Linux.
|
||||
* [`Readme`](README.md): this readme file.
|
||||
|
||||
## Instructions for Linux
|
||||
|
||||
By executing:
|
||||
|
||||
```sh
|
||||
$ make
|
||||
```
|
||||
|
||||
the library is compiled by default for x64 using clang, optimization level `FAST` that uses assembly-optimized arithmetic
|
||||
(this option requires CPU support for the instructions MULX and ADX).
|
||||
|
||||
Other options for x64:
|
||||
|
||||
```sh
|
||||
$ make CC=[gcc/clang] OPT_LEVEL=[FAST/GENERIC]
|
||||
```
|
||||
|
||||
The use of `OPT_LEVEL=GENERIC` disables the use of assembly-optimized arithmetic.
|
||||
|
||||
To run the different tests and benchmarking results, execute:
|
||||
|
||||
```sh
|
||||
$ ./arith_tests-pXXX
|
||||
$ ./sikeXXX/test_SIKE
|
||||
```
|
||||
|
||||
|
|
@ -0,0 +1,293 @@
|
|||
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Microsoft Visual Studio Solution File, Format Version 12.00
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# Visual Studio 14
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VisualStudioVersion = 14.0.25420.1
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MinimumVisualStudioVersion = 10.0.40219.1
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "P751", "SIDHp751.vcxproj", "{8283DD76-E88A-4B63-ABDE-33F014178413}"
|
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EndProject
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "P503", "SIDHp503.vcxproj", "{BBC8647D-B9E2-469F-A9A4-BB55B614ADBE}"
|
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EndProject
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIKEp503", "..\kem_tests\test-SIKEp503.vcxproj", "{EF9FE361-D94D-4CE0-8873-739A925326A3}"
|
||||
EndProject
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIKEp751", "..\kem_tests\test-SIKEp751.vcxproj", "{0D570915-7551-4D5F-A2F0-A4A6200185F9}"
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EndProject
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "P434", "SIDHp434.vcxproj", "{E46FD055-7619-4C50-8360-FA3BC2F650FB}"
|
||||
EndProject
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIKEp434", "..\kem_tests\test-SIKEp434.vcxproj", "{53B2CD97-2FE6-4927-86A7-B16E436CFBD5}"
|
||||
EndProject
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "P377", "SIDHp377.vcxproj", "{05CEF530-F410-4C21-AC70-A7EF991DEE6A}"
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EndProject
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIKEp377", "..\kem_tests\test-SIKEp377.vcxproj", "{0D497554-D408-4061-BA26-2A65F4272841}"
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EndProject
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "arith_tests-P377", "..\arith_tests\arith_tests-P377.vcxproj", "{10C4B543-0224-43D3-B84D-390665AA6C25}"
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EndProject
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "arith_tests-P434", "..\arith_tests\arith_tests-P434.vcxproj", "{8944AC47-A218-4F4D-8AF1-AF704160A727}"
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EndProject
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "arith_tests-P503", "..\arith_tests\arith_tests-P503.vcxproj", "{464B689B-7C93-47A2-B2F5-FE162A4EF404}"
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EndProject
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "arith_tests-P610", "..\arith_tests\arith_tests-P610.vcxproj", "{2A6A9BF4-B07F-4F2F-B418-6C39E54F8C6F}"
|
||||
EndProject
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "arith_tests-P751", "..\arith_tests\arith_tests-P751.vcxproj", "{C9639168-C3FF-4427-BC3B-D907FF11DE73}"
|
||||
EndProject
|
||||
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "P610", "SIDHp610.vcxproj", "{ED1BA17A-58EA-4D9F-9B19-7061395E22BB}"
|
||||
EndProject
|
||||
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIKEp610", "..\kem_tests\test-SIKEp610.vcxproj", "{DC10CB31-A905-402E-B466-46ADCD1AD61C}"
|
||||
EndProject
|
||||
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "P546", "SIDHp546.vcxproj", "{48010B78-5594-4FE9-81AC-909B670C1516}"
|
||||
EndProject
|
||||
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "arith_tests-P546", "..\arith_tests\arith_tests-P546.vcxproj", "{5572CD5B-7F2F-4F44-B7AC-844291850C6E}"
|
||||
EndProject
|
||||
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIKEp546", "..\kem_tests\test-SIKEp546.vcxproj", "{E52D3FE9-FD9F-4D93-9712-8172DB469831}"
|
||||
EndProject
|
||||
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "arith_tests-P697", "..\arith_tests\arith_tests-P697.vcxproj", "{C0892335-7EB7-48D4-83A1-500953D0526B}"
|
||||
EndProject
|
||||
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test-SIKEp697", "..\kem_tests\test-SIKEp697.vcxproj", "{1B4248D6-99FD-47E0-B91F-8EF78F3A5D7B}"
|
||||
EndProject
|
||||
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "P697", "SIDHp697.vcxproj", "{F7447653-7518-4BF0-934D-65801C74D42A}"
|
||||
EndProject
|
||||
Global
|
||||
GlobalSection(SolutionConfigurationPlatforms) = preSolution
|
||||
Debug|x64 = Debug|x64
|
||||
Debug|x86 = Debug|x86
|
||||
Fast|x64 = Fast|x64
|
||||
Fast|x86 = Fast|x86
|
||||
Generic|x64 = Generic|x64
|
||||
Generic|x86 = Generic|x86
|
||||
EndGlobalSection
|
||||
GlobalSection(ProjectConfigurationPlatforms) = postSolution
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||||
{8283DD76-E88A-4B63-ABDE-33F014178413}.Debug|x64.ActiveCfg = Debug|x64
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{8283DD76-E88A-4B63-ABDE-33F014178413}.Debug|x64.Build.0 = Debug|x64
|
||||
{8283DD76-E88A-4B63-ABDE-33F014178413}.Debug|x86.ActiveCfg = Debug|Win32
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||||
{8283DD76-E88A-4B63-ABDE-33F014178413}.Debug|x86.Build.0 = Debug|Win32
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||||
{8283DD76-E88A-4B63-ABDE-33F014178413}.Fast|x64.ActiveCfg = Fast|x64
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{8283DD76-E88A-4B63-ABDE-33F014178413}.Fast|x64.Build.0 = Fast|x64
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{8283DD76-E88A-4B63-ABDE-33F014178413}.Fast|x86.ActiveCfg = Fast|Win32
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||||
{8283DD76-E88A-4B63-ABDE-33F014178413}.Generic|x64.ActiveCfg = Generic|x64
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{8283DD76-E88A-4B63-ABDE-33F014178413}.Generic|x64.Build.0 = Generic|x64
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||||
{8283DD76-E88A-4B63-ABDE-33F014178413}.Generic|x86.ActiveCfg = Generic|Win32
|
||||
{8283DD76-E88A-4B63-ABDE-33F014178413}.Generic|x86.Build.0 = Generic|Win32
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||||
{BBC8647D-B9E2-469F-A9A4-BB55B614ADBE}.Debug|x64.ActiveCfg = Debug|x64
|
||||
{BBC8647D-B9E2-469F-A9A4-BB55B614ADBE}.Debug|x64.Build.0 = Debug|x64
|
||||
{BBC8647D-B9E2-469F-A9A4-BB55B614ADBE}.Debug|x86.ActiveCfg = Debug|Win32
|
||||
{BBC8647D-B9E2-469F-A9A4-BB55B614ADBE}.Debug|x86.Build.0 = Debug|Win32
|
||||
{BBC8647D-B9E2-469F-A9A4-BB55B614ADBE}.Fast|x64.ActiveCfg = Fast|x64
|
||||
{BBC8647D-B9E2-469F-A9A4-BB55B614ADBE}.Fast|x64.Build.0 = Fast|x64
|
||||
{BBC8647D-B9E2-469F-A9A4-BB55B614ADBE}.Fast|x86.ActiveCfg = Fast|Win32
|
||||
{BBC8647D-B9E2-469F-A9A4-BB55B614ADBE}.Generic|x64.ActiveCfg = Generic|x64
|
||||
{BBC8647D-B9E2-469F-A9A4-BB55B614ADBE}.Generic|x64.Build.0 = Generic|x64
|
||||
{BBC8647D-B9E2-469F-A9A4-BB55B614ADBE}.Generic|x86.ActiveCfg = Generic|Win32
|
||||
{BBC8647D-B9E2-469F-A9A4-BB55B614ADBE}.Generic|x86.Build.0 = Generic|Win32
|
||||
{EF9FE361-D94D-4CE0-8873-739A925326A3}.Debug|x64.ActiveCfg = Debug|x64
|
||||
{EF9FE361-D94D-4CE0-8873-739A925326A3}.Debug|x64.Build.0 = Debug|x64
|
||||
{EF9FE361-D94D-4CE0-8873-739A925326A3}.Debug|x86.ActiveCfg = Debug|Win32
|
||||
{EF9FE361-D94D-4CE0-8873-739A925326A3}.Debug|x86.Build.0 = Debug|Win32
|
||||
{EF9FE361-D94D-4CE0-8873-739A925326A3}.Fast|x64.ActiveCfg = Fast|x64
|
||||
{EF9FE361-D94D-4CE0-8873-739A925326A3}.Fast|x64.Build.0 = Fast|x64
|
||||
{EF9FE361-D94D-4CE0-8873-739A925326A3}.Fast|x86.ActiveCfg = Fast|Win32
|
||||
{EF9FE361-D94D-4CE0-8873-739A925326A3}.Generic|x64.ActiveCfg = Generic|x64
|
||||
{EF9FE361-D94D-4CE0-8873-739A925326A3}.Generic|x64.Build.0 = Generic|x64
|
||||
{EF9FE361-D94D-4CE0-8873-739A925326A3}.Generic|x86.ActiveCfg = Generic|Win32
|
||||
{EF9FE361-D94D-4CE0-8873-739A925326A3}.Generic|x86.Build.0 = Generic|Win32
|
||||
{0D570915-7551-4D5F-A2F0-A4A6200185F9}.Debug|x64.ActiveCfg = Debug|x64
|
||||
{0D570915-7551-4D5F-A2F0-A4A6200185F9}.Debug|x64.Build.0 = Debug|x64
|
||||
{0D570915-7551-4D5F-A2F0-A4A6200185F9}.Debug|x86.ActiveCfg = Debug|Win32
|
||||
{0D570915-7551-4D5F-A2F0-A4A6200185F9}.Debug|x86.Build.0 = Debug|Win32
|
||||
{0D570915-7551-4D5F-A2F0-A4A6200185F9}.Fast|x64.ActiveCfg = Fast|x64
|
||||
{0D570915-7551-4D5F-A2F0-A4A6200185F9}.Fast|x64.Build.0 = Fast|x64
|
||||
{0D570915-7551-4D5F-A2F0-A4A6200185F9}.Fast|x86.ActiveCfg = Fast|Win32
|
||||
{0D570915-7551-4D5F-A2F0-A4A6200185F9}.Generic|x64.ActiveCfg = Generic|x64
|
||||
{0D570915-7551-4D5F-A2F0-A4A6200185F9}.Generic|x64.Build.0 = Generic|x64
|
||||
{0D570915-7551-4D5F-A2F0-A4A6200185F9}.Generic|x86.ActiveCfg = Generic|Win32
|
||||
{0D570915-7551-4D5F-A2F0-A4A6200185F9}.Generic|x86.Build.0 = Generic|Win32
|
||||
{E46FD055-7619-4C50-8360-FA3BC2F650FB}.Debug|x64.ActiveCfg = Debug|x64
|
||||
{E46FD055-7619-4C50-8360-FA3BC2F650FB}.Debug|x64.Build.0 = Debug|x64
|
||||
{E46FD055-7619-4C50-8360-FA3BC2F650FB}.Debug|x86.ActiveCfg = Debug|Win32
|
||||
{E46FD055-7619-4C50-8360-FA3BC2F650FB}.Debug|x86.Build.0 = Debug|Win32
|
||||
{E46FD055-7619-4C50-8360-FA3BC2F650FB}.Fast|x64.ActiveCfg = Fast|x64
|
||||
{E46FD055-7619-4C50-8360-FA3BC2F650FB}.Fast|x64.Build.0 = Fast|x64
|
||||
{E46FD055-7619-4C50-8360-FA3BC2F650FB}.Fast|x86.ActiveCfg = Fast|Win32
|
||||
{E46FD055-7619-4C50-8360-FA3BC2F650FB}.Generic|x64.ActiveCfg = Generic|x64
|
||||
{E46FD055-7619-4C50-8360-FA3BC2F650FB}.Generic|x64.Build.0 = Generic|x64
|
||||
{E46FD055-7619-4C50-8360-FA3BC2F650FB}.Generic|x86.ActiveCfg = Generic|Win32
|
||||
{E46FD055-7619-4C50-8360-FA3BC2F650FB}.Generic|x86.Build.0 = Generic|Win32
|
||||
{53B2CD97-2FE6-4927-86A7-B16E436CFBD5}.Debug|x64.ActiveCfg = Debug|x64
|
||||
{53B2CD97-2FE6-4927-86A7-B16E436CFBD5}.Debug|x64.Build.0 = Debug|x64
|
||||
{53B2CD97-2FE6-4927-86A7-B16E436CFBD5}.Debug|x86.ActiveCfg = Debug|Win32
|
||||
{53B2CD97-2FE6-4927-86A7-B16E436CFBD5}.Debug|x86.Build.0 = Debug|Win32
|
||||
{53B2CD97-2FE6-4927-86A7-B16E436CFBD5}.Fast|x64.ActiveCfg = Fast|x64
|
||||
{53B2CD97-2FE6-4927-86A7-B16E436CFBD5}.Fast|x64.Build.0 = Fast|x64
|
||||
{53B2CD97-2FE6-4927-86A7-B16E436CFBD5}.Fast|x86.ActiveCfg = Fast|Win32
|
||||
{53B2CD97-2FE6-4927-86A7-B16E436CFBD5}.Generic|x64.ActiveCfg = Generic|x64
|
||||
{53B2CD97-2FE6-4927-86A7-B16E436CFBD5}.Generic|x64.Build.0 = Generic|x64
|
||||
{53B2CD97-2FE6-4927-86A7-B16E436CFBD5}.Generic|x86.ActiveCfg = Generic|Win32
|
||||
{53B2CD97-2FE6-4927-86A7-B16E436CFBD5}.Generic|x86.Build.0 = Generic|Win32
|
||||
{05CEF530-F410-4C21-AC70-A7EF991DEE6A}.Debug|x64.ActiveCfg = Debug|x64
|
||||
{05CEF530-F410-4C21-AC70-A7EF991DEE6A}.Debug|x64.Build.0 = Debug|x64
|
||||
{05CEF530-F410-4C21-AC70-A7EF991DEE6A}.Debug|x86.ActiveCfg = Debug|Win32
|
||||
{05CEF530-F410-4C21-AC70-A7EF991DEE6A}.Debug|x86.Build.0 = Debug|Win32
|
||||
{05CEF530-F410-4C21-AC70-A7EF991DEE6A}.Fast|x64.ActiveCfg = Fast|x64
|
||||
{05CEF530-F410-4C21-AC70-A7EF991DEE6A}.Fast|x64.Build.0 = Fast|x64
|
||||
{05CEF530-F410-4C21-AC70-A7EF991DEE6A}.Fast|x86.ActiveCfg = Fast|Win32
|
||||
{05CEF530-F410-4C21-AC70-A7EF991DEE6A}.Generic|x64.ActiveCfg = Generic|x64
|
||||
{05CEF530-F410-4C21-AC70-A7EF991DEE6A}.Generic|x64.Build.0 = Generic|x64
|
||||
{05CEF530-F410-4C21-AC70-A7EF991DEE6A}.Generic|x86.ActiveCfg = Generic|Win32
|
||||
{05CEF530-F410-4C21-AC70-A7EF991DEE6A}.Generic|x86.Build.0 = Generic|Win32
|
||||
{0D497554-D408-4061-BA26-2A65F4272841}.Debug|x64.ActiveCfg = Debug|x64
|
||||
{0D497554-D408-4061-BA26-2A65F4272841}.Debug|x64.Build.0 = Debug|x64
|
||||
{0D497554-D408-4061-BA26-2A65F4272841}.Debug|x86.ActiveCfg = Debug|Win32
|
||||
{0D497554-D408-4061-BA26-2A65F4272841}.Debug|x86.Build.0 = Debug|Win32
|
||||
{0D497554-D408-4061-BA26-2A65F4272841}.Fast|x64.ActiveCfg = Fast|x64
|
||||
{0D497554-D408-4061-BA26-2A65F4272841}.Fast|x64.Build.0 = Fast|x64
|
||||
{0D497554-D408-4061-BA26-2A65F4272841}.Fast|x86.ActiveCfg = Fast|Win32
|
||||
{0D497554-D408-4061-BA26-2A65F4272841}.Generic|x64.ActiveCfg = Generic|x64
|
||||
{0D497554-D408-4061-BA26-2A65F4272841}.Generic|x64.Build.0 = Generic|x64
|
||||
{0D497554-D408-4061-BA26-2A65F4272841}.Generic|x86.ActiveCfg = Generic|Win32
|
||||
{0D497554-D408-4061-BA26-2A65F4272841}.Generic|x86.Build.0 = Generic|Win32
|
||||
{10C4B543-0224-43D3-B84D-390665AA6C25}.Debug|x64.ActiveCfg = Debug|x64
|
||||
{10C4B543-0224-43D3-B84D-390665AA6C25}.Debug|x64.Build.0 = Debug|x64
|
||||
{10C4B543-0224-43D3-B84D-390665AA6C25}.Debug|x86.ActiveCfg = Debug|Win32
|
||||
{10C4B543-0224-43D3-B84D-390665AA6C25}.Debug|x86.Build.0 = Debug|Win32
|
||||
{10C4B543-0224-43D3-B84D-390665AA6C25}.Fast|x64.ActiveCfg = Fast|x64
|
||||
{10C4B543-0224-43D3-B84D-390665AA6C25}.Fast|x64.Build.0 = Fast|x64
|
||||
{10C4B543-0224-43D3-B84D-390665AA6C25}.Fast|x86.ActiveCfg = Fast|Win32
|
||||
{10C4B543-0224-43D3-B84D-390665AA6C25}.Generic|x64.ActiveCfg = Generic|x64
|
||||
{10C4B543-0224-43D3-B84D-390665AA6C25}.Generic|x64.Build.0 = Generic|x64
|
||||
{10C4B543-0224-43D3-B84D-390665AA6C25}.Generic|x86.ActiveCfg = Generic|Win32
|
||||
{10C4B543-0224-43D3-B84D-390665AA6C25}.Generic|x86.Build.0 = Generic|Win32
|
||||
{8944AC47-A218-4F4D-8AF1-AF704160A727}.Debug|x64.ActiveCfg = Debug|x64
|
||||
{8944AC47-A218-4F4D-8AF1-AF704160A727}.Debug|x64.Build.0 = Debug|x64
|
||||
{8944AC47-A218-4F4D-8AF1-AF704160A727}.Debug|x86.ActiveCfg = Debug|Win32
|
||||
{8944AC47-A218-4F4D-8AF1-AF704160A727}.Debug|x86.Build.0 = Debug|Win32
|
||||
{8944AC47-A218-4F4D-8AF1-AF704160A727}.Fast|x64.ActiveCfg = Fast|x64
|
||||
{8944AC47-A218-4F4D-8AF1-AF704160A727}.Fast|x64.Build.0 = Fast|x64
|
||||
{8944AC47-A218-4F4D-8AF1-AF704160A727}.Fast|x86.ActiveCfg = Fast|Win32
|
||||
{8944AC47-A218-4F4D-8AF1-AF704160A727}.Generic|x64.ActiveCfg = Generic|x64
|
||||
{8944AC47-A218-4F4D-8AF1-AF704160A727}.Generic|x64.Build.0 = Generic|x64
|
||||
{8944AC47-A218-4F4D-8AF1-AF704160A727}.Generic|x86.ActiveCfg = Generic|Win32
|
||||
{8944AC47-A218-4F4D-8AF1-AF704160A727}.Generic|x86.Build.0 = Generic|Win32
|
||||
{464B689B-7C93-47A2-B2F5-FE162A4EF404}.Debug|x64.ActiveCfg = Debug|x64
|
||||
{464B689B-7C93-47A2-B2F5-FE162A4EF404}.Debug|x64.Build.0 = Debug|x64
|
||||
{464B689B-7C93-47A2-B2F5-FE162A4EF404}.Debug|x86.ActiveCfg = Debug|Win32
|
||||
{464B689B-7C93-47A2-B2F5-FE162A4EF404}.Debug|x86.Build.0 = Debug|Win32
|
||||
{464B689B-7C93-47A2-B2F5-FE162A4EF404}.Fast|x64.ActiveCfg = Fast|x64
|
||||
{464B689B-7C93-47A2-B2F5-FE162A4EF404}.Fast|x64.Build.0 = Fast|x64
|
||||
{464B689B-7C93-47A2-B2F5-FE162A4EF404}.Fast|x86.ActiveCfg = Fast|Win32
|
||||
{464B689B-7C93-47A2-B2F5-FE162A4EF404}.Generic|x64.ActiveCfg = Generic|x64
|
||||
{464B689B-7C93-47A2-B2F5-FE162A4EF404}.Generic|x64.Build.0 = Generic|x64
|
||||
{464B689B-7C93-47A2-B2F5-FE162A4EF404}.Generic|x86.ActiveCfg = Generic|Win32
|
||||
{464B689B-7C93-47A2-B2F5-FE162A4EF404}.Generic|x86.Build.0 = Generic|Win32
|
||||
{2A6A9BF4-B07F-4F2F-B418-6C39E54F8C6F}.Debug|x64.ActiveCfg = Debug|x64
|
||||
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|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: modular arithmetic optimized for x64 platforms for P377
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P377_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p377[NWORDS_FIELD];
|
||||
extern const uint64_t p377p1[NWORDS_FIELD];
|
||||
extern const uint64_t p377x2[NWORDS_FIELD];
|
||||
extern const uint64_t p377x4[NWORDS_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub377_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
#if (OS_TARGET == OS_WIN) || defined(GENERIC_IMPLEMENTATION) || (TARGET == TARGET_ARM) || (TARGET == TARGET_ARM64 && NBITS_FIELD == 610)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p377x2)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub377_p2_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub377_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
#if (OS_TARGET == OS_WIN) || defined(GENERIC_IMPLEMENTATION) || (TARGET == TARGET_ARM) || (TARGET == TARGET_ARM64 && NBITS_FIELD == 610)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p377x4)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub377_p4_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd377(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p377.
|
||||
// Inputs: a, b in [0, 2*p377-1]
|
||||
// Output: c in [0, 2*p377-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p377x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p377x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpadd377_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub377(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p377.
|
||||
// Inputs: a, b in [0, 2*p377-1]
|
||||
// Output: c in [0, 2*p377-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p377x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpsub377_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg377(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p377.
|
||||
// Input/output: a in [0, 2*p377-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p377x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_377(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p377.
|
||||
// Input : a in [0, 2*p377-1]
|
||||
// Output: c in [0, 2*p377-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p377
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p377)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection377(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p377-1] to [0, p377-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p377)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p377)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
|
||||
(void)nwords;
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
unsigned int carry = 0;
|
||||
|
||||
MULADD128(a[0], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[5], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
c[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[5], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
c[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[5], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
c[8] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[5], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
c[9] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
|
||||
MULADD128(a[5], b[5], uv, carry, uv);
|
||||
c[10] = uv[0];
|
||||
c[11] = uv[1];
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mul377_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Montgomery reduction exploiting special form of the prime.
|
||||
// mc = ma*R^-1 mod p377x2, where R = 2^384.
|
||||
// If ma < 2^384*p377, the output mc is in the range [0, 2*p377-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int carry;
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
|
||||
mc[0] = ma[0];
|
||||
mc[1] = ma[1];
|
||||
MUL128(mc[0], ((digit_t*)p377p1)[2], uv);
|
||||
ADDC(0, uv[0], ma[2], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
mc[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p377p1)[3], uv, carry, uv);
|
||||
MULADD128(mc[1], ((digit_t*)p377p1)[2], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[3], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p377p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p377p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p377p1)[2], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[4], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p377p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p377p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p377p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p377p1)[2], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[5], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[1], ((digit_t*)p377p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p377p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p377p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p377p1)[2], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[6], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[2], ((digit_t*)p377p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p377p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p377p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p377p1)[2], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[7], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[3], ((digit_t*)p377p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p377p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p377p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[8], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[4], ((digit_t*)p377p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p377p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[9], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[5], ((digit_t*)p377p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[10], carry, mc[4]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
ADDC(0, uv[1], ma[11], carry, mc[5]);
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
rdc377_asm(ma, mc);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,747 @@
|
|||
//*******************************************************************************************
|
||||
// SIDH: an efficient supersingular isogeny cryptography library
|
||||
// Copyright (c) Microsoft Corporation
|
||||
//
|
||||
// Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
// Released under MIT license
|
||||
//
|
||||
// Abstract: field arithmetic in x64 assembly for P377 on Linux
|
||||
//*******************************************************************************************
|
||||
|
||||
.intel_syntax noprefix
|
||||
|
||||
// Format function and variable names for Mac OS X
|
||||
#if defined(__APPLE__)
|
||||
#define fmt(f) _##f
|
||||
#else
|
||||
#define fmt(f) f
|
||||
#endif
|
||||
|
||||
// Registers that are used for parameter passing:
|
||||
#define reg_p1 rdi
|
||||
#define reg_p2 rsi
|
||||
#define reg_p3 rdx
|
||||
|
||||
// Define addition instructions
|
||||
#ifdef _MULX_
|
||||
#ifdef _ADX_
|
||||
|
||||
#define ADD adcx
|
||||
#define ADC adcx
|
||||
|
||||
#else
|
||||
|
||||
#define ADD add
|
||||
#define ADC adc
|
||||
|
||||
#endif
|
||||
#endif
|
||||
|
||||
|
||||
.text
|
||||
//***********************************************************************
|
||||
// Field addition
|
||||
// Operation: c [reg_p3] = a [reg_p1] + b [reg_p2]
|
||||
//***********************************************************************
|
||||
.global fmt(fpadd377_asm)
|
||||
fmt(fpadd377_asm):
|
||||
push r12
|
||||
push r13
|
||||
push r14
|
||||
push r15
|
||||
|
||||
xor rax, rax
|
||||
mov r8, [reg_p1]
|
||||
mov r9, [reg_p1+8]
|
||||
mov r10, [reg_p1+16]
|
||||
mov r11, [reg_p1+24]
|
||||
mov r12, [reg_p1+32]
|
||||
mov r13, [reg_p1+40]
|
||||
add r8, [reg_p2]
|
||||
adc r9, [reg_p2+8]
|
||||
adc r10, [reg_p2+16]
|
||||
adc r11, [reg_p2+24]
|
||||
adc r12, [reg_p2+32]
|
||||
adc r13, [reg_p2+40]
|
||||
|
||||
mov rcx, [rip+p377x2]
|
||||
sub r8, rcx
|
||||
mov rdi, [rip+p377x2+8]
|
||||
sbb r9, rdi
|
||||
sbb r10, rdi
|
||||
mov rsi, [rip+p377x2+24]
|
||||
sbb r11, rsi
|
||||
mov r14, [rip+p377x2+32]
|
||||
sbb r12, r14
|
||||
mov r15, [rip+p377x2+40]
|
||||
sbb r13, r15
|
||||
sbb rax, 0
|
||||
|
||||
and rcx, rax
|
||||
and rdi, rax
|
||||
and rsi, rax
|
||||
and r14, rax
|
||||
and r15, rax
|
||||
|
||||
add r8, rcx
|
||||
adc r9, rdi
|
||||
adc r10, rdi
|
||||
adc r11, rsi
|
||||
adc r12, r14
|
||||
adc r13, r15
|
||||
mov [reg_p3], r8
|
||||
mov [reg_p3+8], r9
|
||||
mov [reg_p3+16], r10
|
||||
mov [reg_p3+24], r11
|
||||
mov [reg_p3+32], r12
|
||||
mov [reg_p3+40], r13
|
||||
|
||||
pop r15
|
||||
pop r14
|
||||
pop r13
|
||||
pop r12
|
||||
ret
|
||||
|
||||
|
||||
//***********************************************************************
|
||||
// Field subtraction
|
||||
// Operation: c [reg_p3] = a [reg_p1] - b [reg_p2]
|
||||
//***********************************************************************
|
||||
.global fmt(fpsub377_asm)
|
||||
fmt(fpsub377_asm):
|
||||
push r12
|
||||
push r13
|
||||
|
||||
xor rax, rax
|
||||
mov r8, [reg_p1]
|
||||
mov r9, [reg_p1+8]
|
||||
mov r10, [reg_p1+16]
|
||||
mov r11, [reg_p1+24]
|
||||
mov r12, [reg_p1+32]
|
||||
mov r13, [reg_p1+40]
|
||||
sub r8, [reg_p2]
|
||||
sbb r9, [reg_p2+8]
|
||||
sbb r10, [reg_p2+16]
|
||||
sbb r11, [reg_p2+24]
|
||||
sbb r12, [reg_p2+32]
|
||||
sbb r13, [reg_p2+40]
|
||||
sbb rax, 0
|
||||
|
||||
mov rcx, [rip+p377x2]
|
||||
mov rdi, [rip+p377x2+8]
|
||||
mov rsi, [rip+p377x2+24]
|
||||
and rcx, rax
|
||||
and rdi, rax
|
||||
and rsi, rax
|
||||
add r8, rcx
|
||||
adc r9, rdi
|
||||
adc r10, rdi
|
||||
adc r11, rsi
|
||||
mov [reg_p3], r8
|
||||
mov [reg_p3+8], r9
|
||||
mov [reg_p3+16], r10
|
||||
mov [reg_p3+24], r11
|
||||
setc cl
|
||||
|
||||
mov rdi, [rip+p377x2+32]
|
||||
mov rsi, [rip+p377x2+40]
|
||||
and rdi, rax
|
||||
and rsi, rax
|
||||
bt rcx, 0
|
||||
adc r12, rdi
|
||||
adc r13, rsi
|
||||
mov [reg_p3+32], r12
|
||||
mov [reg_p3+40], r13
|
||||
|
||||
pop r13
|
||||
pop r12
|
||||
ret
|
||||
|
||||
|
||||
///////////////////////////////////////////////////////////////// MACRO
|
||||
.macro SUB377_PX P0
|
||||
mov r8, [reg_p1]
|
||||
mov r9, [reg_p1+8]
|
||||
mov r10, [reg_p1+16]
|
||||
mov r11, [reg_p1+24]
|
||||
mov rax, [reg_p1+32]
|
||||
mov rcx, [reg_p1+40]
|
||||
sub r8, [reg_p2]
|
||||
sbb r9, [reg_p2+8]
|
||||
sbb r10, [reg_p2+16]
|
||||
sbb r11, [reg_p2+24]
|
||||
sbb rax, [reg_p2+32]
|
||||
sbb rcx, [reg_p2+40]
|
||||
|
||||
mov rdi, [rip+\P0]
|
||||
mov rsi, [rip+\P0+8]
|
||||
add r8, rdi
|
||||
adc r9, rsi
|
||||
adc r10, rsi
|
||||
mov rdi, [rip+\P0+24]
|
||||
mov rsi, [rip+\P0+32]
|
||||
adc r11, rdi
|
||||
mov rdi, [rip+\P0+40]
|
||||
adc rax, rsi
|
||||
adc rcx, rdi
|
||||
mov [reg_p3], r8
|
||||
mov [reg_p3+8], r9
|
||||
mov [reg_p3+16], r10
|
||||
mov [reg_p3+24], r11
|
||||
mov [reg_p3+32], rax
|
||||
mov [reg_p3+40], rcx
|
||||
.endm
|
||||
|
||||
|
||||
//***********************************************************************
|
||||
// Multiprecision subtraction with correction with 2*p377
|
||||
// Operation: c [reg_p3] = a [reg_p1] - b [reg_p2] + 2*p377
|
||||
//***********************************************************************
|
||||
.global fmt(mp_sub377_p2_asm)
|
||||
fmt(mp_sub377_p2_asm):
|
||||
|
||||
SUB377_PX p377x2
|
||||
ret
|
||||
|
||||
|
||||
//***********************************************************************
|
||||
// Multiprecision subtraction with correction with 4*p377
|
||||
// Operation: c [reg_p3] = a [reg_p1] - b [reg_p2] + 4*p377
|
||||
//***********************************************************************
|
||||
.global fmt(mp_sub377_p4_asm)
|
||||
fmt(mp_sub377_p4_asm):
|
||||
|
||||
SUB377_PX p377x4
|
||||
ret
|
||||
|
||||
|
||||
#ifdef _MULX_
|
||||
|
||||
///////////////////////////////////////////////////////////////// MACRO
|
||||
// Schoolbook integer multiplication
|
||||
// Inputs: memory pointers M0 and M1
|
||||
// Outputs: memory pointer C and regs T1, T2, T0
|
||||
// Temps: regs T0:T6
|
||||
/////////////////////////////////////////////////////////////////
|
||||
|
||||
#ifdef _ADX_
|
||||
.macro MUL192_SCHOOL M0, M1, C, T0, T1, T2, T3, T4, T5, T6
|
||||
mov rdx, \M0
|
||||
mulx \T0, \T1, \M1 // T0:T1 = A0*B0
|
||||
mov \C, \T1 // C0_final
|
||||
mulx \T1, \T2, 8\M1 // T1:T2 = A0*B1
|
||||
xor rax, rax
|
||||
adox \T0, \T2
|
||||
mulx \T2, \T3, 16\M1 // T2:T3 = A0*B2
|
||||
adox \T1, \T3
|
||||
|
||||
mov rdx, 8\M0
|
||||
mulx \T3, \T4, \M1 // T3:T4 = A1*B0
|
||||
adox \T2, rax
|
||||
xor rax, rax
|
||||
mulx \T5, \T6, 8\M1 // T5:T6 = A1*B1
|
||||
adox \T4, \T0
|
||||
mov 8\C, \T4 // C1_final
|
||||
adcx \T3, \T6
|
||||
mulx \T6, \T0, 16\M1 // T6:T0 = A1*B2
|
||||
adox \T3, \T1
|
||||
adcx \T5, \T0
|
||||
adcx \T6, rax
|
||||
adox \T5, \T2
|
||||
|
||||
mov rdx, 16\M0
|
||||
mulx \T1, \T0, \M1 // T1:T0 = A2*B0
|
||||
adox \T6, rax
|
||||
xor rax, rax
|
||||
mulx \T2, \T4, 8\M1 // T2:T4 = A2*B1
|
||||
adox \T0, \T3
|
||||
mov 16\C, \T0 // C2_final
|
||||
adcx \T1, \T5
|
||||
mulx \T0, \T3, 16\M1 // T0:T3 = A2*B2
|
||||
adcx \T2, \T6
|
||||
adcx \T0, rax
|
||||
adox \T1, \T4
|
||||
adox \T2, \T3
|
||||
adox \T0, rax
|
||||
.endm
|
||||
|
||||
#else
|
||||
|
||||
.macro MUL192_SCHOOL M0, M1, C, T0, T1, T2, T3, T4, T5, T6
|
||||
mov rdx, \M0
|
||||
mulx \T0, \T1, \M1 // T0:T1 = A0*B0
|
||||
mov \C, \T1 // C0_final
|
||||
mulx \T1, \T2, 8\M1 // T1:T2 = A0*B1
|
||||
add \T0, \T2
|
||||
mulx \T2, \T3, 16\M1 // T2:T3 = A0*B2
|
||||
adc \T1, \T3
|
||||
|
||||
mov rdx, 8\M0
|
||||
mulx \T3, \T4, \M1 // T3:T4 = A1*B0
|
||||
adc \T2, 0
|
||||
mulx \T5, \T6, 8\M1 // T5:T6 = A1*B1
|
||||
add \T4, \T0
|
||||
mov 8\C, \T4 // C1_final
|
||||
adc \T3, \T1
|
||||
adc \T5, \T2
|
||||
mulx \T2, \T1, 16\M1 // T2:T1 = A1*B2
|
||||
adc \T2, 0
|
||||
|
||||
add \T3, \T6
|
||||
adc \T5, \T1
|
||||
adc \T2, 0
|
||||
|
||||
mov rdx, 16\M0
|
||||
mulx \T1, \T0, \M1 // T1:T0 = A2*B0
|
||||
add \T0, \T3
|
||||
mov 16\C, \T0 // C2_final
|
||||
mulx \T4, \T6, 8\M1 // T4:T6 = A2*B1
|
||||
adc \T1, \T5
|
||||
adc \T2, \T4
|
||||
mulx \T0, \T3, 16\M1 // T0:T3 = A2*B2
|
||||
adc \T0, 0
|
||||
add \T1, \T6
|
||||
adc \T2, \T3
|
||||
adc \T0, 0
|
||||
.endm
|
||||
#endif
|
||||
|
||||
|
||||
//*****************************************************************************
|
||||
// 377-bit multiplication using Karatsuba (one level), schoolbook (one level)
|
||||
//*****************************************************************************
|
||||
.global fmt(mul377_asm)
|
||||
fmt(mul377_asm):
|
||||
push r14
|
||||
push r15
|
||||
mov rcx, reg_p3
|
||||
|
||||
// r8-r10 <- AH + AL, rax <- mask
|
||||
xor rax, rax
|
||||
mov r8, [reg_p1]
|
||||
mov r9, [reg_p1+8]
|
||||
mov r10, [reg_p1+16]
|
||||
push rbx
|
||||
push rbp
|
||||
add r8, [reg_p1+24]
|
||||
adc r9, [reg_p1+32]
|
||||
adc r10, [reg_p1+40]
|
||||
sbb rax, 0
|
||||
push r12
|
||||
push r13
|
||||
|
||||
// r11-r13 <- BH + BL, rbx <- mask
|
||||
xor rbx, rbx
|
||||
mov r11, [reg_p2]
|
||||
mov r12, [reg_p2+8]
|
||||
mov r13, [reg_p2+16]
|
||||
sub rsp, 48
|
||||
add r11, [reg_p2+24]
|
||||
adc r12, [reg_p2+32]
|
||||
adc r13, [reg_p2+40]
|
||||
sbb rbx, 0
|
||||
mov [rsp], r8
|
||||
mov [rsp+8], r9
|
||||
mov [rsp+16], r10
|
||||
mov [rsp+24], r11
|
||||
mov [rsp+32], r12
|
||||
mov [rsp+40], r13
|
||||
|
||||
// r11-r13 <- masked (BH + BL)
|
||||
and r11, rax
|
||||
and r12, rax
|
||||
and r13, rax
|
||||
|
||||
// r8-r10 <- masked (AH + AL)
|
||||
and r8, rbx
|
||||
and r9, rbx
|
||||
and r10, rbx
|
||||
|
||||
// r8-r10 <- masked (AH + AL) + masked (AH + AL)
|
||||
add r8, r11
|
||||
adc r9, r12
|
||||
adc r10, r13
|
||||
|
||||
// [rcx+48] <- (AH+AL) x (BH+BL), low part
|
||||
MUL192_SCHOOL [rsp], [rsp+24], [rcx+48], r15, rbx, rbp, r11, r12, r13, r14
|
||||
mov [rcx+72], rbx
|
||||
mov [rcx+80], rbp
|
||||
mov [rcx+88], r15
|
||||
|
||||
// [rcx] <- AL x BL
|
||||
MUL192_SCHOOL [reg_p1], [reg_p2], [rcx], r15, rbx, rbp, r11, r12, r13, r14 // Result C0-C2
|
||||
mov [rcx+24], rbx
|
||||
mov [rcx+32], rbp
|
||||
mov [rcx+40], r15
|
||||
|
||||
// [rsp], rbx, rbp, r15 <- AH x BH
|
||||
MUL192_SCHOOL [reg_p1+24], [reg_p2+24], [rsp], r15, rbx, rbp, r11, r12, r13, r14
|
||||
|
||||
// r8-r10 <- (AH+AL) x (BH+BL), final step
|
||||
add r8, [rcx+72]
|
||||
adc r9, [rcx+80]
|
||||
adc r10, [rcx+88]
|
||||
|
||||
// r11-r13, r8-r10 <- (AH+AL) x (BH+BL) - ALxBL
|
||||
mov r11, [rcx+48]
|
||||
mov r12, [rcx+56]
|
||||
mov r13, [rcx+64]
|
||||
sub r11, [rcx]
|
||||
sbb r12, [rcx+8]
|
||||
sbb r13, [rcx+16]
|
||||
sbb r8, [rcx+24]
|
||||
sbb r9, [rcx+32]
|
||||
sbb r10, [rcx+40]
|
||||
|
||||
// r11-r13, r8-r10 <- (AH+AL) x (BH+BL) - ALxBL - AHxBH
|
||||
mov rdi, [rsp]
|
||||
mov rsi, [rsp+8]
|
||||
mov rdx, [rsp+16]
|
||||
add rsp, 48
|
||||
sub r11, rdi
|
||||
sbb r12, rsi
|
||||
sbb r13, rdx
|
||||
sbb r8, rbx
|
||||
sbb r9, rbp
|
||||
sbb r10, r15
|
||||
|
||||
add r11, [rcx+24]
|
||||
adc r12, [rcx+32]
|
||||
adc r13, [rcx+40]
|
||||
mov [rcx+24], r11 // Result C3-C5
|
||||
mov [rcx+32], r12
|
||||
mov [rcx+40], r13
|
||||
pop r13
|
||||
pop r12
|
||||
adc r8, rdi
|
||||
adc r9, rsi
|
||||
adc r10, rdx
|
||||
mov [rcx+48], r8 // Result C6-C8
|
||||
mov [rcx+56], r9
|
||||
mov [rcx+64], r10
|
||||
adc rbx, 0
|
||||
adc rbp, 0
|
||||
adc r15, 0
|
||||
mov [rcx+72], rbx // Result C9-C11
|
||||
mov [rcx+80], rbp
|
||||
mov [rcx+88], r15
|
||||
|
||||
pop rbp
|
||||
pop rbx
|
||||
pop r15
|
||||
pop r14
|
||||
ret
|
||||
|
||||
#else
|
||||
|
||||
# error "CONFIGURATION NOT SUPPORTED. TRY USE_MULX=TRUE"
|
||||
|
||||
#endif
|
||||
|
||||
|
||||
#ifdef _MULX_
|
||||
|
||||
///////////////////////////////////////////////////////////////// MACRO
|
||||
// Schoolbook integer multiplication
|
||||
// Inputs: regs I0, I1 and memory pointer M1
|
||||
// Outputs: regs T0:T4
|
||||
// Temp: regs T0:T5
|
||||
/////////////////////////////////////////////////////////////////
|
||||
|
||||
.macro MUL128x192_SCHOOL I0, I1, M1, T0, T1, T2, T3, T4, T5
|
||||
xor rax, rax
|
||||
mulx \T3, \T5, 16\M1
|
||||
ADD \T1, \T4
|
||||
ADC \T2, \T5
|
||||
ADC \T3, rax
|
||||
|
||||
xor rax, rax
|
||||
mov rdx, \I1
|
||||
mulx \T4, \T5, \M1
|
||||
ADD \T1, \T5 // T1 <- C1_final
|
||||
ADC \T2, \T4
|
||||
mulx \T4, \T5, 8\M1
|
||||
ADC \T3, rax
|
||||
ADD \T2, \T5 // T2 <- C2_final
|
||||
ADC \T3, \T4
|
||||
mulx \T4, \T5, 16\M1
|
||||
ADC \T4, rax
|
||||
ADD \T3, \T5 // T3 <- C3_final
|
||||
ADC \T4, rax // T4 <- C4_final
|
||||
.endm
|
||||
|
||||
|
||||
//**************************************************************************************
|
||||
// Montgomery reduction, shifted
|
||||
// Based on method described in Faz-Hernandez et al. https://eprint.iacr.org/2017/1015
|
||||
// Operation: c [reg_p2] = a [reg_p1]
|
||||
//**************************************************************************************
|
||||
.global fmt(rdc377_asm)
|
||||
fmt(rdc377_asm):
|
||||
|
||||
// a[0-1] x 2xp377p1_nz --> result: r8:r12
|
||||
mov rdx, [reg_p1]
|
||||
mov rcx, [reg_p1+8]
|
||||
mulx r9, r8, [rip+p377p1x2] // result r8
|
||||
push r15
|
||||
push rbp
|
||||
push r14
|
||||
push r12
|
||||
mulx r10, r12, [rip+p377p1x2+8]
|
||||
push rbx
|
||||
push r13
|
||||
MUL128x192_SCHOOL rdx, rcx, [rip+p377p1x2], r8, r9, r10, r11, r12, r13
|
||||
|
||||
xor rdx, rdx
|
||||
shrd rdx, r8, 1
|
||||
shrd r8, r9, 1
|
||||
shrd r9, r10, 1
|
||||
shrd r10, r11, 1
|
||||
shrd r11, r12, 1
|
||||
shr r12, 1
|
||||
add rdx, [reg_p1+16]
|
||||
adc r8, [reg_p1+24]
|
||||
adc r9, [reg_p1+32]
|
||||
adc r10, [reg_p1+40]
|
||||
mulx rbx, rcx, [rip+p377p1x2] // result rcx
|
||||
adc r11, [reg_p1+48]
|
||||
adc r12, [reg_p1+56]
|
||||
mov [reg_p2], r9
|
||||
mov [reg_p2+8], r10
|
||||
mov [reg_p2+16], r11
|
||||
mov r9, [reg_p1+64]
|
||||
mov r10, [reg_p1+72]
|
||||
mov r11, [reg_p1+80]
|
||||
mov rdi, [reg_p1+88]
|
||||
mulx rbp, r15, [rip+p377p1x2+8]
|
||||
adc r9, 0
|
||||
adc r10, 0
|
||||
adc r11, 0
|
||||
adc rdi, 0
|
||||
|
||||
// a[2-3] x 2xp377p1_nz --> result: rcx, rbx, rbp, r14:r15
|
||||
MUL128x192_SCHOOL rdx, r8, [rip+p377p1x2], rcx, rbx, rbp, r14, r15, r13
|
||||
|
||||
xor rdx, rdx
|
||||
shrd rdx, rcx, 1
|
||||
shrd rcx, rbx, 1
|
||||
shrd rbx, rbp, 1
|
||||
shrd rbp, r14, 1
|
||||
shrd r14, r15, 1
|
||||
shr r15, 1
|
||||
add rdx, [reg_p2]
|
||||
adc rcx, [reg_p2+8]
|
||||
adc rbx, [reg_p2+16]
|
||||
mov [reg_p2+16], rbx
|
||||
adc r12, rbp
|
||||
mulx rbp, rbx, [rip+p377p1x2] // result rbx
|
||||
adc r14, r9
|
||||
adc r15, r10
|
||||
mulx r10, r8, [rip+p377p1x2+8]
|
||||
adc r11, 0
|
||||
adc rdi, 0
|
||||
|
||||
// a[4-5] x 2xp377p1_nz --> result: rbx, rbp, r10:r8
|
||||
MUL128x192_SCHOOL rdx, rcx, [rip+p377p1x2], rbx, rbp, r10, r9, r8, r13
|
||||
|
||||
xor rdx, rdx
|
||||
pop r13
|
||||
shrd rdx, rbx, 1
|
||||
shrd rbx, rbp, 1
|
||||
shrd rbp, r10, 1
|
||||
shrd r10, r9, 1
|
||||
shrd r9, r8, 1
|
||||
shr r8, 1
|
||||
add rdx, [reg_p2+16]
|
||||
adc rbx, r12
|
||||
mov [reg_p2+8], rbx
|
||||
pop rbx
|
||||
pop r12
|
||||
adc rbp, r14
|
||||
pop r14
|
||||
mov [reg_p2+16], rbp
|
||||
pop rbp
|
||||
adc r10, r15
|
||||
pop r15
|
||||
mov [reg_p2+24], r10
|
||||
adc r9, r11
|
||||
adc r8, rdi
|
||||
mov [reg_p2], rdx // Final result c0-c5
|
||||
mov [reg_p2+32], r9
|
||||
mov [reg_p2+40], r8
|
||||
ret
|
||||
|
||||
#else
|
||||
|
||||
# error "CONFIGURATION NOT SUPPORTED. TRY USE_MULX=TRUE"
|
||||
|
||||
#endif
|
||||
|
||||
|
||||
//***********************************************************************
|
||||
// 377-bit multiprecision addition
|
||||
// Operation: c [reg_p3] = a [reg_p1] + b [reg_p2]
|
||||
//***********************************************************************
|
||||
.global fmt(mp_add377_asm)
|
||||
fmt(mp_add377_asm):
|
||||
mov r8, [reg_p1]
|
||||
mov r9, [reg_p1+8]
|
||||
mov r10, [reg_p1+16]
|
||||
mov r11, [reg_p1+24]
|
||||
add r8, [reg_p2]
|
||||
adc r9, [reg_p2+8]
|
||||
adc r10, [reg_p2+16]
|
||||
adc r11, [reg_p2+24]
|
||||
mov [reg_p3], r8
|
||||
mov [reg_p3+8], r9
|
||||
mov [reg_p3+16], r10
|
||||
mov [reg_p3+24], r11
|
||||
|
||||
mov r8, [reg_p1+32]
|
||||
mov r9, [reg_p1+40]
|
||||
adc r8, [reg_p2+32]
|
||||
adc r9, [reg_p2+40]
|
||||
mov [reg_p3+32], r8
|
||||
mov [reg_p3+40], r9
|
||||
ret
|
||||
|
||||
|
||||
//***************************************************************************
|
||||
// 2x377-bit multiprecision subtraction/addition
|
||||
// Operation: c [reg_p3] = a [reg_p1] - b [reg_p2] + p377*p377*2^16
|
||||
//***************************************************************************
|
||||
.global fmt(mp_subadd377x2_asm)
|
||||
fmt(mp_subadd377x2_asm):
|
||||
push r12
|
||||
push r13
|
||||
|
||||
mov r8, [reg_p1]
|
||||
mov r9, [reg_p1+8]
|
||||
mov r10, [reg_p1+16]
|
||||
mov r11, [reg_p1+24]
|
||||
mov r12, [reg_p1+32]
|
||||
mov r13, [reg_p1+40]
|
||||
mov rcx, [rip+p377x16p]
|
||||
add r8, rcx
|
||||
adc r9, 0
|
||||
adc r10, 0
|
||||
mov rcx, [rip+p377x16p+24]
|
||||
adc r11, rcx
|
||||
mov rcx, [rip+p377x16p+32]
|
||||
adc r12, rcx
|
||||
mov rcx, [rip+p377x16p+40]
|
||||
adc r13, rcx
|
||||
setc al
|
||||
sub r8, [reg_p2]
|
||||
sbb r9, [reg_p2+8]
|
||||
sbb r10, [reg_p2+16]
|
||||
sbb r11, [reg_p2+24]
|
||||
sbb r12, [reg_p2+32]
|
||||
sbb r13, [reg_p2+40]
|
||||
setc cl
|
||||
mov [reg_p3], r8
|
||||
mov [reg_p3+8], r9
|
||||
mov [reg_p3+16], r10
|
||||
mov [reg_p3+24], r11
|
||||
mov [reg_p3+32], r12
|
||||
mov [reg_p3+40], r13
|
||||
|
||||
mov r8, [reg_p1+48]
|
||||
mov r9, [reg_p1+56]
|
||||
mov r10, [reg_p1+64]
|
||||
mov r11, [reg_p1+72]
|
||||
mov r12, [reg_p1+80]
|
||||
mov r13, [reg_p1+88]
|
||||
bt rax, 0
|
||||
adc r8, [rip+p377x16p+48]
|
||||
adc r9, [rip+p377x16p+56]
|
||||
adc r10, [rip+p377x16p+64]
|
||||
adc r11, [rip+p377x16p+72]
|
||||
adc r12, [rip+p377x16p+80]
|
||||
adc r13, [rip+p377x16p+88]
|
||||
bt rcx, 0
|
||||
sbb r8, [reg_p2+48]
|
||||
sbb r9, [reg_p2+56]
|
||||
sbb r10, [reg_p2+64]
|
||||
sbb r11, [reg_p2+72]
|
||||
sbb r12, [reg_p2+80]
|
||||
sbb r13, [reg_p2+88]
|
||||
|
||||
mov [reg_p3+48], r8
|
||||
mov [reg_p3+56], r9
|
||||
mov [reg_p3+64], r10
|
||||
mov [reg_p3+72], r11
|
||||
mov [reg_p3+80], r12
|
||||
mov [reg_p3+88], r13
|
||||
|
||||
pop r13
|
||||
pop r12
|
||||
ret
|
||||
|
||||
|
||||
//***********************************************************************
|
||||
// Double 2x377-bit multiprecision subtraction
|
||||
// Operation: c [reg_p3] = c [reg_p3] - a [reg_p1] - b [reg_p2]
|
||||
//***********************************************************************
|
||||
.global fmt(mp_dblsub377x2_asm)
|
||||
fmt(mp_dblsub377x2_asm):
|
||||
push r12
|
||||
push r13
|
||||
|
||||
mov r8, [reg_p3]
|
||||
mov r9, [reg_p3+8]
|
||||
mov r10, [reg_p3+16]
|
||||
mov r11, [reg_p3+24]
|
||||
mov r12, [reg_p3+32]
|
||||
mov r13, [reg_p3+40]
|
||||
sub r8, [reg_p1]
|
||||
sbb r9, [reg_p1+8]
|
||||
sbb r10, [reg_p1+16]
|
||||
sbb r11, [reg_p1+24]
|
||||
sbb r12, [reg_p1+32]
|
||||
sbb r13, [reg_p1+40]
|
||||
setc al
|
||||
sub r8, [reg_p2]
|
||||
sbb r9, [reg_p2+8]
|
||||
sbb r10, [reg_p2+16]
|
||||
sbb r11, [reg_p2+24]
|
||||
sbb r12, [reg_p2+32]
|
||||
sbb r13, [reg_p2+40]
|
||||
setc cl
|
||||
mov [reg_p3], r8
|
||||
mov [reg_p3+8], r9
|
||||
mov [reg_p3+16], r10
|
||||
mov [reg_p3+24], r11
|
||||
mov [reg_p3+32], r12
|
||||
mov [reg_p3+40], r13
|
||||
|
||||
mov r8, [reg_p3+48]
|
||||
mov r9, [reg_p3+56]
|
||||
mov r10, [reg_p3+64]
|
||||
mov r11, [reg_p3+72]
|
||||
mov r12, [reg_p3+80]
|
||||
mov r13, [reg_p3+88]
|
||||
bt rax, 0
|
||||
sbb r8, [reg_p1+48]
|
||||
sbb r9, [reg_p1+56]
|
||||
sbb r10, [reg_p1+64]
|
||||
sbb r11, [reg_p1+72]
|
||||
sbb r12, [reg_p1+80]
|
||||
sbb r13, [reg_p1+88]
|
||||
bt rcx, 0
|
||||
sbb r8, [reg_p2+48]
|
||||
sbb r9, [reg_p2+56]
|
||||
sbb r10, [reg_p2+64]
|
||||
sbb r11, [reg_p2+72]
|
||||
sbb r12, [reg_p2+80]
|
||||
sbb r13, [reg_p2+88]
|
||||
mov [reg_p3+48], r8
|
||||
mov [reg_p3+56], r9
|
||||
mov [reg_p3+64], r10
|
||||
mov [reg_p3+72], r11
|
||||
mov [reg_p3+80], r12
|
||||
mov [reg_p3+88], r13
|
||||
|
||||
pop r13
|
||||
pop r12
|
||||
ret
|
||||
|
|
@ -0,0 +1,114 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: supersingular isogeny parameters and generation of functions for P377
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "P377_api.h"
|
||||
#include "P377_internal.h"
|
||||
#include "../internal.h"
|
||||
|
||||
|
||||
// Encoding of field elements, elements over Z_order, elements over GF(p^2) and elliptic curve points:
|
||||
// --------------------------------------------------------------------------------------------------
|
||||
// Elements over GF(p) and Z_order are encoded with the least significant octet (and digit) located at the leftmost position (i.e., little endian format).
|
||||
// Elements (a+b*i) over GF(p^2), where a and b are defined over GF(p), are encoded as {a, b}, with a in the least significant position.
|
||||
// Elliptic curve points P = (x,y) are encoded as {x, y}, with x in the least significant position.
|
||||
// Internally, the number of digits used to represent all these elements is obtained by approximating the number of bits to the immediately greater multiple of 32.
|
||||
// For example, a 377-bit field element is represented with Ceil(377 / 64) = 6 64-bit digits or Ceil(377 / 32) = 12 32-bit digits.
|
||||
|
||||
//
|
||||
// Curve isogeny system "SIDHp377". Base curve: Montgomery curve By^2 = Cx^3 + Ax^2 + Cx defined over GF(p377^2), where A=6, B=1, C=1 and p377 = 2^191*3^117-1
|
||||
//
|
||||
|
||||
const uint64_t p377[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x7FFFFFFFFFFFFFFF, 0x0B46D546BC2A5699, 0xA879CC6988CE7CF5, 0x015B702E0C542196 };
|
||||
const uint64_t p377x2[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x168DAA8D7854AD32, 0x50F398D3119CF9EA, 0x02B6E05C18A8432D };
|
||||
const uint64_t p377x4[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFC, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x2D1B551AF0A95A65, 0xA1E731A62339F3D4, 0x056DC0B83150865A };
|
||||
const uint64_t p377p1[NWORDS64_FIELD] = { 0x0000000000000000, 0x0000000000000000, 0x8000000000000000, 0x0B46D546BC2A5699, 0xA879CC6988CE7CF5, 0x015B702E0C542196 };
|
||||
const uint64_t p377p1x2[NWORDS64_FIELD/2] = { 0x168DAA8D7854AD33, 0x50F398D3119CF9EA, 0x02B6E05C18A8432D };
|
||||
const uint64_t p377x16p[2*NWORDS64_FIELD] = { 0x0000000000000010, 0x0000000000000000, 0x0000000000000000, 0x972557287AB52CD0, 0xF0C672CEE630615E, 0xD491FA3E757BCD2A,
|
||||
0x2830123FBA97E0A3, 0x44E67AC0C81C9117, 0x942C5A8EFDDE690C, 0x63BDE5C206F0021D, 0xAA49E8B73CCD899E, 0x001D7894DFDBF251 };
|
||||
// Order of Alice's subgroup
|
||||
const uint64_t Alice_order[NWORDS64_ORDER] = { 0x0000000000000000, 0x0000000000000000, 0x8000000000000000 };
|
||||
// Order of Bob's subgroup
|
||||
const uint64_t Bob_order[NWORDS64_ORDER] = { 0x168DAA8D7854AD33, 0x50F398D3119CF9EA, 0x02B6E05C18A8432D };
|
||||
// Alice's generator values {XPA0 + XPA1*i, XQA0 + xQA1*i, XRA0 + XRA1*i} in GF(p377^2), expressed in Montgomery representation
|
||||
const uint64_t A_gen[6*NWORDS64_FIELD] = { 0x8AE392AA8312F880, 0xDB7F6BA38CC56011, 0x896F67240AD52C67, 0x21B9C0BD6C0584FF, 0xF064B97DDD0B2BD4, 0x0102EA98B786D4CC, // XPA0
|
||||
0x583DE90ED3D09845, 0x131B1BDFBBE25620, 0x054B16A62F3D59F1, 0x1C3A458EEFFD4A0B, 0x1FBC000608BE1F7A, 0x00225F4BEEF34209, // XPA1
|
||||
0x8AA130E98FE00DE5, 0x6B54CC5A0A538778, 0x46D96D4F04F6605D, 0x069A3CAB971973AE, 0x8923D0F2112DA219, 0x0085C1C47AD21A2A, // XQA0
|
||||
0x50981EA202812D84, 0x61883F048CF1682A, 0x2DBC9EC88567E391, 0xD5E238E99DD189E7, 0x1BFE095BC910EA7D, 0x00203E87957453EB, // XQA1
|
||||
0x296CA63890082DB3, 0x02E16D4D70C2C55A, 0xD4B8FE9CB9481E99, 0xF95F9798C3BECDFB, 0x71B3A2D8A38CB84B, 0x0118DD7682525B04, // XRA0
|
||||
0xF64DD26CEC6E9DF5, 0xBC02B5979FF4F94C, 0x5D8B16849129DE49, 0xE44435C64BEFB9E9, 0x1077D183B5A4727B, 0x0019A2DF755CF268 }; // XRA1
|
||||
// Bob's generator values {XPB0, XQB0, XRB0 + XRB1*i} in GF(p377^2), expressed in Montgomery representation
|
||||
const uint64_t B_gen[6*NWORDS64_FIELD] = { 0x436424EE3C9446F8, 0xB013A914D96E976D, 0x30C376697D926658, 0xE99792AFAA115E68, 0x935421EF522A946B, 0x0032474AECB8799E, // XPB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XPB1
|
||||
0x5EDE445E538850BC, 0x5BA7DAD976595394, 0xF01F46B8519CD118, 0x9DFA5CB5B40775A1, 0xC7E535F99811B56B, 0x0025BF8D8B00A170, // XQB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XQB1
|
||||
0xA35AA9C8EA887C42, 0xE5A1BF165361C81A, 0x719BB1C6D6C727C7, 0x348590861EB46882, 0xB57273062A50C238, 0x002C53E0163A1C34, // XRB0
|
||||
0xF12E87A9F00803D8, 0x49C966997253584C, 0x58BBD82219B363ED, 0x6232DFE1A85929F5, 0xC85434A71BF3CC30, 0x005DE7FAB257510D }; // XRB1
|
||||
// Montgomery constant Montgomery_R2 = (2^384)^2 mod p377
|
||||
const uint64_t Montgomery_R2[NWORDS64_FIELD] = { 0x826E131D3839C923, 0x54892C7B7D73E7F7, 0x3F8957D221B867A3, 0xD1217CD71D03BB94, 0xDCCBFB71E3AE5457, 0x00FCC56B6CD4B219 };
|
||||
// Value one in Montgomery representation
|
||||
const uint64_t Montgomery_one[NWORDS64_FIELD] = { 0x00000000000000BC, 0x0000000000000000, 0x0000000000000000, 0xB7FB600DD0E86746, 0x468DE27F885C3C0B, 0x00D99E2EF237555C };
|
||||
|
||||
|
||||
// Fixed parameters for isogeny tree computation
|
||||
const unsigned int strat_Alice[MAX_Alice-1] = {
|
||||
38, 26, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 11, 7, 4, 2, 1, 1, 2,
|
||||
1, 1, 3, 2, 1, 1, 1, 1, 4, 3, 2, 1, 1, 1, 1, 2, 1, 1, 17, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8,
|
||||
4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1 };
|
||||
|
||||
const unsigned int strat_Bob[MAX_Bob-1] = {
|
||||
54, 31, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 15, 8, 4, 2, 1, 1,
|
||||
2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 23, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1,
|
||||
1, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 9, 6, 4, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1 };
|
||||
|
||||
// Setting up macro defines and including GF(p), GF(p^2), curve, isogeny and kex functions
|
||||
#define fpcopy fpcopy377
|
||||
#define fpzero fpzero377
|
||||
#define fpadd fpadd377
|
||||
#define fpsub fpsub377
|
||||
#define fpneg fpneg377
|
||||
#define fpdiv2 fpdiv2_377
|
||||
#define fpcorrection fpcorrection377
|
||||
#define fpmul_mont fpmul377_mont
|
||||
#define fpsqr_mont fpsqr377_mont
|
||||
#define fpinv_mont fpinv377_mont
|
||||
#define fpinv_chain_mont fpinv377_chain_mont
|
||||
#define fp2copy fp2copy377
|
||||
#define fp2zero fp2zero377
|
||||
#define fp2add fp2add377
|
||||
#define fp2sub fp2sub377
|
||||
#define mp_sub_p2 mp_sub377_p2
|
||||
#define mp_sub_p4 mp_sub377_p4
|
||||
#define sub_p4 mp_sub_p4
|
||||
#define fp2neg fp2neg377
|
||||
#define fp2div2 fp2div2_377
|
||||
#define fp2correction fp2correction377
|
||||
#define fp2mul_mont fp2mul377_mont
|
||||
#define fp2sqr_mont fp2sqr377_mont
|
||||
#define fp2inv_mont fp2inv377_mont
|
||||
#define fp2inv_mont_ct fp2inv377_mont_ct
|
||||
#define fp2inv_mont_bingcd fp2inv377_mont_bingcd
|
||||
#define fpequal_non_constant_time fpequal377_non_constant_time
|
||||
#define mp_add_asm mp_add377_asm
|
||||
#define mp_subaddx2_asm mp_subadd377x2_asm
|
||||
#define mp_dblsubx2_asm mp_dblsub377x2_asm
|
||||
#define crypto_kem_keypair crypto_kem_keypair_SIKEp377
|
||||
#define crypto_kem_enc crypto_kem_enc_SIKEp377
|
||||
#define crypto_kem_dec crypto_kem_dec_SIKEp377
|
||||
#define random_mod_order_A random_mod_order_A_SIDHp377
|
||||
#define random_mod_order_B random_mod_order_B_SIDHp377
|
||||
#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp377
|
||||
#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp377
|
||||
#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp377
|
||||
#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp377
|
||||
|
||||
#include "../fpx.c"
|
||||
#include "../ec_isogeny.c"
|
||||
#include "../sidh.c"
|
||||
#include "../sike.c"
|
||||
|
|
@ -0,0 +1,112 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: API header file for P377
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P377_API_H
|
||||
#define P377_API_H
|
||||
|
||||
|
||||
/*********************** Key encapsulation mechanism API ***********************/
|
||||
|
||||
#define CRYPTO_SECRETKEYBYTES 328 // MSG_BYTES + SECRETKEY_B_BYTES + CRYPTO_PUBLICKEYBYTES bytes
|
||||
#define CRYPTO_PUBLICKEYBYTES 288
|
||||
#define CRYPTO_BYTES 16
|
||||
#define CRYPTO_CIPHERTEXTBYTES 304 // CRYPTO_PUBLICKEYBYTES + MSG_BYTES bytes
|
||||
|
||||
// Algorithm name
|
||||
#define CRYPTO_ALGNAME "SIKEp377"
|
||||
|
||||
// SIKE's key generation
|
||||
// It produces a private key sk and computes the public key pk.
|
||||
// Outputs: secret key sk (CRYPTO_SECRETKEYBYTES = 322 bytes)
|
||||
// public key pk (CRYPTO_PUBLICKEYBYTES = 288 bytes)
|
||||
int crypto_kem_keypair_SIKEp377(unsigned char *pk, unsigned char *sk);
|
||||
|
||||
// SIKE's encapsulation
|
||||
// Input: public key pk (CRYPTO_PUBLICKEYBYTES = 288 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 10 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 298 bytes)
|
||||
int crypto_kem_enc_SIKEp377(unsigned char *ct, unsigned char *ss, const unsigned char *pk);
|
||||
|
||||
// SIKE's decapsulation
|
||||
// Input: secret key sk (CRYPTO_SECRETKEYBYTES = 322 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 298 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 10 bytes)
|
||||
int crypto_kem_dec_SIKEp377(unsigned char *ss, const unsigned char *ct, const unsigned char *sk);
|
||||
|
||||
|
||||
// Encoding of keys for KEM-based isogeny system "SIKEp377" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p377) are encoded in 48 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p377^2), where a and b are defined over GF(p377), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys sk consist of the concatenation of a 10-byte random value, a value in the range [0, 2^Floor(Log(2,3^117))-1] and the public key pk. In the SIKE API,
|
||||
// private keys are encoded in 322 octets in little endian format.
|
||||
// Public keys pk consist of 3 elements in GF(p377^2). In the SIKE API, pk is encoded in 288 octets.
|
||||
// Ciphertexts ct consist of the concatenation of a public key value and a 10-byte value. In the SIKE API, ct is encoded in 288 + 10 = 298 octets.
|
||||
// Shared keys ss consist of a value of 10 octets.
|
||||
|
||||
|
||||
/*********************** Ephemeral key exchange API ***********************/
|
||||
|
||||
#define SIDH_SECRETKEYBYTES_A 24
|
||||
#define SIDH_SECRETKEYBYTES_B 24
|
||||
#define SIDH_PUBLICKEYBYTES 288
|
||||
#define SIDH_BYTES 96
|
||||
|
||||
// SECURITY NOTE: SIDH supports ephemeral Diffie-Hellman key exchange. It is NOT secure to use it with static keys.
|
||||
// See "On the Security of Supersingular Isogeny Cryptosystems", S.D. Galbraith, C. Petit, B. Shani and Y.B. Ti, in ASIACRYPT 2010, 2010.
|
||||
// Extended version available at: http://eprint.iacr.org/2010/859
|
||||
|
||||
// Generation of Alice's secret key
|
||||
// Outputs random value in [0, 2^191 - 1] to be used as Alice's private key
|
||||
void random_mod_order_A_SIDHp377(unsigned char* random_digits);
|
||||
|
||||
// Generation of Bob's secret key
|
||||
// Outputs random value in [0, 2^Floor(Log(2,3^117)) - 1] to be used as Bob's private key
|
||||
void random_mod_order_B_SIDHp377(unsigned char* random_digits);
|
||||
|
||||
// Alice's ephemeral public key generation
|
||||
// Input: a private key PrivateKeyA in the range [0, 2^191 - 1], stored in 24 bytes.
|
||||
// Output: the public key PublicKeyA consisting of 3 GF(p377^2) elements encoded in 288 bytes.
|
||||
int EphemeralKeyGeneration_A_SIDHp377(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA);
|
||||
|
||||
// Bob's ephemeral key-pair generation
|
||||
// It produces a private key PrivateKeyB and computes the public key PublicKeyB.
|
||||
// The private key is an integer in the range [0, 2^Floor(Log(2,3^117)) - 1], stored in 24 bytes.
|
||||
// The public key consists of 3 GF(p377^2) elements encoded in 288 bytes.
|
||||
int EphemeralKeyGeneration_B_SIDHp377(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB);
|
||||
|
||||
// Alice's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB
|
||||
// Inputs: Alice's PrivateKeyA is an integer in the range [0, 2^191 - 1], stored in 24 bytes.
|
||||
// Bob's PublicKeyB consists of 3 GF(p377^2) elements encoded in 288 bytes.
|
||||
// Output: a shared secret SharedSecretA that consists of one element in GF(p377^2) encoded in 96 bytes.
|
||||
int EphemeralSecretAgreement_A_SIDHp377(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA);
|
||||
|
||||
// Bob's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA
|
||||
// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,3^117)) - 1], stored in 24 bytes.
|
||||
// Alice's PublicKeyA consists of 3 GF(p377^2) elements encoded in 288 bytes.
|
||||
// Output: a shared secret SharedSecretB that consists of one element in GF(p377^2) encoded in 96 bytes.
|
||||
int EphemeralSecretAgreement_B_SIDHp377(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB);
|
||||
|
||||
|
||||
// Encoding of keys for KEX-based isogeny system "SIDHp377" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p377) are encoded in 48 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p377^2), where a and b are defined over GF(p377), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys PrivateKeyA and PrivateKeyB can have values in the range [0, 2^191-1] and [0, 2^Floor(Log(2,3^117)) - 1], resp. In the SIDH API,
|
||||
// Alice's and Bob's private keys are encoded in 24 octets in little endian format.
|
||||
// Public keys PublicKeyA and PublicKeyB consist of 3 elements in GF(p377^2). In the SIDH API, they are encoded in 288 octets.
|
||||
// Shared keys SharedSecretA and SharedSecretB consist of one element in GF(p377^2). In the SIDH API, they are encoded in 96 octets.
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,165 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: internal header file for P377
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P377_INTERNAL_H
|
||||
#define P377_INTERNAL_H
|
||||
|
||||
#include "../config.h"
|
||||
|
||||
|
||||
#if (TARGET == TARGET_AMD64) || (TARGET == TARGET_ARM64)
|
||||
#define NWORDS_FIELD 6 // Number of words of a 377-bit field element
|
||||
#define p377_ZERO_WORDS 2 // Number of "0" digits in the least significant part of p377 + 1
|
||||
#elif (TARGET == TARGET_x86)
|
||||
#define NWORDS_FIELD 12
|
||||
#define p377_ZERO_WORDS 5
|
||||
#endif
|
||||
|
||||
|
||||
// Basic constants
|
||||
|
||||
#define NBITS_FIELD 377
|
||||
#define MAXBITS_FIELD 384
|
||||
#define MAXWORDS_FIELD ((MAXBITS_FIELD+RADIX-1)/RADIX) // Max. number of words to represent field elements
|
||||
#define NWORDS64_FIELD ((NBITS_FIELD+63)/64) // Number of 64-bit words of a 377-bit field element
|
||||
#define NBITS_ORDER 192
|
||||
#define NWORDS_ORDER ((NBITS_ORDER+RADIX-1)/RADIX) // Number of words of oA and oB, where oA and oB are the subgroup orders of Alice and Bob, resp.
|
||||
#define NWORDS64_ORDER ((NBITS_ORDER+63)/64) // Number of 64-bit words of a 192-bit element
|
||||
#define MAXBITS_ORDER NBITS_ORDER
|
||||
#define ALICE 0
|
||||
#define BOB 1
|
||||
#define OALICE_BITS 191
|
||||
#define OBOB_BITS 186
|
||||
#define OBOB_EXPON 117
|
||||
#define MASK_ALICE 0x7F
|
||||
#define MASK_BOB 0x01
|
||||
#define PRIME p377
|
||||
#define PARAM_A 6
|
||||
#define PARAM_C 1
|
||||
// Fixed parameters for isogeny tree computation
|
||||
#define MAX_INT_POINTS_ALICE 7
|
||||
#define MAX_INT_POINTS_BOB 8
|
||||
#define MAX_Alice 95
|
||||
#define MAX_Bob 117
|
||||
#define MSG_BYTES 16
|
||||
#define SECRETKEY_A_BYTES ((OALICE_BITS + 7) / 8)
|
||||
#define SECRETKEY_B_BYTES ((OBOB_BITS - 1 + 7) / 8)
|
||||
#define FP2_ENCODED_BYTES 2*((NBITS_FIELD + 7) / 8)
|
||||
|
||||
|
||||
// SIDH's basic element definitions and point representations
|
||||
|
||||
typedef digit_t felm_t[NWORDS_FIELD]; // Datatype for representing 377-bit field elements (384-bit max.)
|
||||
typedef digit_t dfelm_t[2*NWORDS_FIELD]; // Datatype for representing double-precision 2x377-bit field elements (2x384-bit max.)
|
||||
typedef felm_t f2elm_t[2]; // Datatype for representing quadratic extension field elements GF(p377^2)
|
||||
|
||||
typedef struct { f2elm_t X; f2elm_t Z; } point_proj; // Point representation in projective XZ Montgomery coordinates.
|
||||
typedef point_proj point_proj_t[1];
|
||||
|
||||
|
||||
|
||||
/**************** Function prototypes ****************/
|
||||
/************* Multiprecision functions **************/
|
||||
|
||||
// 377-bit multiprecision addition, c = a+b
|
||||
void mp_add377(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_add377_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 377-bit multiprecision subtraction, c = a-b+2p or c = a-b+4p
|
||||
extern void mp_sub377_p2(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void mp_sub377_p4(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub377_p2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub377_p4_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 2x377-bit multiprecision subtraction followed by addition with p377*2^384, c = a-b+(p377*2^384) if a-b < 0, otherwise c=a-b
|
||||
void mp_subaddx2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_subadd377x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Double 2x377-bit multiprecision subtraction, c = c-a-b, where c > a and c > b
|
||||
void mp_dblsub377x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
/************ Field arithmetic functions *************/
|
||||
|
||||
// Copy of a field element, c = a
|
||||
void fpcopy377(const digit_t* a, digit_t* c);
|
||||
|
||||
// Zeroing a field element, a = 0
|
||||
void fpzero377(digit_t* a);
|
||||
|
||||
// Non constant-time comparison of two field elements. If a = b return TRUE, otherwise, return FALSE
|
||||
bool fpequal377_non_constant_time(const digit_t* a, const digit_t* b);
|
||||
|
||||
// Modular addition, c = a+b mod p377
|
||||
extern void fpadd377(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpadd377_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular subtraction, c = a-b mod p377
|
||||
extern void fpsub377(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpsub377_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular negation, a = -a mod p377
|
||||
extern void fpneg377(digit_t* a);
|
||||
|
||||
// Modular division by two, c = a/2 mod p377.
|
||||
void fpdiv2_377(const digit_t* a, digit_t* c);
|
||||
|
||||
// Modular correction to reduce field element a in [0, 2*p377-1] to [0, p377-1].
|
||||
void fpcorrection377(digit_t* a);
|
||||
|
||||
// 377-bit Montgomery reduction, c = a mod p
|
||||
void rdc377_asm(digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field multiplication using Montgomery arithmetic, c = a*b*R^-1 mod p377, where R=2^768
|
||||
void fpmul377_mont(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mul377_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Field squaring using Montgomery arithmetic, c = a*b*R^-1 mod p377, where R=2^768
|
||||
void fpsqr377_mont(const digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field inversion, a = a^-1 in GF(p377)
|
||||
void fpinv377_mont(digit_t* a);
|
||||
|
||||
// Chain to compute (p377-3)/4 using Montgomery arithmetic
|
||||
void fpinv377_chain_mont(digit_t* a);
|
||||
|
||||
/************ GF(p^2) arithmetic functions *************/
|
||||
|
||||
// Copy of a GF(p377^2) element, c = a
|
||||
void fp2copy377(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Zeroing a GF(p377^2) element, a = 0
|
||||
void fp2zero377(f2elm_t a);
|
||||
|
||||
// GF(p377^2) negation, a = -a in GF(p377^2)
|
||||
void fp2neg377(f2elm_t a);
|
||||
|
||||
// GF(p377^2) addition, c = a+b in GF(p377^2)
|
||||
extern void fp2add377(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p377^2) subtraction, c = a-b in GF(p377^2)
|
||||
extern void fp2sub377(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p377^2) division by two, c = a/2 in GF(p377^2)
|
||||
void fp2div2_377(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Modular correction, a = a in GF(p377^2)
|
||||
void fp2correction377(f2elm_t a);
|
||||
|
||||
// GF(p377^2) squaring using Montgomery arithmetic, c = a^2 in GF(p377^2)
|
||||
void fp2sqr377_mont(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// GF(p377^2) multiplication using Montgomery arithmetic, c = a*b in GF(p377^2)
|
||||
void fp2mul377_mont(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p377^2) inversion using Montgomery arithmetic, a = (a0-i*a1)/(a0^2+a1^2)
|
||||
void fp2inv377_mont(f2elm_t a);
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,259 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: portable modular arithmetic for P377
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P377_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p377[NWORDS64_FIELD];
|
||||
extern const uint64_t p377p1[NWORDS64_FIELD];
|
||||
extern const uint64_t p377x2[NWORDS64_FIELD];
|
||||
extern const uint64_t p377x4[NWORDS64_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub377_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p377x2)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub377_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p377x4)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd377(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p377.
|
||||
// Inputs: a, b in [0, 2*p377-1]
|
||||
// Output: c in [0, 2*p377-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p377x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p377x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub377(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p377.
|
||||
// Inputs: a, b in [0, 2*p377-1]
|
||||
// Output: c in [0, 2*p377-1]
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p377x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg377(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p377.
|
||||
// Input/output: a in [0, 2*p377-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p377x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_377(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p377.
|
||||
// Input : a in [0, 2*p377-1]
|
||||
// Output: c in [0, 2*p377-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p377
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p377)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection377(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p377-1] to [0, p377-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p377)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p377)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void digit_x_digit(const digit_t a, const digit_t b, digit_t* c)
|
||||
{ // Digit multiplication, digit * digit -> 2-digit result
|
||||
register digit_t al, ah, bl, bh, temp;
|
||||
digit_t albl, albh, ahbl, ahbh, res1, res2, res3, carry;
|
||||
digit_t mask_low = (digit_t)(-1) >> (sizeof(digit_t)*4), mask_high = (digit_t)(-1) << (sizeof(digit_t)*4);
|
||||
|
||||
al = a & mask_low; // Low part
|
||||
ah = a >> (sizeof(digit_t) * 4); // High part
|
||||
bl = b & mask_low;
|
||||
bh = b >> (sizeof(digit_t) * 4);
|
||||
|
||||
albl = al*bl;
|
||||
albh = al*bh;
|
||||
ahbl = ah*bl;
|
||||
ahbh = ah*bh;
|
||||
c[0] = albl & mask_low; // C00
|
||||
|
||||
res1 = albl >> (sizeof(digit_t) * 4);
|
||||
res2 = ahbl & mask_low;
|
||||
res3 = albh & mask_low;
|
||||
temp = res1 + res2 + res3;
|
||||
carry = temp >> (sizeof(digit_t) * 4);
|
||||
c[0] ^= temp << (sizeof(digit_t) * 4); // C01
|
||||
|
||||
res1 = ahbl >> (sizeof(digit_t) * 4);
|
||||
res2 = albh >> (sizeof(digit_t) * 4);
|
||||
res3 = ahbh & mask_low;
|
||||
temp = res1 + res2 + res3 + carry;
|
||||
c[1] = temp & mask_low; // C10
|
||||
carry = temp & mask_high;
|
||||
c[1] ^= (ahbh & mask_high) + carry; // C11
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
unsigned int i, j;
|
||||
digit_t t = 0, u = 0, v = 0, UV[2];
|
||||
unsigned int carry = 0;
|
||||
|
||||
for (i = 0; i < nwords; i++) {
|
||||
for (j = 0; j <= i; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = nwords; i < 2*nwords-1; i++) {
|
||||
for (j = i-nwords+1; j < nwords; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
c[2*nwords-1] = v;
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Efficient Montgomery reduction using comba and exploiting the special form of the prime p377.
|
||||
// mc = ma*R^-1 mod p377x2, where R = 2^384.
|
||||
// If ma < 2^384*p377, the output mc is in the range [0, 2*p377-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
unsigned int i, j, carry, count = p377_ZERO_WORDS;
|
||||
digit_t UV[2], t = 0, u = 0, v = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
mc[i] = 0;
|
||||
}
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
for (j = 0; j < i; j++) {
|
||||
if (j < (i-p377_ZERO_WORDS+1)) {
|
||||
MUL(mc[j], ((digit_t*)p377p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = NWORDS_FIELD; i < 2*NWORDS_FIELD-1; i++) {
|
||||
if (count > 0) {
|
||||
count -= 1;
|
||||
}
|
||||
for (j = i-NWORDS_FIELD+1; j < NWORDS_FIELD; j++) {
|
||||
if (j < (NWORDS_FIELD-count)) {
|
||||
MUL(mc[j], ((digit_t*)p377p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i-NWORDS_FIELD] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
ADDC(0, v, ma[2*NWORDS_FIELD-1], carry, v);
|
||||
mc[NWORDS_FIELD-1] = v;
|
||||
}
|
||||
|
|
@ -0,0 +1,491 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: modular arithmetic optimized for x64 platforms for P434
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P434_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p434[NWORDS_FIELD];
|
||||
extern const uint64_t p434p1[NWORDS_FIELD];
|
||||
extern const uint64_t p434x2[NWORDS_FIELD];
|
||||
extern const uint64_t p434x4[NWORDS_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub434_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p434x2)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub434_p2_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub434_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p434x4)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub434_p4_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd434(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p434.
|
||||
// Inputs: a, b in [0, 2*p434-1]
|
||||
// Output: c in [0, 2*p434-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p434x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p434x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpadd434_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub434(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p434.
|
||||
// Inputs: a, b in [0, 2*p434-1]
|
||||
// Output: c in [0, 2*p434-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p434x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpsub434_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg434(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p434.
|
||||
// Input/output: a in [0, 2*p434-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p434x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_434(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p434.
|
||||
// Input : a in [0, 2*p434-1]
|
||||
// Output: c in [0, 2*p434-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p434
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p434)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection434(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p434-1] to [0, p434-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p434)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p434)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
|
||||
(void)nwords;
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
unsigned int carry = 0;
|
||||
|
||||
MULADD128(a[0], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[6], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
c[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[6], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
c[8] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[6], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
c[9] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[6], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
c[10] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[6], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
c[11] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
|
||||
MULADD128(a[6], b[6], uv, carry, uv);
|
||||
c[12] = uv[0];
|
||||
c[13] = uv[1];
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mul434_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Montgomery reduction exploiting special form of the prime.
|
||||
// mc = ma*R^-1 mod p434x2, where R = 2^448.
|
||||
// If ma < 2^448*p434, the output mc is in the range [0, 2*p434-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int carry;
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
|
||||
mc[0] = ma[0];
|
||||
mc[1] = ma[1];
|
||||
mc[2] = ma[2];
|
||||
MUL128(mc[0], ((digit_t*)p434p1)[3], uv);
|
||||
ADDC(0, uv[0], ma[3], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
mc[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p434p1)[4], uv, carry, uv);
|
||||
MULADD128(mc[1], ((digit_t*)p434p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[4], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p434p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p434p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p434p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[5], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p434p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p434p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p434p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p434p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[6], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[1], ((digit_t*)p434p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p434p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p434p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p434p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[7], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[2], ((digit_t*)p434p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p434p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p434p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p434p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[8], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[3], ((digit_t*)p434p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p434p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p434p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p434p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[9], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[4], ((digit_t*)p434p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p434p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p434p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[10], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[5], ((digit_t*)p434p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p434p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[11], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[6], ((digit_t*)p434p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[12], carry, mc[5]);
|
||||
ADDC(carry, uv[1], ma[13], carry, mc[6]);
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
rdc434_asm(ma, mc);
|
||||
|
||||
#endif
|
||||
}
|
||||
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Загрузить разницу
|
|
@ -0,0 +1,133 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: supersingular isogeny parameters and generation of functions for P434
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "P434_api.h"
|
||||
#include "P434_internal.h"
|
||||
#include "../internal.h"
|
||||
|
||||
|
||||
// Encoding of field elements, elements over Z_order, elements over GF(p^2) and elliptic curve points:
|
||||
// --------------------------------------------------------------------------------------------------
|
||||
// Elements over GF(p) and Z_order are encoded with the least significant octet (and digit) located at the leftmost position (i.e., little endian format).
|
||||
// Elements (a+b*i) over GF(p^2), where a and b are defined over GF(p), are encoded as {a, b}, with a in the least significant position.
|
||||
// Elliptic curve points P = (x,y) are encoded as {x, y}, with x in the least significant position.
|
||||
// Internally, the number of digits used to represent all these elements is obtained by approximating the number of bits to the immediately greater multiple of 32.
|
||||
// For example, a 434-bit field element is represented with Ceil(434 / 64) = 7 64-bit digits or Ceil(434 / 32) = 14 32-bit digits.
|
||||
|
||||
//
|
||||
// Curve isogeny system "SIDHp434". Base curve: Montgomery curve By^2 = Cx^3 + Ax^2 + Cx defined over GF(p434^2), where A=6, B=1, C=1 and p434 = 2^216*3^137-1
|
||||
//
|
||||
|
||||
const uint64_t p434[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFDC1767AE2FFFFFF,
|
||||
0x7BC65C783158AEA3, 0x6CFC5FD681C52056, 0x0002341F27177344 };
|
||||
const uint64_t p434p1[NWORDS64_FIELD] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xFDC1767AE3000000,
|
||||
0x7BC65C783158AEA3, 0x6CFC5FD681C52056, 0x0002341F27177344 };
|
||||
const uint64_t p434x2[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFB82ECF5C5FFFFFF,
|
||||
0xF78CB8F062B15D47, 0xD9F8BFAD038A40AC, 0x0004683E4E2EE688 };
|
||||
const uint64_t p434x4[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFC, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xF705D9EB8BFFFFFF,
|
||||
0xEF1971E0C562BA8F, 0xB3F17F5A07148159, 0x0008D07C9C5DCD11 };
|
||||
const uint64_t p434x16p[2*NWORDS64_FIELD] = { 0x0000000000000010, 0x0000000000000000, 0x0000000000000000, 0x47D130A3A0000000,
|
||||
0x873470F9D4EA2B80, 0x6074052FC75BF530, 0x54497C1B1D119772, 0xC55F373D2CDCA412,
|
||||
0x732CA2221C664B96, 0x6445AB96AF6359A5, 0x221708AB42ABE1B4, 0xAE3D3D0063244F01,
|
||||
0x18B920F2ECF68816, 0x0000004DB194809D };
|
||||
// Order of Alice's subgroup
|
||||
const uint64_t Alice_order[NWORDS64_ORDER] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000001000000 };
|
||||
// Order of Bob's subgroup
|
||||
const uint64_t Bob_order[NWORDS64_ORDER] = { 0x58AEA3FDC1767AE3, 0xC520567BC65C7831, 0x1773446CFC5FD681, 0x0000000002341F27 };
|
||||
// Alice's generator values {XPA0 + XPA1*i, XQA0 + xQA1*i, XRA0 + XRA1*i} in GF(p434^2), expressed in Montgomery representation
|
||||
const uint64_t A_gen[6*NWORDS64_FIELD] = { 0x05ADF455C5C345BF, 0x91935C5CC767AC2B, 0xAFE4E879951F0257, 0x70E792DC89FA27B1,
|
||||
0xF797F526BB48C8CD, 0x2181DB6131AF621F, 0x00000A1C08B1ECC4, // XPA0
|
||||
0x74840EB87CDA7788, 0x2971AA0ECF9F9D0B, 0xCB5732BDF41715D5, 0x8CD8E51F7AACFFAA,
|
||||
0xA7F424730D7E419F, 0xD671EB919A179E8C, 0x0000FFA26C5A924A, // XPA1
|
||||
0xFEC6E64588B7273B, 0xD2A626D74CBBF1C6, 0xF8F58F07A78098C7, 0xE23941F470841B03,
|
||||
0x1B63EDA2045538DD, 0x735CFEB0FFD49215, 0x0001C4CB77542876, // XQA0
|
||||
0xADB0F733C17FFDD6, 0x6AFFBD037DA0A050, 0x680EC43DB144E02F, 0x1E2E5D5FF524E374,
|
||||
0xE2DDA115260E2995, 0xA6E4B552E2EDE508, 0x00018ECCDDF4B53E, // XQA1
|
||||
0x01BA4DB518CD6C7D, 0x2CB0251FE3CC0611, 0x259B0C6949A9121B, 0x60E17AC16D2F82AD,
|
||||
0x3AA41F1CE175D92D, 0x413FBE6A9B9BC4F3, 0x00022A81D8D55643, // XRA0
|
||||
0xB8ADBC70FC82E54A, 0xEF9CDDB0D5FADDED, 0x5820C734C80096A0, 0x7799994BAA96E0E4,
|
||||
0x044961599E379AF8, 0xDB2B94FBF09F27E2, 0x0000B87FC716C0C6 }; // XRA1
|
||||
// Bob's generator values {XPB0, XQB0, XRB0 + XRB1*i} in GF(p434^2), expressed in Montgomery representation
|
||||
const uint64_t B_gen[6*NWORDS64_FIELD] = { 0x6E5497556EDD48A3, 0x2A61B501546F1C05, 0xEB919446D049887D, 0x5864A4A69D450C4F,
|
||||
0xB883F276A6490D2B, 0x22CC287022D5F5B9, 0x0001BED4772E551F, // XPB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XPB1
|
||||
0xFAE2A3F93D8B6B8E, 0x494871F51700FE1C, 0xEF1A94228413C27C, 0x498FF4A4AF60BD62,
|
||||
0xB00AD2A708267E8A, 0xF4328294E017837F, 0x000034080181D8AE, // XQB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XQB1
|
||||
0x283B34FAFEFDC8E4, 0x9208F44977C3E647, 0x7DEAE962816F4E9A, 0x68A2BA8AA262EC9D,
|
||||
0x8176F112EA43F45B, 0x02106D022634F504, 0x00007E8A50F02E37, // XRB0
|
||||
0xB378B7C1DA22CCB1, 0x6D089C99AD1D9230, 0xEBE15711813E2369, 0x2B35A68239D48A53,
|
||||
0x445F6FD138407C93, 0xBEF93B29A3F6B54B, 0x000173FA910377D3 }; // XRB1
|
||||
// Montgomery constant Montgomery_R2 = (2^448)^2 mod p434
|
||||
const uint64_t Montgomery_R2[NWORDS64_FIELD] = { 0x28E55B65DCD69B30, 0xACEC7367768798C2, 0xAB27973F8311688D, 0x175CC6AF8D6C7C0B,
|
||||
0xABCD92BF2DDE347E, 0x69E16A61C7686D9A, 0x000025A89BCDD12A };
|
||||
// Value one in Montgomery representation
|
||||
const uint64_t Montgomery_one[NWORDS64_FIELD] = { 0x000000000000742C, 0x0000000000000000, 0x0000000000000000, 0xB90FF404FC000000,
|
||||
0xD801A4FB559FACD4, 0xE93254545F77410C, 0x0000ECEEA7BD2EDA };
|
||||
|
||||
|
||||
// Fixed parameters for isogeny tree computation
|
||||
const unsigned int strat_Alice[MAX_Alice-1] = {
|
||||
48, 28, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 13, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1,
|
||||
1, 1, 5, 4, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 21, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1,
|
||||
1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1 };
|
||||
|
||||
const unsigned int strat_Bob[MAX_Bob-1] = {
|
||||
66, 33, 17, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 1,
|
||||
2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 32, 16, 8, 4, 3, 1, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2,
|
||||
1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1 };
|
||||
|
||||
// Setting up macro defines and including GF(p), GF(p^2), curve, isogeny and kex functions
|
||||
#define fpcopy fpcopy434
|
||||
#define fpzero fpzero434
|
||||
#define fpadd fpadd434
|
||||
#define fpsub fpsub434
|
||||
#define fpneg fpneg434
|
||||
#define fpdiv2 fpdiv2_434
|
||||
#define fpcorrection fpcorrection434
|
||||
#define fpmul_mont fpmul434_mont
|
||||
#define fpsqr_mont fpsqr434_mont
|
||||
#define fpinv_mont fpinv434_mont
|
||||
#define fpinv_chain_mont fpinv434_chain_mont
|
||||
#define fp2copy fp2copy434
|
||||
#define fp2zero fp2zero434
|
||||
#define fp2add fp2add434
|
||||
#define fp2sub fp2sub434
|
||||
#define mp_sub_p2 mp_sub434_p2
|
||||
#define mp_sub_p4 mp_sub434_p4
|
||||
#define sub_p4 mp_sub_p4
|
||||
#define fp2neg fp2neg434
|
||||
#define fp2div2 fp2div2_434
|
||||
#define fp2correction fp2correction434
|
||||
#define fp2mul_mont fp2mul434_mont
|
||||
#define fp2sqr_mont fp2sqr434_mont
|
||||
#define fp2inv_mont fp2inv434_mont
|
||||
#define fp2inv_mont_ct fp2inv434_mont_ct
|
||||
#define fp2inv_mont_bingcd fp2inv434_mont_bingcd
|
||||
#define fpequal_non_constant_time fpequal434_non_constant_time
|
||||
#define mp_add_asm mp_add434_asm
|
||||
#define mp_subaddx2_asm mp_subadd434x2_asm
|
||||
#define mp_dblsubx2_asm mp_dblsub434x2_asm
|
||||
#define crypto_kem_keypair crypto_kem_keypair_SIKEp434
|
||||
#define crypto_kem_enc crypto_kem_enc_SIKEp434
|
||||
#define crypto_kem_dec crypto_kem_dec_SIKEp434
|
||||
#define random_mod_order_A random_mod_order_A_SIDHp434
|
||||
#define random_mod_order_B random_mod_order_B_SIDHp434
|
||||
#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp434
|
||||
#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp434
|
||||
#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp434
|
||||
#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp434
|
||||
|
||||
#include "../fpx.c"
|
||||
#include "../ec_isogeny.c"
|
||||
#include "../sidh.c"
|
||||
#include "../sike.c"
|
||||
|
|
@ -0,0 +1,112 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: API header file for P434
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P434_API_H
|
||||
#define P434_API_H
|
||||
|
||||
|
||||
/*********************** Key encapsulation mechanism API ***********************/
|
||||
|
||||
#define CRYPTO_SECRETKEYBYTES 374 // MSG_BYTES + SECRETKEY_B_BYTES + CRYPTO_PUBLICKEYBYTES bytes
|
||||
#define CRYPTO_PUBLICKEYBYTES 330
|
||||
#define CRYPTO_BYTES 16
|
||||
#define CRYPTO_CIPHERTEXTBYTES 346 // CRYPTO_PUBLICKEYBYTES + MSG_BYTES bytes
|
||||
|
||||
// Algorithm name
|
||||
#define CRYPTO_ALGNAME "SIKEp434"
|
||||
|
||||
// SIKE's key generation
|
||||
// It produces a private key sk and computes the public key pk.
|
||||
// Outputs: secret key sk (CRYPTO_SECRETKEYBYTES = 374 bytes)
|
||||
// public key pk (CRYPTO_PUBLICKEYBYTES = 330 bytes)
|
||||
int crypto_kem_keypair_SIKEp434(unsigned char *pk, unsigned char *sk);
|
||||
|
||||
// SIKE's encapsulation
|
||||
// Input: public key pk (CRYPTO_PUBLICKEYBYTES = 330 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 16 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 346 bytes)
|
||||
int crypto_kem_enc_SIKEp434(unsigned char *ct, unsigned char *ss, const unsigned char *pk);
|
||||
|
||||
// SIKE's decapsulation
|
||||
// Input: secret key sk (CRYPTO_SECRETKEYBYTES = 374 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 346 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 16 bytes)
|
||||
int crypto_kem_dec_SIKEp434(unsigned char *ss, const unsigned char *ct, const unsigned char *sk);
|
||||
|
||||
|
||||
// Encoding of keys for KEM-based isogeny system "SIKEp434" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p434) are encoded in 55 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p434^2), where a and b are defined over GF(p434), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys sk consist of the concatenation of a 16-byte random value, a value in the range [0, 2^Floor(Log(2,3^137))-1] and the public key pk. In the SIKE API,
|
||||
// private keys are encoded in 374 octets in little endian format.
|
||||
// Public keys pk consist of 3 elements in GF(p434^2). In the SIKE API, pk is encoded in 330 octets.
|
||||
// Ciphertexts ct consist of the concatenation of a public key value and a 16-byte value. In the SIKE API, ct is encoded in 330 + 16 = 346 octets.
|
||||
// Shared keys ss consist of a value of 16 octets.
|
||||
|
||||
|
||||
/*********************** Ephemeral key exchange API ***********************/
|
||||
|
||||
#define SIDH_SECRETKEYBYTES_A 27
|
||||
#define SIDH_SECRETKEYBYTES_B 28
|
||||
#define SIDH_PUBLICKEYBYTES 330
|
||||
#define SIDH_BYTES 110
|
||||
|
||||
// SECURITY NOTE: SIDH supports ephemeral Diffie-Hellman key exchange. It is NOT secure to use it with static keys.
|
||||
// See "On the Security of Supersingular Isogeny Cryptosystems", S.D. Galbraith, C. Petit, B. Shani and Y.B. Ti, in ASIACRYPT 2016, 2016.
|
||||
// Extended version available at: http://eprint.iacr.org/2016/859
|
||||
|
||||
// Generation of Alice's secret key
|
||||
// Outputs random value in [0, 2^216 - 1] to be used as Alice's private key
|
||||
void random_mod_order_A_SIDHp434(unsigned char* random_digits);
|
||||
|
||||
// Generation of Bob's secret key
|
||||
// Outputs random value in [0, 2^Floor(Log(2,3^137)) - 1] to be used as Bob's private key
|
||||
void random_mod_order_B_SIDHp434(unsigned char* random_digits);
|
||||
|
||||
// Alice's ephemeral public key generation
|
||||
// Input: a private key PrivateKeyA in the range [0, 2^216 - 1], stored in 27 bytes.
|
||||
// Output: the public key PublicKeyA consisting of 3 GF(p434^2) elements encoded in 330 bytes.
|
||||
int EphemeralKeyGeneration_A_SIDHp434(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA);
|
||||
|
||||
// Bob's ephemeral key-pair generation
|
||||
// It produces a private key PrivateKeyB and computes the public key PublicKeyB.
|
||||
// The private key is an integer in the range [0, 2^Floor(Log(2,3^137)) - 1], stored in 28 bytes.
|
||||
// The public key consists of 3 GF(p434^2) elements encoded in 330 bytes.
|
||||
int EphemeralKeyGeneration_B_SIDHp434(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB);
|
||||
|
||||
// Alice's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB
|
||||
// Inputs: Alice's PrivateKeyA is an integer in the range [0, 2^216 - 1], stored in 27 bytes.
|
||||
// Bob's PublicKeyB consists of 3 GF(p434^2) elements encoded in 330 bytes.
|
||||
// Output: a shared secret SharedSecretA that consists of one element in GF(p434^2) encoded in 110 bytes.
|
||||
int EphemeralSecretAgreement_A_SIDHp434(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA);
|
||||
|
||||
// Bob's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA
|
||||
// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,3^137)) - 1], stored in 28 bytes.
|
||||
// Alice's PublicKeyA consists of 3 GF(p434^2) elements encoded in 330 bytes.
|
||||
// Output: a shared secret SharedSecretB that consists of one element in GF(p434^2) encoded in 110 bytes.
|
||||
int EphemeralSecretAgreement_B_SIDHp434(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB);
|
||||
|
||||
|
||||
// Encoding of keys for KEX-based isogeny system "SIDHp434" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p434) are encoded in 55 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p434^2), where a and b are defined over GF(p434), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys PrivateKeyA and PrivateKeyB can have values in the range [0, 2^216-1] and [0, 2^Floor(Log(2,3^137)) - 1], resp. In the SIDH API,
|
||||
// Alice's and Bob's private keys are encoded in 27 and 28 octets, resp., in little endian format.
|
||||
// Public keys PublicKeyA and PublicKeyB consist of 3 elements in GF(p434^2). In the SIDH API, they are encoded in 330 octets.
|
||||
// Shared keys SharedSecretA and SharedSecretB consist of one element in GF(p434^2). In the SIDH API, they are encoded in 110 octets.
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,175 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: internal header file for P434
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P434_INTERNAL_H
|
||||
#define P434_INTERNAL_H
|
||||
|
||||
#include "../config.h"
|
||||
|
||||
|
||||
#if (TARGET == TARGET_AMD64) || (TARGET == TARGET_ARM64)
|
||||
#define NWORDS_FIELD 7 // Number of words of a 434-bit field element
|
||||
#define p434_ZERO_WORDS 3 // Number of "0" digits in the least significant part of p434 + 1
|
||||
#elif (TARGET == TARGET_x86)
|
||||
#define NWORDS_FIELD 14
|
||||
#define p434_ZERO_WORDS 6
|
||||
#endif
|
||||
|
||||
|
||||
// Basic constants
|
||||
|
||||
#define NBITS_FIELD 434
|
||||
#define MAXBITS_FIELD 448
|
||||
#define MAXWORDS_FIELD ((MAXBITS_FIELD+RADIX-1)/RADIX) // Max. number of words to represent field elements
|
||||
#define NWORDS64_FIELD ((NBITS_FIELD+63)/64) // Number of 64-bit words of a 434-bit field element
|
||||
#define NBITS_ORDER 256
|
||||
#define NWORDS_ORDER ((NBITS_ORDER+RADIX-1)/RADIX) // Number of words of oA and oB, where oA and oB are the subgroup orders of Alice and Bob, resp.
|
||||
#define NWORDS64_ORDER ((NBITS_ORDER+63)/64) // Number of 64-bit words of a 224-bit element
|
||||
#define MAXBITS_ORDER NBITS_ORDER
|
||||
#define ALICE 0
|
||||
#define BOB 1
|
||||
#define OALICE_BITS 216
|
||||
#define OBOB_BITS 218
|
||||
#define OBOB_EXPON 137
|
||||
#define MASK_ALICE 0xFF
|
||||
#define MASK_BOB 0x01
|
||||
#define PRIME p434
|
||||
#define PARAM_A 6
|
||||
#define PARAM_C 1
|
||||
// Fixed parameters for isogeny tree computation
|
||||
#define MAX_INT_POINTS_ALICE 7
|
||||
#define MAX_INT_POINTS_BOB 8
|
||||
#define MAX_Alice 108
|
||||
#define MAX_Bob 137
|
||||
#define MSG_BYTES 16
|
||||
#define SECRETKEY_A_BYTES ((OALICE_BITS + 7) / 8)
|
||||
#define SECRETKEY_B_BYTES ((OBOB_BITS - 1 + 7) / 8)
|
||||
#define FP2_ENCODED_BYTES 2*((NBITS_FIELD + 7) / 8)
|
||||
|
||||
|
||||
// SIDH's basic element definitions and point representations
|
||||
|
||||
typedef digit_t felm_t[NWORDS_FIELD]; // Datatype for representing 434-bit field elements (448-bit max.)
|
||||
typedef digit_t dfelm_t[2*NWORDS_FIELD]; // Datatype for representing double-precision 2x434-bit field elements (2x448-bit max.)
|
||||
typedef felm_t f2elm_t[2]; // Datatype for representing quadratic extension field elements GF(p434^2)
|
||||
|
||||
typedef struct { f2elm_t X; f2elm_t Z; } point_proj; // Point representation in projective XZ Montgomery coordinates.
|
||||
typedef point_proj point_proj_t[1];
|
||||
|
||||
#ifdef COMPRESS
|
||||
typedef struct { f2elm_t X; f2elm_t Y; f2elm_t Z; } point_full_proj; // Point representation in full projective XYZ Montgomery coordinates
|
||||
typedef point_full_proj point_full_proj_t[1];
|
||||
|
||||
typedef struct { f2elm_t x; f2elm_t y; } point_affine; // Point representation in affine coordinates.
|
||||
typedef point_affine point_t[1];
|
||||
|
||||
typedef f2elm_t publickey_t[3];
|
||||
#endif
|
||||
|
||||
|
||||
|
||||
/**************** Function prototypes ****************/
|
||||
/************* Multiprecision functions **************/
|
||||
|
||||
// 434-bit multiprecision addition, c = a+b
|
||||
void mp_add434(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_add434_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 434-bit multiprecision subtraction, c = a-b+2p or c = a-b+4p
|
||||
extern void mp_sub434_p2(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void mp_sub434_p4(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub434_p2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub434_p4_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 2x434-bit multiprecision subtraction followed by addition with p434*2^448, c = a-b+(p434*2^448) if a-b < 0, otherwise c=a-b
|
||||
void mp_subaddx2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_subadd434x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Double 2x434-bit multiprecision subtraction, c = c-a-b, where c > a and c > b
|
||||
void mp_dblsub434x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
/************ Field arithmetic functions *************/
|
||||
|
||||
// Copy of a field element, c = a
|
||||
void fpcopy434(const digit_t* a, digit_t* c);
|
||||
|
||||
// Zeroing a field element, a = 0
|
||||
void fpzero434(digit_t* a);
|
||||
|
||||
// Non constant-time comparison of two field elements. If a = b return TRUE, otherwise, return FALSE
|
||||
bool fpequal434_non_constant_time(const digit_t* a, const digit_t* b);
|
||||
|
||||
// Modular addition, c = a+b mod p434
|
||||
extern void fpadd434(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpadd434_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular subtraction, c = a-b mod p434
|
||||
extern void fpsub434(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpsub434_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular negation, a = -a mod p434
|
||||
extern void fpneg434(digit_t* a);
|
||||
|
||||
// Modular division by two, c = a/2 mod p434.
|
||||
void fpdiv2_434(const digit_t* a, digit_t* c);
|
||||
|
||||
// Modular correction to reduce field element a in [0, 2*p434-1] to [0, p434-1].
|
||||
void fpcorrection434(digit_t* a);
|
||||
|
||||
// 434-bit Montgomery reduction, c = a mod p
|
||||
void rdc434_asm(digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field multiplication using Montgomery arithmetic, c = a*b*R^-1 mod p434, where R=2^768
|
||||
void fpmul434_mont(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mul434_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Field squaring using Montgomery arithmetic, c = a*b*R^-1 mod p434, where R=2^768
|
||||
void fpsqr434_mont(const digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field inversion, a = a^-1 in GF(p434)
|
||||
void fpinv434_mont(digit_t* a);
|
||||
|
||||
// Chain to compute (p434-3)/4 using Montgomery arithmetic
|
||||
void fpinv434_chain_mont(digit_t* a);
|
||||
|
||||
/************ GF(p^2) arithmetic functions *************/
|
||||
|
||||
// Copy of a GF(p434^2) element, c = a
|
||||
void fp2copy434(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Zeroing a GF(p434^2) element, a = 0
|
||||
void fp2zero434(f2elm_t a);
|
||||
|
||||
// GF(p434^2) negation, a = -a in GF(p434^2)
|
||||
void fp2neg434(f2elm_t a);
|
||||
|
||||
// GF(p434^2) addition, c = a+b in GF(p434^2)
|
||||
extern void fp2add434(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p434^2) subtraction, c = a-b in GF(p434^2)
|
||||
extern void fp2sub434(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p434^2) division by two, c = a/2 in GF(p434^2)
|
||||
void fp2div2_434(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Modular correction, a = a in GF(p434^2)
|
||||
void fp2correction434(f2elm_t a);
|
||||
|
||||
// GF(p434^2) squaring using Montgomery arithmetic, c = a^2 in GF(p434^2)
|
||||
void fp2sqr434_mont(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// GF(p434^2) multiplication using Montgomery arithmetic, c = a*b in GF(p434^2)
|
||||
void fp2mul434_mont(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p434^2) inversion using Montgomery arithmetic, a = (a0-i*a1)/(a0^2+a1^2)
|
||||
void fp2inv434_mont(f2elm_t a);
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,259 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: portable modular arithmetic for P434
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P434_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p434[NWORDS64_FIELD];
|
||||
extern const uint64_t p434p1[NWORDS64_FIELD];
|
||||
extern const uint64_t p434x2[NWORDS64_FIELD];
|
||||
extern const uint64_t p434x4[NWORDS64_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub434_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p434x2)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub434_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p434x4)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd434(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p434.
|
||||
// Inputs: a, b in [0, 2*p434-1]
|
||||
// Output: c in [0, 2*p434-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p434x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p434x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub434(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p434.
|
||||
// Inputs: a, b in [0, 2*p434-1]
|
||||
// Output: c in [0, 2*p434-1]
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p434x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg434(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p434.
|
||||
// Input/output: a in [0, 2*p434-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p434x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_434(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p434.
|
||||
// Input : a in [0, 2*p434-1]
|
||||
// Output: c in [0, 2*p434-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p434
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p434)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection434(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p434-1] to [0, p434-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p434)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p434)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void digit_x_digit(const digit_t a, const digit_t b, digit_t* c)
|
||||
{ // Digit multiplication, digit * digit -> 2-digit result
|
||||
register digit_t al, ah, bl, bh, temp;
|
||||
digit_t albl, albh, ahbl, ahbh, res1, res2, res3, carry;
|
||||
digit_t mask_low = (digit_t)(-1) >> (sizeof(digit_t)*4), mask_high = (digit_t)(-1) << (sizeof(digit_t)*4);
|
||||
|
||||
al = a & mask_low; // Low part
|
||||
ah = a >> (sizeof(digit_t) * 4); // High part
|
||||
bl = b & mask_low;
|
||||
bh = b >> (sizeof(digit_t) * 4);
|
||||
|
||||
albl = al*bl;
|
||||
albh = al*bh;
|
||||
ahbl = ah*bl;
|
||||
ahbh = ah*bh;
|
||||
c[0] = albl & mask_low; // C00
|
||||
|
||||
res1 = albl >> (sizeof(digit_t) * 4);
|
||||
res2 = ahbl & mask_low;
|
||||
res3 = albh & mask_low;
|
||||
temp = res1 + res2 + res3;
|
||||
carry = temp >> (sizeof(digit_t) * 4);
|
||||
c[0] ^= temp << (sizeof(digit_t) * 4); // C01
|
||||
|
||||
res1 = ahbl >> (sizeof(digit_t) * 4);
|
||||
res2 = albh >> (sizeof(digit_t) * 4);
|
||||
res3 = ahbh & mask_low;
|
||||
temp = res1 + res2 + res3 + carry;
|
||||
c[1] = temp & mask_low; // C10
|
||||
carry = temp & mask_high;
|
||||
c[1] ^= (ahbh & mask_high) + carry; // C11
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
unsigned int i, j;
|
||||
digit_t t = 0, u = 0, v = 0, UV[2];
|
||||
unsigned int carry = 0;
|
||||
|
||||
for (i = 0; i < nwords; i++) {
|
||||
for (j = 0; j <= i; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = nwords; i < 2*nwords-1; i++) {
|
||||
for (j = i-nwords+1; j < nwords; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
c[2*nwords-1] = v;
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Efficient Montgomery reduction using comba and exploiting the special form of the prime p434.
|
||||
// mc = ma*R^-1 mod p434x2, where R = 2^448.
|
||||
// If ma < 2^448*p434, the output mc is in the range [0, 2*p434-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
unsigned int i, j, carry, count = p434_ZERO_WORDS;
|
||||
digit_t UV[2], t = 0, u = 0, v = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
mc[i] = 0;
|
||||
}
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
for (j = 0; j < i; j++) {
|
||||
if (j < (i-p434_ZERO_WORDS+1)) {
|
||||
MUL(mc[j], ((digit_t*)p434p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = NWORDS_FIELD; i < 2*NWORDS_FIELD-1; i++) {
|
||||
if (count > 0) {
|
||||
count -= 1;
|
||||
}
|
||||
for (j = i-NWORDS_FIELD+1; j < NWORDS_FIELD; j++) {
|
||||
if (j < (NWORDS_FIELD-count)) {
|
||||
MUL(mc[j], ((digit_t*)p434p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i-NWORDS_FIELD] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
ADDC(0, v, ma[2*NWORDS_FIELD-1], carry, v);
|
||||
mc[NWORDS_FIELD-1] = v;
|
||||
}
|
||||
|
|
@ -0,0 +1,572 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: modular arithmetic optimized for x64 platforms for P503
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P503_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p503[NWORDS_FIELD];
|
||||
extern const uint64_t p503p1[NWORDS_FIELD];
|
||||
extern const uint64_t p503x2[NWORDS_FIELD];
|
||||
extern const uint64_t p503x4[NWORDS_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub503_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p503x2)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub503_p2_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub503_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p503x4)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub503_p4_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd503(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p503.
|
||||
// Inputs: a, b in [0, 2*p503-1]
|
||||
// Output: c in [0, 2*p503-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p503x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p503x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpadd503_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub503(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p503.
|
||||
// Inputs: a, b in [0, 2*p503-1]
|
||||
// Output: c in [0, 2*p503-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p503x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpsub503_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg503(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p503.
|
||||
// Input/output: a in [0, 2*p503-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p503x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_503(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p503.
|
||||
// Input : a in [0, 2*p503-1]
|
||||
// Output: c in [0, 2*p503-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p503
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p503)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection503(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p503-1] to [0, p503-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p503)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p503)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
|
||||
(void)nwords;
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
unsigned int carry = 0;
|
||||
|
||||
MULADD128(a[0], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[7], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
c[8] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[7], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
c[9] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[7], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
c[10] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[7], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
c[11] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[7], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
c[12] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[7], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
c[13] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
|
||||
MULADD128(a[7], b[7], uv, carry, uv);
|
||||
c[14] = uv[0];
|
||||
c[15] = uv[1];
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mul503_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Montgomery reduction exploiting special form of the prime.
|
||||
// mc = ma*R^-1 mod p503x2, where R = 2^512.
|
||||
// If ma < 2^512*p503, the output mc is in the range [0, 2*p503-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int carry;
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
|
||||
mc[0] = ma[0];
|
||||
mc[1] = ma[1];
|
||||
mc[2] = ma[2];
|
||||
MUL128(mc[0], ((digit_t*)p503p1)[3], uv);
|
||||
ADDC(0, uv[0], ma[3], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
mc[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p503p1)[4], uv, carry, uv);
|
||||
MULADD128(mc[1], ((digit_t*)p503p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[4], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p503p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p503p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p503p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[5], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p503p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p503p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p503p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p503p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[6], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p503p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p503p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p503p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p503p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p503p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[7], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[1], ((digit_t*)p503p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p503p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p503p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p503p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p503p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[8], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[2], ((digit_t*)p503p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p503p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p503p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p503p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p503p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[9], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[3], ((digit_t*)p503p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p503p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p503p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p503p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p503p1)[3], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[10], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[4], ((digit_t*)p503p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p503p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p503p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p503p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[11], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[5], ((digit_t*)p503p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p503p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p503p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[12], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[6], ((digit_t*)p503p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p503p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[13], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[7], ((digit_t*)p503p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[14], carry, mc[6]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
ADDC(0, uv[1], ma[15], carry, mc[7]);
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
rdc503_asm(ma, mc);
|
||||
|
||||
#endif
|
||||
}
|
||||
Разница между файлами не показана из-за своего большого размера
Загрузить разницу
|
|
@ -0,0 +1,138 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: supersingular isogeny parameters and generation of functions for P503
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "P503_api.h"
|
||||
#include "P503_internal.h"
|
||||
#include "../internal.h"
|
||||
|
||||
|
||||
// Encoding of field elements, elements over Z_order, elements over GF(p^2) and elliptic curve points:
|
||||
// --------------------------------------------------------------------------------------------------
|
||||
// Elements over GF(p) and Z_order are encoded with the least significant octet (and digit) located at the leftmost position (i.e., little endian format).
|
||||
// Elements (a+b*i) over GF(p^2), where a and b are defined over GF(p), are encoded as {a, b}, with a in the least significant position.
|
||||
// Elliptic curve points P = (x,y) are encoded as {x, y}, with x in the least significant position.
|
||||
// Internally, the number of digits used to represent all these elements is obtained by approximating the number of bits to the immediately greater multiple of 32.
|
||||
// For example, a 503-bit field element is represented with Ceil(503 / 64) = 8 64-bit digits or Ceil(503 / 32) = 16 32-bit digits.
|
||||
|
||||
//
|
||||
// Curve isogeny system "SIDHp503". Base curve: Montgomery curve By^2 = Cx^3 + Ax^2 + Cx defined over GF(p503^2), where A=6, B=1, C=1 and p503 = 2^250*3^159-1
|
||||
//
|
||||
|
||||
const uint64_t p503[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xABFFFFFFFFFFFFFF,
|
||||
0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E };
|
||||
const uint64_t p503p1[NWORDS64_FIELD] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xAC00000000000000,
|
||||
0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E };
|
||||
const uint64_t p503x2[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x57FFFFFFFFFFFFFF,
|
||||
0x2610B7B44423CF41, 0x3737ED90F6FCFB5E, 0xC08B8D7BB4EF49A0, 0x0080CDEA83023C3C };
|
||||
const uint64_t p503x4[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFC, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xAFFFFFFFFFFFFFFF,
|
||||
0x4C216F6888479E82, 0x6E6FDB21EDF9F6BC, 0x81171AF769DE9340, 0x01019BD506047879 };
|
||||
const uint64_t p503p1x64[NWORDS64_FIELD/2] = { 0xC216F6888479E82B, 0xE6FDB21EDF9F6BC4, 0x1171AF769DE93406, 0x1019BD5060478798 };
|
||||
const uint64_t p503x16p[2*NWORDS64_FIELD] = { 0x0000000000000010, 0x0000000000000000, 0x0000000000000000, 0x8000000000000000,
|
||||
0x9EF484BBBDC30BEA, 0x8C8126F090304A1D, 0xF7472844B10B65FC, 0x30F32157CFDC3C33,
|
||||
0x1463AB4329A333F7, 0xDFC933977C47D3A4, 0x338A3767F6F2520B, 0x4F8CB7565CCC13FA,
|
||||
0xDE43B73AACD2189B, 0xBCF845CAC5405FBD, 0x516D02A09E684B7A, 0x0001033A4091BB86 };
|
||||
// Order of Alice's subgroup
|
||||
const uint64_t Alice_order[NWORDS64_ORDER] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0400000000000000 };
|
||||
// Order of Bob's subgroup
|
||||
const uint64_t Bob_order[NWORDS64_ORDER] = { 0xC216F6888479E82B, 0xE6FDB21EDF9F6BC4, 0x1171AF769DE93406, 0x1019BD5060478798 };
|
||||
// Alice's generator values {XPA0 + XPA1*i, XQA0 + XQA1*i, XRA0 + XRA1*i} in GF(p503^2), expressed in Montgomery representation
|
||||
const uint64_t A_gen[6*NWORDS64_FIELD] = { 0x5D083011589AD893, 0xADFD8D2CB67D0637, 0x330C9AC34FFB6361, 0xF0D47489A2E805A2,
|
||||
0x27E2789259C6B8DC, 0x63866A2C121931B9, 0x8D4C65A7137DCF44, 0x003A183AE5967B3F, // XPA0
|
||||
0x7E3541B8C96D1519, 0xD3ADAEEC0D61A26C, 0xC0A2219CE7703DD9, 0xFF3E46658FCDBC52,
|
||||
0xD5B38DEAE6E196FF, 0x1AAC826364956D58, 0xEC9F4875B9A5F27A, 0x001B0B475AB99843, // XPA1
|
||||
0x4D83695107D03BAD, 0x221F3299005E2FCF, 0x78E6AE22F30DECF2, 0x6D982DB5111253E4,
|
||||
0x504C80A8AB4526A8, 0xEFD0C3AA210BB024, 0xCB77483501DC6FCF, 0x001052544A96BDF3, // XQA0
|
||||
0x0D74FE3402BCAE47, 0xDF5B8CDA832D8AED, 0xB86BCF06E4BD837E, 0x892A2933A0FA1F63,
|
||||
0x9F88FC67B6CCB461, 0x822926EA9DDA3AC8, 0xEAC8DDE5855425ED, 0x000618FE6DA37A80, // XQA1
|
||||
0x1D9D32D2DC877C17, 0x5517CD8F71D5B02B, 0x395AFB8F6B60C117, 0x3AE31AC85F9098C8,
|
||||
0x5F5341C198450848, 0xF8C609DBEA435C6A, 0xD832BC7EDC7BA5E4, 0x002AD98AA6968BF5, // XRA0
|
||||
0xC466CAB0F73C2E5B, 0x7B1817148FB2CF9C, 0x873E87C099E470A0, 0xBB17AC6D17A7BAC1,
|
||||
0xA146FDCD0F2E2A58, 0x88B311E9CEAB6201, 0x37604CF5C7951757, 0x0006804071C74BF9 }; // XRA1
|
||||
// Bob's generator values {XPB0, XQB0, XRB0 + XRB1*i} in GF(p503^2), expressed in Montgomery representation
|
||||
const uint64_t B_gen[6*NWORDS64_FIELD] = { 0xDF630FC5FB2468DB, 0xC30C5541C102040E, 0x3CDC9987B76511FC, 0xF54B5A09353D0CDD,
|
||||
0x3ADBA8E00703C42F, 0x8253F9303DDC95D0, 0x62D30778763ABFD7, 0x001CD00FB581CD55, // XPB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XPB1
|
||||
0x2E3457A12B429261, 0x311F94E89627DCF8, 0x5B71C98FD1DB73F6, 0x3671DB7DCFC21541,
|
||||
0xB6D1484C9FE0CF4F, 0x19CD110717356E35, 0xF4F9FB00AC9919DF, 0x0035BC124D38A70B, // XQB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XQB1
|
||||
0x2E08BB99413D2952, 0xD3021467CD088D72, 0x21017AF859752245, 0x26314ED8FFD9DE5C,
|
||||
0x4AF43C73344B6686, 0xCFA1F91149DF0993, 0xF327A95365587A89, 0x000DBF54E03D3906, // XRB0
|
||||
0x03E03FF342F5F304, 0x993D604D7B4B6E56, 0x80412F4D9280E71F, 0x0FFDC9EF990B3982,
|
||||
0xE584E64C51604931, 0x1374F42AC8B0BBD7, 0x07D5BC37DFA41A5F, 0x00396CCFD61FD34C }; // XRB1
|
||||
// Montgomery constant Montgomery_R2 = (2^512)^2 mod p503
|
||||
const uint64_t Montgomery_R2[NWORDS64_FIELD] = { 0x5289A0CF641D011F, 0x9B88257189FED2B9, 0xA3B365D58DC8F17A, 0x5BC57AB6EFF168EC,
|
||||
0x9E51998BD84D4423, 0xBF8999CBAC3B5695, 0x46E9127BCE14CDB6, 0x003F6CFCE8B81771 };
|
||||
// Value one in Montgomery representation
|
||||
const uint64_t Montgomery_one[NWORDS64_FIELD] = { 0x00000000000003F9, 0x0000000000000000, 0x0000000000000000, 0xB400000000000000,
|
||||
0x63CB1A6EA6DED2B4, 0x51689D8D667EB37D, 0x8ACD77C71AB24142, 0x0026FBAEC60F5953 };
|
||||
|
||||
|
||||
// Fixed parameters for isogeny tree computation
|
||||
const unsigned int strat_Alice[MAX_Alice-1] = {
|
||||
61, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1,
|
||||
4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1,
|
||||
1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 29, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1,
|
||||
1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 13, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2,
|
||||
1, 1, 2, 1, 1, 5, 4, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1 };
|
||||
|
||||
const unsigned int strat_Bob[MAX_Bob-1] = {
|
||||
71, 38, 21, 13, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 5, 4, 2, 1, 1, 2, 1,
|
||||
1, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 17, 9,
|
||||
5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1,
|
||||
1, 4, 2, 1, 1, 2, 1, 1, 33, 17, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1,
|
||||
2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 1, 2,
|
||||
1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1 };
|
||||
|
||||
// Setting up macro defines and including GF(p), GF(p^2), curve, isogeny and kex functions
|
||||
#define fpcopy fpcopy503
|
||||
#define fpzero fpzero503
|
||||
#define fpadd fpadd503
|
||||
#define fpsub fpsub503
|
||||
#define fpneg fpneg503
|
||||
#define fpdiv2 fpdiv2_503
|
||||
#define fpcorrection fpcorrection503
|
||||
#define fpmul_mont fpmul503_mont
|
||||
#define fpsqr_mont fpsqr503_mont
|
||||
#define fpinv_mont fpinv503_mont
|
||||
#define fpinv_chain_mont fpinv503_chain_mont
|
||||
#define fp2copy fp2copy503
|
||||
#define fp2zero fp2zero503
|
||||
#define fp2add fp2add503
|
||||
#define fp2sub fp2sub503
|
||||
#define mp_sub_p2 mp_sub503_p2
|
||||
#define mp_sub_p4 mp_sub503_p4
|
||||
#define sub_p4 mp_sub_p4
|
||||
#define fp2neg fp2neg503
|
||||
#define fp2div2 fp2div2_503
|
||||
#define fp2correction fp2correction503
|
||||
#define fp2mul_mont fp2mul503_mont
|
||||
#define fp2sqr_mont fp2sqr503_mont
|
||||
#define fp2inv_mont fp2inv503_mont
|
||||
#define fp2inv_mont_ct fp2inv503_mont_ct
|
||||
#define fp2inv_mont_bingcd fp2inv503_mont_bingcd
|
||||
#define mp_add_asm mp_add503_asm
|
||||
#define mp_subaddx2_asm mp_subadd503x2_asm
|
||||
#define mp_dblsubx2_asm mp_dblsub503x2_asm
|
||||
#define crypto_kem_keypair crypto_kem_keypair_SIKEp503
|
||||
#define crypto_kem_enc crypto_kem_enc_SIKEp503
|
||||
#define crypto_kem_dec crypto_kem_dec_SIKEp503
|
||||
#define random_mod_order_A random_mod_order_A_SIDHp503
|
||||
#define random_mod_order_B random_mod_order_B_SIDHp503
|
||||
#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp503
|
||||
#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp503
|
||||
#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp503
|
||||
#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp503
|
||||
|
||||
#include "../fpx.c"
|
||||
#include "../ec_isogeny.c"
|
||||
#include "../sidh.c"
|
||||
#include "../sike.c"
|
||||
|
|
@ -0,0 +1,112 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: API header file for P503
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P503_API_H
|
||||
#define P503_API_H
|
||||
|
||||
|
||||
/*********************** Key encapsulation mechanism API ***********************/
|
||||
|
||||
#define CRYPTO_SECRETKEYBYTES 434 // MSG_BYTES + SECRETKEY_B_BYTES + CRYPTO_PUBLICKEYBYTES bytes
|
||||
#define CRYPTO_PUBLICKEYBYTES 378
|
||||
#define CRYPTO_BYTES 24
|
||||
#define CRYPTO_CIPHERTEXTBYTES 402 // CRYPTO_PUBLICKEYBYTES + MSG_BYTES bytes
|
||||
|
||||
// Algorithm name
|
||||
#define CRYPTO_ALGNAME "SIKEp503"
|
||||
|
||||
// SIKE's key generation
|
||||
// It produces a private key sk and computes the public key pk.
|
||||
// Outputs: secret key sk (CRYPTO_SECRETKEYBYTES = 434 bytes)
|
||||
// public key pk (CRYPTO_PUBLICKEYBYTES = 378 bytes)
|
||||
int crypto_kem_keypair_SIKEp503(unsigned char *pk, unsigned char *sk);
|
||||
|
||||
// SIKE's encapsulation
|
||||
// Input: public key pk (CRYPTO_PUBLICKEYBYTES = 378 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 24 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 402 bytes)
|
||||
int crypto_kem_enc_SIKEp503(unsigned char *ct, unsigned char *ss, const unsigned char *pk);
|
||||
|
||||
// SIKE's decapsulation
|
||||
// Input: secret key sk (CRYPTO_SECRETKEYBYTES = 434 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 402 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 24 bytes)
|
||||
int crypto_kem_dec_SIKEp503(unsigned char *ss, const unsigned char *ct, const unsigned char *sk);
|
||||
|
||||
|
||||
// Encoding of keys for KEM-based isogeny system "SIKEp503" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p503) are encoded in 63 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p503^2), where a and b are defined over GF(p503), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys sk consist of the concatenation of a 24-byte random value, a value in the range [0, 2^Floor(Log(2,3^159))-1] and the public key pk. In the SIKE API,
|
||||
// private keys are encoded in 434 octets in little endian format.
|
||||
// Public keys pk consist of 3 elements in GF(p503^2). In the SIKE API, pk is encoded in 378 octets.
|
||||
// Ciphertexts ct consist of the concatenation of a public key value and a 24-byte value. In the SIKE API, ct is encoded in 378 + 24 = 402 octets.
|
||||
// Shared keys ss consist of a value of 24 octets.
|
||||
|
||||
|
||||
/*********************** Ephemeral key exchange API ***********************/
|
||||
|
||||
#define SIDH_SECRETKEYBYTES_A 32
|
||||
#define SIDH_SECRETKEYBYTES_B 32
|
||||
#define SIDH_PUBLICKEYBYTES 378
|
||||
#define SIDH_BYTES 126
|
||||
|
||||
// SECURITY NOTE: SIDH supports ephemeral Diffie-Hellman key exchange. It is NOT secure to use it with static keys.
|
||||
// See "On the Security of Supersingular Isogeny Cryptosystems", S.D. Galbraith, C. Petit, B. Shani and Y.B. Ti, in ASIACRYPT 2016, 2016.
|
||||
// Extended version available at: http://eprint.iacr.org/2016/859
|
||||
|
||||
// Generation of Alice's secret key
|
||||
// Outputs random value in [0, 2^250 - 1] to be used as Alice's private key
|
||||
void random_mod_order_A_SIDHp503(unsigned char* random_digits);
|
||||
|
||||
// Generation of Bob's secret key
|
||||
// Outputs random value in [0, 2^Floor(Log(2,3^159)) - 1] to be used as Bob's private key
|
||||
void random_mod_order_B_SIDHp503(unsigned char* random_digits);
|
||||
|
||||
// Alice's ephemeral public key generation
|
||||
// Input: a private key PrivateKeyA in the range [0, 2^250 - 1], stored in 32 bytes.
|
||||
// Output: the public key PublicKeyA consisting of 3 GF(p503^2) elements encoded in 378 bytes.
|
||||
int EphemeralKeyGeneration_A_SIDHp503(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA);
|
||||
|
||||
// Bob's ephemeral key-pair generation
|
||||
// It produces a private key PrivateKeyB and computes the public key PublicKeyB.
|
||||
// The private key is an integer in the range [0, 2^Floor(Log(2,3^159)) - 1], stored in 32 bytes.
|
||||
// The public key consists of 3 GF(p503^2) elements encoded in 378 bytes.
|
||||
int EphemeralKeyGeneration_B_SIDHp503(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB);
|
||||
|
||||
// Alice's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB
|
||||
// Inputs: Alice's PrivateKeyA is an integer in the range [0, 2^250 - 1], stored in 32 bytes.
|
||||
// Bob's PublicKeyB consists of 3 GF(p503^2) elements encoded in 378 bytes.
|
||||
// Output: a shared secret SharedSecretA that consists of one element in GF(p503^2) encoded in 126 bytes.
|
||||
int EphemeralSecretAgreement_A_SIDHp503(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA);
|
||||
|
||||
// Bob's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA
|
||||
// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,3^159)) - 1], stored in 32 bytes.
|
||||
// Alice's PublicKeyA consists of 3 GF(p503^2) elements encoded in 378 bytes.
|
||||
// Output: a shared secret SharedSecretB that consists of one element in GF(p503^2) encoded in 126 bytes.
|
||||
int EphemeralSecretAgreement_B_SIDHp503(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB);
|
||||
|
||||
|
||||
// Encoding of keys for KEX-based isogeny system "SIDHp503" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p503) are encoded in 63 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p503^2), where a and b are defined over GF(p503), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys PrivateKeyA and PrivateKeyB can have values in the range [0, 2^250-1] and [0, 2^Floor(Log(2,3^159)) - 1], resp. In the SIDH API,
|
||||
// Alice's and Bob's private keys are encoded in 32 octets in little endian format.
|
||||
// Public keys PublicKeyA and PublicKeyB consist of 3 elements in GF(p503^2). In the SIDH API, they are encoded in 378 octets.
|
||||
// Shared keys SharedSecretA and SharedSecretB consist of one element in GF(p503^2). In the SIDH API, they are encoded in 126 octets.
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,175 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: internal header file for P503
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P503_INTERNAL_H
|
||||
#define P503_INTERNAL_H
|
||||
|
||||
#include "../config.h"
|
||||
|
||||
|
||||
#if (TARGET == TARGET_AMD64) || (TARGET == TARGET_ARM64)
|
||||
#define NWORDS_FIELD 8 // Number of words of a 503-bit field element
|
||||
#define p503_ZERO_WORDS 3 // Number of "0" digits in the least significant part of p503 + 1
|
||||
#elif (TARGET == TARGET_x86)
|
||||
#define NWORDS_FIELD 16
|
||||
#define p503_ZERO_WORDS 7
|
||||
#endif
|
||||
|
||||
|
||||
// Basic constants
|
||||
|
||||
#define NBITS_FIELD 503
|
||||
#define MAXBITS_FIELD 512
|
||||
#define MAXWORDS_FIELD ((MAXBITS_FIELD+RADIX-1)/RADIX) // Max. number of words to represent field elements
|
||||
#define NWORDS64_FIELD ((NBITS_FIELD+63)/64) // Number of 64-bit words of a 503-bit field element
|
||||
#define NBITS_ORDER 256
|
||||
#define NWORDS_ORDER ((NBITS_ORDER+RADIX-1)/RADIX) // Number of words of oA and oB, where oA and oB are the subgroup orders of Alice and Bob, resp.
|
||||
#define NWORDS64_ORDER ((NBITS_ORDER+63)/64) // Number of 64-bit words of a 256-bit element
|
||||
#define MAXBITS_ORDER NBITS_ORDER
|
||||
#define ALICE 0
|
||||
#define BOB 1
|
||||
#define OALICE_BITS 250
|
||||
#define OBOB_BITS 253
|
||||
#define OBOB_EXPON 159
|
||||
#define MASK_ALICE 0x03
|
||||
#define MASK_BOB 0x0F
|
||||
#define PRIME p503
|
||||
#define PARAM_A 6
|
||||
#define PARAM_C 1
|
||||
// Fixed parameters for isogeny tree computation
|
||||
#define MAX_INT_POINTS_ALICE 7
|
||||
#define MAX_INT_POINTS_BOB 8
|
||||
#define MAX_Alice 125
|
||||
#define MAX_Bob 159
|
||||
#define MSG_BYTES 24
|
||||
#define SECRETKEY_A_BYTES ((OALICE_BITS + 7) / 8)
|
||||
#define SECRETKEY_B_BYTES ((OBOB_BITS - 1 + 7) / 8)
|
||||
#define FP2_ENCODED_BYTES 2*((NBITS_FIELD + 7) / 8)
|
||||
|
||||
|
||||
// SIDH's basic element definitions and point representations
|
||||
|
||||
typedef digit_t felm_t[NWORDS_FIELD]; // Datatype for representing 503-bit field elements (512-bit max.)
|
||||
typedef digit_t dfelm_t[2*NWORDS_FIELD]; // Datatype for representing double-precision 2x503-bit field elements (2x512-bit max.)
|
||||
typedef felm_t f2elm_t[2]; // Datatype for representing quadratic extension field elements GF(p503^2)
|
||||
|
||||
typedef struct { f2elm_t X; f2elm_t Z; } point_proj; // Point representation in projective XZ Montgomery coordinates.
|
||||
typedef point_proj point_proj_t[1];
|
||||
|
||||
#ifdef COMPRESS
|
||||
typedef struct { f2elm_t X; f2elm_t Y; f2elm_t Z; } point_full_proj; // Point representation in full projective XYZ Montgomery coordinates
|
||||
typedef point_full_proj point_full_proj_t[1];
|
||||
|
||||
typedef struct { f2elm_t x; f2elm_t y; } point_affine; // Point representation in affine coordinates.
|
||||
typedef point_affine point_t[1];
|
||||
|
||||
typedef f2elm_t publickey_t[3];
|
||||
#endif
|
||||
|
||||
|
||||
|
||||
/**************** Function prototypes ****************/
|
||||
/************* Multiprecision functions **************/
|
||||
|
||||
// 503-bit multiprecision addition, c = a+b
|
||||
void mp_add503(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_add503_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 503-bit multiprecision subtraction, c = a-b+2p or c = a-b+4p
|
||||
extern void mp_sub503_p2(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void mp_sub503_p4(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub503_p2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub503_p4_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 2x503-bit multiprecision subtraction followed by addition with p503*2^512, c = a-b+(p503*2^512) if a-b < 0, otherwise c=a-b
|
||||
void mp_subaddx2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_subadd503x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Double 2x503-bit multiprecision subtraction, c = c-a-b, where c > a and c > b
|
||||
void mp_dblsub503x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
/************ Field arithmetic functions *************/
|
||||
|
||||
// Copy of a field element, c = a
|
||||
void fpcopy503(const digit_t* a, digit_t* c);
|
||||
|
||||
// Zeroing a field element, a = 0
|
||||
void fpzero503(digit_t* a);
|
||||
|
||||
// Non constant-time comparison of two field elements. If a = b return TRUE, otherwise, return FALSE
|
||||
bool fpequal503_non_constant_time(const digit_t* a, const digit_t* b);
|
||||
|
||||
// Modular addition, c = a+b mod p503
|
||||
extern void fpadd503(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpadd503_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular subtraction, c = a-b mod p503
|
||||
extern void fpsub503(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpsub503_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular negation, a = -a mod p503
|
||||
extern void fpneg503(digit_t* a);
|
||||
|
||||
// Modular division by two, c = a/2 mod p503.
|
||||
void fpdiv2_503(const digit_t* a, digit_t* c);
|
||||
|
||||
// Modular correction to reduce field element a in [0, 2*p503-1] to [0, p503-1].
|
||||
void fpcorrection503(digit_t* a);
|
||||
|
||||
// 503-bit Montgomery reduction, c = a mod p
|
||||
void rdc503_asm(digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field multiplication using Montgomery arithmetic, c = a*b*R^-1 mod p503, where R=2^768
|
||||
void fpmul503_mont(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mul503_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Field squaring using Montgomery arithmetic, c = a*b*R^-1 mod p503, where R=2^768
|
||||
void fpsqr503_mont(const digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field inversion, a = a^-1 in GF(p503)
|
||||
void fpinv503_mont(digit_t* a);
|
||||
|
||||
// Chain to compute (p503-3)/4 using Montgomery arithmetic
|
||||
void fpinv503_chain_mont(digit_t* a);
|
||||
|
||||
/************ GF(p^2) arithmetic functions *************/
|
||||
|
||||
// Copy of a GF(p503^2) element, c = a
|
||||
void fp2copy503(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Zeroing a GF(p503^2) element, a = 0
|
||||
void fp2zero503(f2elm_t a);
|
||||
|
||||
// GF(p503^2) negation, a = -a in GF(p503^2)
|
||||
void fp2neg503(f2elm_t a);
|
||||
|
||||
// GF(p503^2) addition, c = a+b in GF(p503^2)
|
||||
extern void fp2add503(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p503^2) subtraction, c = a-b in GF(p503^2)
|
||||
extern void fp2sub503(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p503^2) division by two, c = a/2 in GF(p503^2)
|
||||
void fp2div2_503(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Modular correction, a = a in GF(p503^2)
|
||||
void fp2correction503(f2elm_t a);
|
||||
|
||||
// GF(p503^2) squaring using Montgomery arithmetic, c = a^2 in GF(p503^2)
|
||||
void fp2sqr503_mont(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// GF(p503^2) multiplication using Montgomery arithmetic, c = a*b in GF(p503^2)
|
||||
void fp2mul503_mont(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p503^2) inversion using Montgomery arithmetic, a = (a0-i*a1)/(a0^2+a1^2)
|
||||
void fp2inv503_mont(f2elm_t a);
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,259 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: portable modular arithmetic for P503
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P503_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p503[NWORDS64_FIELD];
|
||||
extern const uint64_t p503p1[NWORDS64_FIELD];
|
||||
extern const uint64_t p503x2[NWORDS64_FIELD];
|
||||
extern const uint64_t p503x4[NWORDS64_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub503_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p503x2)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub503_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p503x4)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd503(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p503.
|
||||
// Inputs: a, b in [0, 2*p503-1]
|
||||
// Output: c in [0, 2*p503-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p503x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p503x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub503(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p503.
|
||||
// Inputs: a, b in [0, 2*p503-1]
|
||||
// Output: c in [0, 2*p503-1]
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p503x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg503(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p503.
|
||||
// Input/output: a in [0, 2*p503-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p503x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_503(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p503.
|
||||
// Input : a in [0, 2*p503-1]
|
||||
// Output: c in [0, 2*p503-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p503
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p503)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection503(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p503-1] to [0, p503-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p503)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p503)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void digit_x_digit(const digit_t a, const digit_t b, digit_t* c)
|
||||
{ // Digit multiplication, digit * digit -> 2-digit result
|
||||
register digit_t al, ah, bl, bh, temp;
|
||||
digit_t albl, albh, ahbl, ahbh, res1, res2, res3, carry;
|
||||
digit_t mask_low = (digit_t)(-1) >> (sizeof(digit_t)*4), mask_high = (digit_t)(-1) << (sizeof(digit_t)*4);
|
||||
|
||||
al = a & mask_low; // Low part
|
||||
ah = a >> (sizeof(digit_t) * 4); // High part
|
||||
bl = b & mask_low;
|
||||
bh = b >> (sizeof(digit_t) * 4);
|
||||
|
||||
albl = al*bl;
|
||||
albh = al*bh;
|
||||
ahbl = ah*bl;
|
||||
ahbh = ah*bh;
|
||||
c[0] = albl & mask_low; // C00
|
||||
|
||||
res1 = albl >> (sizeof(digit_t) * 4);
|
||||
res2 = ahbl & mask_low;
|
||||
res3 = albh & mask_low;
|
||||
temp = res1 + res2 + res3;
|
||||
carry = temp >> (sizeof(digit_t) * 4);
|
||||
c[0] ^= temp << (sizeof(digit_t) * 4); // C01
|
||||
|
||||
res1 = ahbl >> (sizeof(digit_t) * 4);
|
||||
res2 = albh >> (sizeof(digit_t) * 4);
|
||||
res3 = ahbh & mask_low;
|
||||
temp = res1 + res2 + res3 + carry;
|
||||
c[1] = temp & mask_low; // C10
|
||||
carry = temp & mask_high;
|
||||
c[1] ^= (ahbh & mask_high) + carry; // C11
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
unsigned int i, j;
|
||||
digit_t t = 0, u = 0, v = 0, UV[2];
|
||||
unsigned int carry = 0;
|
||||
|
||||
for (i = 0; i < nwords; i++) {
|
||||
for (j = 0; j <= i; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = nwords; i < 2*nwords-1; i++) {
|
||||
for (j = i-nwords+1; j < nwords; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
c[2*nwords-1] = v;
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Efficient Montgomery reduction using comba and exploiting the special form of the prime p503.
|
||||
// mc = ma*R^-1 mod p503x2, where R = 2^512.
|
||||
// If ma < 2^512*p503, the output mc is in the range [0, 2*p503-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
unsigned int i, j, carry, count = p503_ZERO_WORDS;
|
||||
digit_t UV[2], t = 0, u = 0, v = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
mc[i] = 0;
|
||||
}
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
for (j = 0; j < i; j++) {
|
||||
if (j < (i-p503_ZERO_WORDS+1)) {
|
||||
MUL(mc[j], ((digit_t*)p503p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = NWORDS_FIELD; i < 2*NWORDS_FIELD-1; i++) {
|
||||
if (count > 0) {
|
||||
count -= 1;
|
||||
}
|
||||
for (j = i-NWORDS_FIELD+1; j < NWORDS_FIELD; j++) {
|
||||
if (j < (NWORDS_FIELD-count)) {
|
||||
MUL(mc[j], ((digit_t*)p503p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i-NWORDS_FIELD] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
ADDC(0, v, ma[2*NWORDS_FIELD-1], carry, v);
|
||||
mc[NWORDS_FIELD-1] = v;
|
||||
}
|
||||
|
|
@ -0,0 +1,634 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: modular arithmetic optimized for x64 platforms for P546
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P546_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p546[NWORDS_FIELD];
|
||||
extern const uint64_t p546p1[NWORDS_FIELD];
|
||||
extern const uint64_t p546x2[NWORDS_FIELD];
|
||||
extern const uint64_t p546x4[NWORDS_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub546_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p546x2)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub546_p2_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub546_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p546x4)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub546_p4_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd546(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p546.
|
||||
// Inputs: a, b in [0, 2*p546-1]
|
||||
// Output: c in [0, 2*p546-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p546x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p546x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpadd546_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub546(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p546.
|
||||
// Inputs: a, b in [0, 2*p546-1]
|
||||
// Output: c in [0, 2*p546-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p546x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpsub546_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg546(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p546.
|
||||
// Input/output: a in [0, 2*p546-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p546x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_546(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p546.
|
||||
// Input : a in [0, 2*p546-1]
|
||||
// Output: c in [0, 2*p546-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p546
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p546)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection546(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p546-1] to [0, p546-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p546)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p546)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
|
||||
(void)nwords;
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
unsigned int carry = 0;
|
||||
|
||||
MULADD128(a[0], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[8] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[8], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
c[9] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[8], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
c[10] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[8], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
c[11] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[8], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
c[12] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[8], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
c[13] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[8], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
c[14] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[8], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
c[15] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
|
||||
MULADD128(a[8], b[8], uv, carry, uv);
|
||||
c[16] = uv[0];
|
||||
c[17] = uv[1];
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mul546_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Montgomery reduction exploiting special form of the prime.
|
||||
// mc = ma*R^-1 mod p546x2, where R = 2^576.
|
||||
// If ma < 2^576*p546, the output mc is in the range [0, 2*p546-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int carry;
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
|
||||
mc[0] = ma[0];
|
||||
mc[1] = ma[1];
|
||||
mc[2] = ma[2];
|
||||
mc[3] = ma[3];
|
||||
MUL128(mc[0], ((digit_t*)p546p1)[4], uv);
|
||||
ADDC(0, uv[0], ma[4], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
mc[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p546p1)[5], uv, carry, uv);
|
||||
MULADD128(mc[1], ((digit_t*)p546p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[5], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p546p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p546p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p546p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[6], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p546p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p546p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p546p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p546p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[7], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p546p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p546p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p546p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p546p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p546p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[8], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[8] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[1], ((digit_t*)p546p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p546p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p546p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p546p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p546p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[9], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[2], ((digit_t*)p546p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p546p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p546p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p546p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p546p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[10], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[3], ((digit_t*)p546p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p546p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p546p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p546p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p546p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[11], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[4], ((digit_t*)p546p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p546p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p546p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p546p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p546p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[12], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[5], ((digit_t*)p546p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p546p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p546p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p546p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[13], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[6], ((digit_t*)p546p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p546p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p546p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[14], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[7], ((digit_t*)p546p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p546p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[15], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[8], ((digit_t*)p546p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[16], carry, mc[7]);
|
||||
ADDC(carry, uv[1], ma[17], carry, mc[8]);
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
rdc546_asm(ma, mc);
|
||||
|
||||
#endif
|
||||
}
|
||||
Разница между файлами не показана из-за своего большого размера
Загрузить разницу
|
|
@ -0,0 +1,135 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: supersingular isogeny parameters and generation of functions for P546
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "P546_api.h"
|
||||
#include "P546_internal.h"
|
||||
#include "../internal.h"
|
||||
|
||||
|
||||
// Encoding of field elements, elements over Z_order, elements over GF(p^2) and elliptic curve points:
|
||||
// --------------------------------------------------------------------------------------------------
|
||||
// Elements over GF(p) and Z_order are encoded with the least significant octet (and digit) located at the leftmost position (i.e., little endian format).
|
||||
// Elements (a+b*i) over GF(p^2), where a and b are defined over GF(p), are encoded as {a, b}, with a in the least significant position.
|
||||
// Elliptic curve points P = (x,y) are encoded as {x, y}, with x in the least significant position.
|
||||
// Internally, the number of digits used to represent all these elements is obtained by approximating the number of bits to the immediately greater multiple of 32.
|
||||
// For example, a 546-bit field element is represented with Ceil(546 / 64) = 9 64-bit digits or Ceil(546 / 32) = 18 32-bit digits.
|
||||
|
||||
//
|
||||
// Curve isogeny system "SIDHp546". Base curve: Montgomery curve By^2 = Cx^3 + Ax^2 + Cx defined over GF(p546^2), where A=6, B=1, C=1 and p546 = 2^273*3^172-1
|
||||
//
|
||||
|
||||
const uint64_t p546[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xC1CCF59098E1FFFF,
|
||||
0x91CA3591A0810F4F, 0xC3A747738CBAAD7D, 0x3E568459654D5F6B, 0x000000030F5EBA42 };
|
||||
const uint64_t p546p1[NWORDS64_FIELD] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xC1CCF59098E20000,
|
||||
0x91CA3591A0810F4F, 0xC3A747738CBAAD7D, 0x3E568459654D5F6B, 0x000000030F5EBA42 };
|
||||
const uint64_t p546x2[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x8399EB2131C3FFFF,
|
||||
0x23946B2341021E9F, 0x874E8EE719755AFB, 0x7CAD08B2CA9ABED7, 0x000000061EBD7484 };
|
||||
const uint64_t p546x4[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFC, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x0733D6426387FFFF,
|
||||
0x4728D64682043D3F, 0x0E9D1DCE32EAB5F6, 0xF95A116595357DAF, 0x0000000C3D7AE908 };
|
||||
// Order of Alice's subgroup
|
||||
const uint64_t Alice_order[NWORDS64_ORDER] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000020000 };
|
||||
// Order of Bob's subgroup
|
||||
const uint64_t Bob_order[NWORDS64_ORDER] = { 0x87A7E0E67AC84C71, 0x56BEC8E51AC8D040, 0xAFB5E1D3A3B9C65D, 0x5D211F2B422CB2A6, 0x00000000000187AF };
|
||||
// Alice's generator values {XPA0 + XPA1*i, XQA0 + XQA1*i, XRA0 + XRA1*i} in GF(p546^2), expressed in Montgomery representation
|
||||
const uint64_t A_gen[6*NWORDS64_FIELD] = { 0x8BF8B5CDA3529A11, 0x920F7AF8D8EDA1CE, 0x6A4FD6F4E65D2601, 0xAA5FDD88E6C8C053, 0x2DDFECC4564DD092,
|
||||
0xB5AE8E8B63CDD2EB, 0xF5530B1581D37EFC, 0xBB69799BE0974397, 0x000000029E924174, // XPA0
|
||||
0x02BAA3F5AA08FBA0, 0xDF5E66F9718B1DB3, 0x7AAD305C4C16B9B5, 0xEFC538F7C899EC44, 0xB2B7A11B88589305,
|
||||
0xF4C2FE11D652F55A, 0x45F5A4010B37F36F, 0x68C0BE35B4414691, 0x00000002974A76B9, // XPA1
|
||||
0x6655849EE4AD62B0, 0xA7B09BDA24F18E3D, 0xD9DC9DF1EFE6D4E3, 0x5618AE214D22122F, 0x35CE7CD8878AB07,
|
||||
0xDFBE3687D874F305, 0x0FFAC636361A0289, 0x732304C3E314E9F3, 0x00000002D4829F4D, // XQA0
|
||||
0xD433C9386F41F07B, 0x591D74E6B6E16886, 0x1E91924E4D82BEA1, 0xE9ED0654FE5D746F, 0x95029EF76C0961D9,
|
||||
0x9C5798078846CCA8, 0xB8AD7EC5421DCE49, 0xEBEF3DD3098146F8, 0x000000010E9A2BCA, // XQA1
|
||||
0xC218DF11E1FCA67A, 0x8C622C3530976AAF, 0xC5A558DA88A028C1, 0x5B0E218835EB3EEA, 0x63B412D6B77F6E5F,
|
||||
0x44265EEA17A1F58C, 0xD7A6BD5FE291AA13, 0xC0918F65ED8D3D23, 0x000000005562DBCD, // XRA0
|
||||
0x071F4177BDD2E021, 0xDC8F3873504C93E7, 0x77038B491A006DB7, 0x9E205A8C15B8F717, 0x701734570E79CC07,
|
||||
0x0790455A85462B3D, 0x19AC9F7FC32A9F20, 0x04B599768492F2D5, 0x0000000248379BC7 }; // XRA1
|
||||
// Bob's generator values {XPB0, XQB0, XRB0 + XRB1*i} in GF(p546^2), expressed in Montgomery representation
|
||||
const uint64_t B_gen[6*NWORDS64_FIELD] = { 0xC60DC8B9DD8A126C, 0x2841B16BD9C550AB, 0x33EB13E27326D027, 0xB4E345D7318893D7, 0x4F7BD19633EAA269,
|
||||
0xA93049DB038741F4, 0x93222D9F331C2848, 0x15FFBA19339361F0, 0x0000000089E90060, // XPB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XPB1
|
||||
0xA07EEF3334ACF340, 0x417F1E66A839DFCB, 0x45C32C88DAA25A10, 0x563B27FA6991C6BF, 0x4BE0CC5C10D513A9,
|
||||
0xE4E1756C009BD03E, 0xAFDFBF640F2717AC, 0xDC5EE9B702D8E56C, 0x0000000182A09EB0, // XQB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XQB1
|
||||
0x74937ACDD796D6EE, 0x7C5E906509CE108B, 0xDA57EBEF8BA73940, 0x1E5CB85A8E1C9A4C, 0xD4EBE9C3A955BB62,
|
||||
0xBA4C02A05B39742F, 0x21A4B5BCACC33156, 0xE96E8BD54B98A20C, 0x0000000104B99E73, // XRB0
|
||||
0xEEFADB5C4965D7A8, 0xE653CE9D2DB5CD75, 0xB511FF5416DEAB7C, 0xA5D5B131D1112DEF, 0x72D33ED20BB3EB46,
|
||||
0x96809017849D85DF, 0x00BA691C5F526CFF, 0x9B384D1CF1873823, 0x0000000152691238 }; // XRB1
|
||||
// Montgomery constant Montgomery_R2 = (2^576)^2 mod p546
|
||||
const uint64_t Montgomery_R2[NWORDS64_FIELD] = { 0x52EB0249395B3348, 0x984F8851AEFDB3F3, 0x913744158E52803C, 0x1EC818C9E0CA0DA3, 0x4C2396C7E7350E87,
|
||||
0x75D4E9F73AC13B39, 0x1640A26835D93C44, 0x5D441830B61AD042, 0x00000001357E298F };
|
||||
// Value one in Montgomery representation
|
||||
const uint64_t Montgomery_one[NWORDS64_FIELD] = { 0x0000000053A8B821, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xAB9ED029DADE0000,
|
||||
0x7FD34034A42F114D, 0x319FDC331E9125F5, 0xF1361EF3C5499C8A, 0x00000001393B6AF7 };
|
||||
|
||||
|
||||
// Fixed parameters for isogeny tree computation
|
||||
const unsigned int strat_Alice[MAX_Alice-1] = {
|
||||
65, 33, 17, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4,
|
||||
2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2,
|
||||
1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 32, 16, 8, 4, 2, 1,
|
||||
1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1,
|
||||
16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1,
|
||||
1, 2, 1, 1 };
|
||||
|
||||
const unsigned int strat_Bob[MAX_Bob-1] = {
|
||||
71, 43, 27, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1,
|
||||
1, 3, 2, 1, 1, 1, 1, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1,
|
||||
1, 1, 2, 1, 1, 1, 17, 11, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 4, 3, 2, 1, 1,
|
||||
1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 33, 17, 9, 5, 3, 2,
|
||||
1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1,
|
||||
1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1,
|
||||
1, 4, 2, 1, 1, 2, 1, 1 };
|
||||
|
||||
// Setting up macro defines and including GF(p), GF(p^2), curve, isogeny and kex functions
|
||||
#define fpcopy fpcopy546
|
||||
#define fpzero fpzero546
|
||||
#define fpadd fpadd546
|
||||
#define fpsub fpsub546
|
||||
#define fpneg fpneg546
|
||||
#define fpdiv2 fpdiv2_546
|
||||
#define fpcorrection fpcorrection546
|
||||
#define fpmul_mont fpmul546_mont
|
||||
#define fpsqr_mont fpsqr546_mont
|
||||
#define fpinv_mont fpinv546_mont
|
||||
#define fpinv_chain_mont fpinv546_chain_mont
|
||||
#define fp2copy fp2copy546
|
||||
#define fp2zero fp2zero546
|
||||
#define fp2add fp2add546
|
||||
#define fp2sub fp2sub546
|
||||
#define mp_sub_p2 mp_sub546_p2
|
||||
#define mp_sub_p4 mp_sub546_p4
|
||||
#define sub_p4 mp_sub_p4
|
||||
#define fp2neg fp2neg546
|
||||
#define fp2div2 fp2div2_546
|
||||
#define fp2correction fp2correction546
|
||||
#define fp2mul_mont fp2mul546_mont
|
||||
#define fp2sqr_mont fp2sqr546_mont
|
||||
#define fp2inv_mont fp2inv546_mont
|
||||
#define fp2inv_mont_ct fp2inv546_mont_ct
|
||||
#define fp2inv_mont_bingcd fp2inv546_mont_bingcd
|
||||
#define mp_add_asm mp_add546_asm
|
||||
#define mp_subaddx2_asm mp_subadd546x2_asm
|
||||
#define mp_dblsubx2_asm mp_dblsub546x2_asm
|
||||
#define crypto_kem_keypair crypto_kem_keypair_SIKEp546
|
||||
#define crypto_kem_enc crypto_kem_enc_SIKEp546
|
||||
#define crypto_kem_dec crypto_kem_dec_SIKEp546
|
||||
#define random_mod_order_A random_mod_order_A_SIDHp546
|
||||
#define random_mod_order_B random_mod_order_B_SIDHp546
|
||||
#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp546
|
||||
#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp546
|
||||
#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp546
|
||||
#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp546
|
||||
|
||||
#include "../fpx.c"
|
||||
#include "../ec_isogeny.c"
|
||||
#include "../sidh.c"
|
||||
#include "../sike.c"
|
||||
|
|
@ -0,0 +1,112 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: API header file for P546
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P546_API_H
|
||||
#define P546_API_H
|
||||
|
||||
|
||||
/*********************** Key encapsulation mechanism API ***********************/
|
||||
|
||||
#define CRYPTO_SECRETKEYBYTES 472 // MSG_BYTES + SECRETKEY_B_BYTES + CRYPTO_PUBLICKEYBYTES bytes
|
||||
#define CRYPTO_PUBLICKEYBYTES 414
|
||||
#define CRYPTO_BYTES 24
|
||||
#define CRYPTO_CIPHERTEXTBYTES 438 // CRYPTO_PUBLICKEYBYTES + MSG_BYTES bytes
|
||||
|
||||
// Algorithm name
|
||||
#define CRYPTO_ALGNAME "SIKEp546"
|
||||
|
||||
// SIKE's key generation
|
||||
// It produces a private key sk and computes the public key pk.
|
||||
// Outputs: secret key sk (CRYPTO_SECRETKEYBYTES = 472 bytes)
|
||||
// public key pk (CRYPTO_PUBLICKEYBYTES = 414 bytes)
|
||||
int crypto_kem_keypair_SIKEp546(unsigned char *pk, unsigned char *sk);
|
||||
|
||||
// SIKE's encapsulation
|
||||
// Input: public key pk (CRYPTO_PUBLICKEYBYTES = 414 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 24 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 438 bytes)
|
||||
int crypto_kem_enc_SIKEp546(unsigned char *ct, unsigned char *ss, const unsigned char *pk);
|
||||
|
||||
// SIKE's decapsulation
|
||||
// Input: secret key sk (CRYPTO_SECRETKEYBYTES = 472 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 438 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 24 bytes)
|
||||
int crypto_kem_dec_SIKEp546(unsigned char *ss, const unsigned char *ct, const unsigned char *sk);
|
||||
|
||||
|
||||
// Encoding of keys for KEM-based isogeny system "SIKEp546" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p546) are encoded in 63 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p546^2), where a and b are defined over GF(p546), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys sk consist of the concatenation of a 24-byte random value, a value in the range [0, 2^Floor(Log(2,3^172))-1] and the public key pk. In the SIKE API,
|
||||
// private keys are encoded in 472 octets in little endian format.
|
||||
// Public keys pk consist of 3 elements in GF(p546^2). In the SIKE API, pk is encoded in 414 octets.
|
||||
// Ciphertexts ct consist of the concatenation of a public key value and a 24-byte value. In the SIKE API, ct is encoded in 414 + 24 = 438 octets.
|
||||
// Shared keys ss consist of a value of 24 octets.
|
||||
|
||||
|
||||
/*********************** Ephemeral key exchange API ***********************/
|
||||
|
||||
#define SIDH_SECRETKEYBYTES_A 35
|
||||
#define SIDH_SECRETKEYBYTES_B 34
|
||||
#define SIDH_PUBLICKEYBYTES 414
|
||||
#define SIDH_BYTES 138
|
||||
|
||||
// SECURITY NOTE: SIDH supports ephemeral Diffie-Hellman key exchange. It is NOT secure to use it with static keys.
|
||||
// See "On the Security of Supersingular Isogeny Cryptosystems", S.D. Galbraith, C. Petit, B. Shani and Y.B. Ti, in ASIACRYPT 2016, 2016.
|
||||
// Extended version available at: http://eprint.iacr.org/2016/859
|
||||
|
||||
// Generation of Alice's secret key
|
||||
// Outputs random value in [0, 2^273 - 1] to be used as Alice's private key
|
||||
void random_mod_order_A_SIDHp546(unsigned char* random_digits);
|
||||
|
||||
// Generation of Bob's secret key
|
||||
// Outputs random value in [0, 2^Floor(Log(2,3^172)) - 1] to be used as Bob's private key
|
||||
void random_mod_order_B_SIDHp546(unsigned char* random_digits);
|
||||
|
||||
// Alice's ephemeral public key generation
|
||||
// Input: a private key PrivateKeyA in the range [0, 2^273 - 1], stored in 35 bytes.
|
||||
// Output: the public key PublicKeyA consisting of 3 GF(p546^2) elements encoded in 414 bytes.
|
||||
int EphemeralKeyGeneration_A_SIDHp546(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA);
|
||||
|
||||
// Bob's ephemeral key-pair generation
|
||||
// It produces a private key PrivateKeyB and computes the public key PublicKeyB.
|
||||
// The private key is an integer in the range [0, 2^Floor(Log(2,3^172)) - 1], stored in 34 bytes.
|
||||
// The public key consists of 3 GF(p546^2) elements encoded in 414 bytes.
|
||||
int EphemeralKeyGeneration_B_SIDHp546(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB);
|
||||
|
||||
// Alice's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB
|
||||
// Inputs: Alice's PrivateKeyA is an integer in the range [0, 2^273 - 1], stored in 35 bytes.
|
||||
// Bob's PublicKeyB consists of 3 GF(p546^2) elements encoded in 414 bytes.
|
||||
// Output: a shared secret SharedSecretA that consists of one element in GF(p546^2) encoded in 138 bytes.
|
||||
int EphemeralSecretAgreement_A_SIDHp546(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA);
|
||||
|
||||
// Bob's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA
|
||||
// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,3^172)) - 1], stored in 34 bytes.
|
||||
// Alice's PublicKeyA consists of 3 GF(p546^2) elements encoded in 414 bytes.
|
||||
// Output: a shared secret SharedSecretB that consists of one element in GF(p546^2) encoded in 138 bytes.
|
||||
int EphemeralSecretAgreement_B_SIDHp546(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB);
|
||||
|
||||
|
||||
// Encoding of keys for KEX-based isogeny system "SIDHp546" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p546) are encoded in 63 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p546^2), where a and b are defined over GF(p546), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys PrivateKeyA and PrivateKeyB can have values in the range [0, 2^273-1] and [0, 2^Floor(Log(2,3^172)) - 1], resp. In the SIDH API,
|
||||
// Alice's and Bob's private keys are encoded in 35 and 34 octets, resp., in little endian format.
|
||||
// Public keys PublicKeyA and PublicKeyB consist of 3 elements in GF(p546^2). In the SIDH API, they are encoded in 414 octets.
|
||||
// Shared keys SharedSecretA and SharedSecretB consist of one element in GF(p546^2). In the SIDH API, they are encoded in 138 octets.
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,175 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: internal header file for P546
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P546_INTERNAL_H
|
||||
#define P546_INTERNAL_H
|
||||
|
||||
#include "../config.h"
|
||||
|
||||
|
||||
#if (TARGET == TARGET_AMD64) || (TARGET == TARGET_ARM64)
|
||||
#define NWORDS_FIELD 9 // Number of words of a 546-bit field element
|
||||
#define p546_ZERO_WORDS 4 // Number of "0" digits in the least significant part of p546 + 1
|
||||
#elif (TARGET == TARGET_x86)
|
||||
#define NWORDS_FIELD 18
|
||||
#define p546_ZERO_WORDS 8
|
||||
#endif
|
||||
|
||||
|
||||
// Basic constants
|
||||
|
||||
#define NBITS_FIELD 546
|
||||
#define MAXBITS_FIELD 576
|
||||
#define MAXWORDS_FIELD ((MAXBITS_FIELD+RADIX-1)/RADIX) // Max. number of words to represent field elements
|
||||
#define NWORDS64_FIELD ((NBITS_FIELD+63)/64) // Number of 64-bit words of a 546-bit field element
|
||||
#define NBITS_ORDER 320
|
||||
#define NWORDS_ORDER ((NBITS_ORDER+RADIX-1)/RADIX) // Number of words of oA and oB, where oA and oB are the subgroup orders of Alice and Bob, resp.
|
||||
#define NWORDS64_ORDER ((NBITS_ORDER+63)/64) // Number of 64-bit words of a 256-bit element
|
||||
#define MAXBITS_ORDER NBITS_ORDER
|
||||
#define ALICE 0
|
||||
#define BOB 1
|
||||
#define OALICE_BITS 273
|
||||
#define OBOB_BITS 273
|
||||
#define OBOB_EXPON 172
|
||||
#define MASK_ALICE 0x01
|
||||
#define MASK_BOB 0xFF
|
||||
#define PRIME p546
|
||||
#define PARAM_A 6
|
||||
#define PARAM_C 1
|
||||
// Fixed parameters for isogeny tree computation
|
||||
#define MAX_INT_POINTS_ALICE 8
|
||||
#define MAX_INT_POINTS_BOB 8
|
||||
#define MAX_Alice 136
|
||||
#define MAX_Bob 172
|
||||
#define MSG_BYTES 24
|
||||
#define SECRETKEY_A_BYTES ((OALICE_BITS + 7) / 8)
|
||||
#define SECRETKEY_B_BYTES ((OBOB_BITS - 1 + 7) / 8)
|
||||
#define FP2_ENCODED_BYTES 2*((NBITS_FIELD + 7) / 8)
|
||||
|
||||
|
||||
// SIDH's basic element definitions and point representations
|
||||
|
||||
typedef digit_t felm_t[NWORDS_FIELD]; // Datatype for representing 546-bit field elements (576-bit max.)
|
||||
typedef digit_t dfelm_t[2*NWORDS_FIELD]; // Datatype for representing double-precision 2x546-bit field elements (2x576-bit max.)
|
||||
typedef felm_t f2elm_t[2]; // Datatype for representing quadratic extension field elements GF(p546^2)
|
||||
|
||||
typedef struct { f2elm_t X; f2elm_t Z; } point_proj; // Point representation in projective XZ Montgomery coordinates.
|
||||
typedef point_proj point_proj_t[1];
|
||||
|
||||
#ifdef COMPRESS
|
||||
typedef struct { f2elm_t X; f2elm_t Y; f2elm_t Z; } point_full_proj; // Point representation in full projective XYZ Montgomery coordinates
|
||||
typedef point_full_proj point_full_proj_t[1];
|
||||
|
||||
typedef struct { f2elm_t x; f2elm_t y; } point_affine; // Point representation in affine coordinates.
|
||||
typedef point_affine point_t[1];
|
||||
|
||||
typedef f2elm_t publickey_t[3];
|
||||
#endif
|
||||
|
||||
|
||||
|
||||
/**************** Function prototypes ****************/
|
||||
/************* Multiprecision functions **************/
|
||||
|
||||
// 546-bit multiprecision addition, c = a+b
|
||||
void mp_add546(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_add546_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 546-bit multiprecision subtraction, c = a-b+2p or c = a-b+4p
|
||||
extern void mp_sub546_p2(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void mp_sub546_p4(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub546_p2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub546_p4_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 2x546-bit multiprecision subtraction followed by addition with p546*2^576, c = a-b+(p546*2^576) if a-b < 0, otherwise c=a-b
|
||||
void mp_subaddx2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_subadd546x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Double 2x546-bit multiprecision subtraction, c = c-a-b, where c > a and c > b
|
||||
void mp_dblsub546x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
/************ Field arithmetic functions *************/
|
||||
|
||||
// Copy of a field element, c = a
|
||||
void fpcopy546(const digit_t* a, digit_t* c);
|
||||
|
||||
// Zeroing a field element, a = 0
|
||||
void fpzero546(digit_t* a);
|
||||
|
||||
// Non constant-time comparison of two field elements. If a = b return TRUE, otherwise, return FALSE
|
||||
bool fpequal546_non_constant_time(const digit_t* a, const digit_t* b);
|
||||
|
||||
// Modular addition, c = a+b mod p546
|
||||
extern void fpadd546(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpadd546_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular subtraction, c = a-b mod p546
|
||||
extern void fpsub546(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpsub546_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular negation, a = -a mod p546
|
||||
extern void fpneg546(digit_t* a);
|
||||
|
||||
// Modular division by two, c = a/2 mod p546.
|
||||
void fpdiv2_546(const digit_t* a, digit_t* c);
|
||||
|
||||
// Modular correction to reduce field element a in [0, 2*p546-1] to [0, p546-1].
|
||||
void fpcorrection546(digit_t* a);
|
||||
|
||||
// 546-bit Montgomery reduction, c = a mod p
|
||||
void rdc546_asm(digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field multiplication using Montgomery arithmetic, c = a*b*R^-1 mod p546, where R=2^768
|
||||
void fpmul546_mont(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mul546_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Field squaring using Montgomery arithmetic, c = a*b*R^-1 mod p546, where R=2^768
|
||||
void fpsqr546_mont(const digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field inversion, a = a^-1 in GF(p546)
|
||||
void fpinv546_mont(digit_t* a);
|
||||
|
||||
// Chain to compute (p546-3)/4 using Montgomery arithmetic
|
||||
void fpinv546_chain_mont(digit_t* a);
|
||||
|
||||
/************ GF(p^2) arithmetic functions *************/
|
||||
|
||||
// Copy of a GF(p546^2) element, c = a
|
||||
void fp2copy546(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Zeroing a GF(p546^2) element, a = 0
|
||||
void fp2zero546(f2elm_t a);
|
||||
|
||||
// GF(p546^2) negation, a = -a in GF(p546^2)
|
||||
void fp2neg546(f2elm_t a);
|
||||
|
||||
// GF(p546^2) addition, c = a+b in GF(p546^2)
|
||||
extern void fp2add546(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p546^2) subtraction, c = a-b in GF(p546^2)
|
||||
extern void fp2sub546(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p546^2) division by two, c = a/2 in GF(p546^2)
|
||||
void fp2div2_546(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Modular correction, a = a in GF(p546^2)
|
||||
void fp2correction546(f2elm_t a);
|
||||
|
||||
// GF(p546^2) squaring using Montgomery arithmetic, c = a^2 in GF(p546^2)
|
||||
void fp2sqr546_mont(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// GF(p546^2) multiplication using Montgomery arithmetic, c = a*b in GF(p546^2)
|
||||
void fp2mul546_mont(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p546^2) inversion using Montgomery arithmetic, a = (a0-i*a1)/(a0^2+a1^2)
|
||||
void fp2inv546_mont(f2elm_t a);
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,259 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: portable modular arithmetic for P546
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P546_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p546[NWORDS64_FIELD];
|
||||
extern const uint64_t p546p1[NWORDS64_FIELD];
|
||||
extern const uint64_t p546x2[NWORDS64_FIELD];
|
||||
extern const uint64_t p546x4[NWORDS64_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub546_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p546x2)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub546_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p546x4)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd546(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p546.
|
||||
// Inputs: a, b in [0, 2*p546-1]
|
||||
// Output: c in [0, 2*p546-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p546x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p546x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub546(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p546.
|
||||
// Inputs: a, b in [0, 2*p546-1]
|
||||
// Output: c in [0, 2*p546-1]
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p546x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg546(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p546.
|
||||
// Input/output: a in [0, 2*p546-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p546x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_546(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p546.
|
||||
// Input : a in [0, 2*p546-1]
|
||||
// Output: c in [0, 2*p546-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p546
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p546)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection546(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p546-1] to [0, p546-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p546)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p546)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void digit_x_digit(const digit_t a, const digit_t b, digit_t* c)
|
||||
{ // Digit multiplication, digit * digit -> 2-digit result
|
||||
register digit_t al, ah, bl, bh, temp;
|
||||
digit_t albl, albh, ahbl, ahbh, res1, res2, res3, carry;
|
||||
digit_t mask_low = (digit_t)(-1) >> (sizeof(digit_t)*4), mask_high = (digit_t)(-1) << (sizeof(digit_t)*4);
|
||||
|
||||
al = a & mask_low; // Low part
|
||||
ah = a >> (sizeof(digit_t) * 4); // High part
|
||||
bl = b & mask_low;
|
||||
bh = b >> (sizeof(digit_t) * 4);
|
||||
|
||||
albl = al*bl;
|
||||
albh = al*bh;
|
||||
ahbl = ah*bl;
|
||||
ahbh = ah*bh;
|
||||
c[0] = albl & mask_low; // C00
|
||||
|
||||
res1 = albl >> (sizeof(digit_t) * 4);
|
||||
res2 = ahbl & mask_low;
|
||||
res3 = albh & mask_low;
|
||||
temp = res1 + res2 + res3;
|
||||
carry = temp >> (sizeof(digit_t) * 4);
|
||||
c[0] ^= temp << (sizeof(digit_t) * 4); // C01
|
||||
|
||||
res1 = ahbl >> (sizeof(digit_t) * 4);
|
||||
res2 = albh >> (sizeof(digit_t) * 4);
|
||||
res3 = ahbh & mask_low;
|
||||
temp = res1 + res2 + res3 + carry;
|
||||
c[1] = temp & mask_low; // C10
|
||||
carry = temp & mask_high;
|
||||
c[1] ^= (ahbh & mask_high) + carry; // C11
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
unsigned int i, j;
|
||||
digit_t t = 0, u = 0, v = 0, UV[2];
|
||||
unsigned int carry = 0;
|
||||
|
||||
for (i = 0; i < nwords; i++) {
|
||||
for (j = 0; j <= i; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = nwords; i < 2*nwords-1; i++) {
|
||||
for (j = i-nwords+1; j < nwords; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
c[2*nwords-1] = v;
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Efficient Montgomery reduction using comba and exploiting the special form of the prime p546.
|
||||
// mc = ma*R^-1 mod p546x2, where R = 2^576.
|
||||
// If ma < 2^576*p546, the output mc is in the range [0, 2*p546-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
unsigned int i, j, carry, count = p546_ZERO_WORDS;
|
||||
digit_t UV[2], t = 0, u = 0, v = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
mc[i] = 0;
|
||||
}
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
for (j = 0; j < i; j++) {
|
||||
if (j < (i-p546_ZERO_WORDS+1)) {
|
||||
MUL(mc[j], ((digit_t*)p546p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = NWORDS_FIELD; i < 2*NWORDS_FIELD-1; i++) {
|
||||
if (count > 0) {
|
||||
count -= 1;
|
||||
}
|
||||
for (j = i-NWORDS_FIELD+1; j < NWORDS_FIELD; j++) {
|
||||
if (j < (NWORDS_FIELD-count)) {
|
||||
MUL(mc[j], ((digit_t*)p546p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i-NWORDS_FIELD] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
ADDC(0, v, ma[2*NWORDS_FIELD-1], carry, v);
|
||||
mc[NWORDS_FIELD-1] = v;
|
||||
}
|
||||
|
|
@ -0,0 +1,729 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: modular arithmetic optimized for x64 platforms for P610
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P610_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p610[NWORDS_FIELD];
|
||||
extern const uint64_t p610p1[NWORDS_FIELD];
|
||||
extern const uint64_t p610x2[NWORDS_FIELD];
|
||||
extern const uint64_t p610x4[NWORDS_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub610_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p610x2)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub610_p2_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub610_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p610x4)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub610_p4_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd610(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p610.
|
||||
// Inputs: a, b in [0, 2*p610-1]
|
||||
// Output: c in [0, 2*p610-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p610x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p610x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpadd610_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub610(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p610.
|
||||
// Inputs: a, b in [0, 2*p610-1]
|
||||
// Output: c in [0, 2*p610-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p610x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpsub610_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg610(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p610.
|
||||
// Input/output: a in [0, 2*p610-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p610x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_610(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p610.
|
||||
// Input : a in [0, 2*p610-1]
|
||||
// Output: c in [0, 2*p610-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p610
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p610)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection610(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p610-1] to [0, p610-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p610)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p610)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
|
||||
(void)nwords;
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
unsigned int carry = 0;
|
||||
|
||||
MULADD128(a[0], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[8] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[9] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[9], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
c[10] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[9], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
c[11] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[9], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
c[12] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[9], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
c[13] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[9], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
c[14] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[9], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
c[15] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[9], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
c[16] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[9], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
c[17] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
|
||||
MULADD128(a[9], b[9], uv, carry, uv);
|
||||
c[18] = uv[0];
|
||||
c[19] = uv[1];
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mul610_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Montgomery reduction exploiting special form of the prime.
|
||||
// mc = ma*R^-1 mod p610x2, where R = 2^640.
|
||||
// If ma < 2^640*p610, the output mc is in the range [0, 2*p610-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int carry;
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
|
||||
mc[0] = ma[0];
|
||||
mc[1] = ma[1];
|
||||
mc[2] = ma[2];
|
||||
mc[3] = ma[3];
|
||||
MUL128(mc[0], ((digit_t*)p610p1)[4], uv);
|
||||
ADDC(0, uv[0], ma[4], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
mc[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p610p1)[5], uv, carry, uv);
|
||||
MULADD128(mc[1], ((digit_t*)p610p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[5], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p610p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p610p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p610p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[6], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p610p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p610p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p610p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p610p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[7], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p610p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p610p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p610p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p610p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p610p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[8], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[8] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p610p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p610p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p610p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p610p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p610p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p610p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[9], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[9] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[1], ((digit_t*)p610p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p610p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p610p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p610p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p610p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p610p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[10], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[2], ((digit_t*)p610p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p610p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p610p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p610p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p610p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p610p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[11], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[3], ((digit_t*)p610p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p610p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p610p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p610p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p610p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p610p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[12], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[4], ((digit_t*)p610p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p610p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p610p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p610p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p610p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p610p1)[4], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[13], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[5], ((digit_t*)p610p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p610p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p610p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p610p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p610p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[14], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[6], ((digit_t*)p610p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p610p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p610p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p610p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[15], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[7], ((digit_t*)p610p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p610p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p610p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[16], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[8], ((digit_t*)p610p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p610p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[17], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[9], ((digit_t*)p610p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[18], carry, mc[8]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
ADDC(0, uv[1], ma[19], carry, mc[9]);
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
rdc610_asm(ma, mc);
|
||||
|
||||
#endif
|
||||
}
|
||||
Разница между файлами не показана из-за своего большого размера
Загрузить разницу
|
|
@ -0,0 +1,140 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: supersingular isogeny parameters and generation of functions for P610
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "P610_api.h"
|
||||
#include "P610_internal.h"
|
||||
#include "../internal.h"
|
||||
|
||||
|
||||
// Encoding of field elements, elements over Z_order, elements over GF(p^2) and elliptic curve points:
|
||||
// --------------------------------------------------------------------------------------------------
|
||||
// Elements over GF(p) and Z_order are encoded with the least significant octet (and digit) located at the leftmost position (i.e., little endian format).
|
||||
// Elements (a+b*i) over GF(p^2), where a and b are defined over GF(p), are encoded as {a, b}, with a in the least significant position.
|
||||
// Elliptic curve points P = (x,y) are encoded as {x, y}, with x in the least significant position.
|
||||
// Internally, the number of digits used to represent all these elements is obtained by approximating the number of bits to the immediately greater multiple of 32.
|
||||
// For example, a 610-bit field element is represented with Ceil(610 / 64) = 10 64-bit digits or Ceil(610 / 32) = 20 32-bit digits.
|
||||
|
||||
//
|
||||
// Curve isogeny system "SIDHp610". Base curve: Montgomery curve By^2 = Cx^3 + Ax^2 + Cx defined over GF(p610^2), where A=6, B=1, C=1 and p610 = 2^305*3^192-1
|
||||
//
|
||||
|
||||
const uint64_t p610[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x6E01FFFFFFFFFFFF,
|
||||
0xB1784DE8AA5AB02E, 0x9AE7BF45048FF9AB, 0xB255B2FA10C4252A, 0x819010C251E7D88C, 0x000000027BF6A768 };
|
||||
const uint64_t p610x2[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xDC03FFFFFFFFFFFF,
|
||||
0x62F09BD154B5605C, 0x35CF7E8A091FF357, 0x64AB65F421884A55, 0x03202184A3CFB119, 0x00000004F7ED4ED1 };
|
||||
const uint64_t p610x4[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFC, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xB807FFFFFFFFFFFF,
|
||||
0xC5E137A2A96AC0B9, 0x6B9EFD14123FE6AE, 0xC956CBE8431094AA, 0x06404309479F6232, 0x00000009EFDA9DA2 };
|
||||
const uint64_t p610p1[NWORDS64_FIELD] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x6E02000000000000,
|
||||
0xB1784DE8AA5AB02E, 0x9AE7BF45048FF9AB, 0xB255B2FA10C4252A, 0x819010C251E7D88C, 0x000000027BF6A768 };
|
||||
const uint64_t p610x16p[2*NWORDS64_FIELD] = { 0x0000000000000010, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x3FC0000000000000,
|
||||
0xD0F642EAB4A9FA32, 0xA308175F6E00CA89, 0xB549A0BDE77B5AAC, 0xCDFDE7B5C304EE69, 0x7FDB7FF0812B12EF,
|
||||
0xE09BA529B9FE1167, 0xD249C196DAB8CD7F, 0xD4E22754A3F20928, 0x97825638B19A7CCE, 0x05E04550FC4CCE0D,
|
||||
0x8FB5DA1152CDE50C, 0xF9649BA3EA408644, 0x4473C93E6441063D, 0xBE190269D1337B7B, 0x0000000000000062 };
|
||||
// Order of Alice's subgroup
|
||||
const uint64_t Alice_order[NWORDS64_ORDER] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0002000000000000 };
|
||||
// Order of Bob's subgroup
|
||||
const uint64_t Bob_order[NWORDS64_ORDER] = { 0x26F4552D58173701, 0xDFA28247FCD5D8BC, 0xD97D086212954D73, 0x086128F3EC46592A, 0x00013DFB53B440C8 };
|
||||
// Alice's generator values {XPA0 + XPA1*i, XQA0 + xQA1*i, XRA0 + XRA1*i} in GF(p610^2), expressed in Montgomery representation
|
||||
const uint64_t A_gen[6 * NWORDS64_FIELD] = { 0x5019EC96A75AC57A, 0x8AEA0E717712C6F1, 0x03C067C819D29E5E, 0x59F454425FE307D9, 0x6D29215D9AD5E6D4,
|
||||
0xD8C5A27CDC9DD34A, 0x972DC274DAB435B3, 0x82A597C70A80E10F, 0x48175986EFED547F, 0x00000000671A3592, // XPA0
|
||||
0xE4BA9CC3EEEC53F4, 0xBD34E4FEDB0132D3, 0x1B7125C87BEE960C, 0x25D615BF3CFAA355, 0xFC8EC20DC367D66A,
|
||||
0xB44F3FD1CC73289C, 0xD84BF51195C2E012, 0x38D7C756EB370F48, 0xBBC236249F94F72A, 0x000000013020CC63, // XPA1
|
||||
0x1D7C945D3DBCC38C, 0x9A5F7C12CA8BA5B9, 0x1E8F87985B01CBE3, 0xD2CABF82F5BC5235, 0x3BDE474ECCA9FAA2,
|
||||
0xB98CD975DF9FB0A8, 0x444E4464B9C67790, 0xCB2E888565CE6AD9, 0xDB64FFE2A1C350E2, 0x00000001D7532756, // XQA0
|
||||
0x1E8B3AA2382C9079, 0x28CB31E08A943C00, 0xE04D02266E8A63E1, 0x84A2D260214EF65F, 0xD5933DA25018E226,
|
||||
0xBC8BF038928C4BA9, 0x91E9D0CB7EAF58A9, 0x04A4627B75E008E1, 0x58CEF27583E50C2E, 0x00000002170DDF44, // XQA1
|
||||
0x261DD0782CEC958D, 0xC25B3AE64BBC0311, 0x9F21B8A8981B15FE, 0xA3C0B52CD5FFC45B, 0x5D2E65A016702C6A,
|
||||
0x8C5586CA98722EDE, 0x61490A967A6B4B1A, 0xFA64E30231F719AF, 0x9CEAB8B6301BB2DF, 0x00000000CF5AEA7D, // XRA0
|
||||
0xB980435A77B912C0, 0x2B4A97F70E0FC873, 0x415C7FA4DE96F43C, 0xE5EED95643E443FD, 0xCBE18DB57C51B354,
|
||||
0x51C96C3FFABD2D46, 0x5C14637B9A5765D6, 0x45D2369C4D0199A5, 0x25A1F9C5BBF1E683, 0x000000025AD7A11B }; // XRA1
|
||||
// Bob's generator values {XPB0, XQB0, XRB0 + XRB1*i} in GF(p610^2), expressed in Montgomery representation
|
||||
const uint64_t B_gen[6 * NWORDS64_FIELD] = { 0xC6C8E180E41884BA, 0x2161D2F4FBC32B95, 0xCBF83091BDB34092, 0xD742CC0AD4CC7E38, 0x61A1FA7E1B14FBD7,
|
||||
0xF0E5FC70137597C4, 0x1F0C8F2585E20B1F, 0xC68E44A1C032A4C2, 0xE3C65FB8AF155A0D, 0x00000001409EE8D5, // XPB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XPB1
|
||||
0xF586DB4A16BE1880, 0x712F10D95E6C65A9, 0x9D5AAC3B83584B87, 0x4ECDAA98182C8261, 0xAD7D4C15588FD230,
|
||||
0x4197C54E96B7D926, 0xED15BB13E8C588ED, 0x3E299AEAD5AAD7C7, 0xF36B25F1BD579F79, 0x000000021CE65B5B, // XQB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XQB1
|
||||
0x7A87897A0C4C3FD7, 0x3C1879ECD4D33D76, 0x595C28A36FFBA1A0, 0xF53FF66A2A7FD0FB, 0xB39F5A91230E56FA,
|
||||
0x81F21610DA3EA8B5, 0xEBB3B9A627428A90, 0x8661123B35748010, 0xE196173B9C48781D, 0x00000002198166AC, // XRB0
|
||||
0x5E3CC79B37006D6A, 0xE0358A9AB2EA7923, 0x3B725CB595180951, 0x0724637F1DD0C191, 0x7BB031B67DAB9D19,
|
||||
0x53CCB8BECEDD3435, 0xEE5DF7FFEBFA7A0A, 0x899EDB7D8B9694C4, 0x0CA38EB4AE5506B6, 0x00000001489DE1CD }; // XRB1
|
||||
// Montgomery constant Montgomery_R2 = (2^640)^2 mod p610
|
||||
const uint64_t Montgomery_R2[NWORDS64_FIELD] = { 0xE75F5D201A197727, 0xE0B85963B627392E, 0x6BC1707818DE493D, 0xDC7F419940D1A0C5, 0x7358030979EDE54A,
|
||||
0x84F4BEBDEED75A5C, 0x7ECCA66E13427B47, 0xC5BB4E65280080B3, 0x7019950F516DA19A, 0x000000008E290FF3 };
|
||||
// Value one in Montgomery representation
|
||||
const uint64_t Montgomery_one[NWORDS64_FIELD] = { 0x00000000670CC8E6, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x9A34000000000000,
|
||||
0x4D99C2BD28717A3F, 0x0A4A1839A323D41C, 0xD2B62215D06AD1E2, 0x1369026E862CAF3D, 0x000000010894E964 };
|
||||
|
||||
|
||||
// Fixed parameters for isogeny tree computation
|
||||
const unsigned int strat_Alice[MAX_Alice-1] = {
|
||||
67, 37, 21, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1,
|
||||
2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 16, 9,
|
||||
5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1,
|
||||
1, 4, 2, 1, 1, 2, 1, 1, 33, 16, 8, 5, 2, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1,
|
||||
1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 1, 2, 1, 1,
|
||||
4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1 };
|
||||
|
||||
const unsigned int strat_Bob[MAX_Bob-1] = {
|
||||
86, 48, 27, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1,
|
||||
1, 3, 2, 1, 1, 1, 1, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1,
|
||||
1, 1, 2, 1, 1, 1, 21, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1,
|
||||
1, 1, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 38,
|
||||
21, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1,
|
||||
9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 17, 9, 5, 3, 2, 1, 1,
|
||||
1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2,
|
||||
1, 1 };
|
||||
|
||||
// Setting up macro defines and including GF(p), GF(p^2), curve, isogeny and kex functions
|
||||
#define fpcopy fpcopy610
|
||||
#define fpzero fpzero610
|
||||
#define fpadd fpadd610
|
||||
#define fpsub fpsub610
|
||||
#define fpneg fpneg610
|
||||
#define fpdiv2 fpdiv2_610
|
||||
#define fpcorrection fpcorrection610
|
||||
#define fpmul_mont fpmul610_mont
|
||||
#define fpsqr_mont fpsqr610_mont
|
||||
#define fpinv_mont fpinv610_mont
|
||||
#define fpinv_chain_mont fpinv610_chain_mont
|
||||
#define fp2copy fp2copy610
|
||||
#define fp2zero fp2zero610
|
||||
#define fp2add fp2add610
|
||||
#define fp2sub fp2sub610
|
||||
#define mp_sub_p2 mp_sub610_p2
|
||||
#define mp_sub_p4 mp_sub610_p4
|
||||
#define sub_p4 mp_sub_p4
|
||||
#define fp2neg fp2neg610
|
||||
#define fp2div2 fp2div2_610
|
||||
#define fp2correction fp2correction610
|
||||
#define fp2mul_mont fp2mul610_mont
|
||||
#define fp2sqr_mont fp2sqr610_mont
|
||||
#define fp2inv_mont fp2inv610_mont
|
||||
#define fp2inv_mont_bingcd fp2inv610_mont_bingcd
|
||||
#define fpequal_non_constant_time fpequal610_non_constant_time
|
||||
#define mp_add_asm mp_add610_asm
|
||||
#define mp_subaddx2_asm mp_subadd610x2_asm
|
||||
#define mp_dblsubx2_asm mp_dblsub610x2_asm
|
||||
#define crypto_kem_keypair crypto_kem_keypair_SIKEp610
|
||||
#define crypto_kem_enc crypto_kem_enc_SIKEp610
|
||||
#define crypto_kem_dec crypto_kem_dec_SIKEp610
|
||||
#define random_mod_order_A random_mod_order_A_SIDHp610
|
||||
#define random_mod_order_B random_mod_order_B_SIDHp610
|
||||
#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp610
|
||||
#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp610
|
||||
#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp610
|
||||
#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp610
|
||||
|
||||
#include "../fpx.c"
|
||||
#include "../ec_isogeny.c"
|
||||
#include "../sidh.c"
|
||||
#include "../sike.c"
|
||||
|
|
@ -0,0 +1,112 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: API header file for P610
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P610_API_H
|
||||
#define P610_API_H
|
||||
|
||||
|
||||
/*********************** Key encapsulation mechanism API ***********************/
|
||||
|
||||
#define CRYPTO_SECRETKEYBYTES 524 // MSG_BYTES + SECRETKEY_B_BYTES + CRYPTO_PUBLICKEYBYTES bytes
|
||||
#define CRYPTO_PUBLICKEYBYTES 462
|
||||
#define CRYPTO_BYTES 24
|
||||
#define CRYPTO_CIPHERTEXTBYTES 486 // CRYPTO_PUBLICKEYBYTES + MSG_BYTES bytes
|
||||
|
||||
// Algorithm name
|
||||
#define CRYPTO_ALGNAME "SIKEp610"
|
||||
|
||||
// SIKE's key generation
|
||||
// It produces a private key sk and computes the public key pk.
|
||||
// Outputs: secret key sk (CRYPTO_SECRETKEYBYTES = 524 bytes)
|
||||
// public key pk (CRYPTO_PUBLICKEYBYTES = 462 bytes)
|
||||
int crypto_kem_keypair_SIKEp610(unsigned char *pk, unsigned char *sk);
|
||||
|
||||
// SIKE's encapsulation
|
||||
// Input: public key pk (CRYPTO_PUBLICKEYBYTES = 462 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 24 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 486 bytes)
|
||||
int crypto_kem_enc_SIKEp610(unsigned char *ct, unsigned char *ss, const unsigned char *pk);
|
||||
|
||||
// SIKE's decapsulation
|
||||
// Input: secret key sk (CRYPTO_SECRETKEYBYTES = 524 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 486 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 24 bytes)
|
||||
int crypto_kem_dec_SIKEp610(unsigned char *ss, const unsigned char *ct, const unsigned char *sk);
|
||||
|
||||
|
||||
// Encoding of keys for KEM-based isogeny system "SIKEp610" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p610) are encoded in 77 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p610^2), where a and b are defined over GF(p610), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys sk consist of the concatenation of a 24-byte random value, a value in the range [0, 2^Floor(Log(2,3^192))-1] and the public key pk. In the SIKE API,
|
||||
// private keys are encoded in 524 octets in little endian format.
|
||||
// Public keys pk consist of 3 elements in GF(p610^2). In the SIKE API, pk is encoded in 462 octets.
|
||||
// Ciphertexts ct consist of the concatenation of a public key value and a 24-byte value. In the SIKE API, ct is encoded in 462 + 24 = 486 octets.
|
||||
// Shared keys ss consist of a value of 24 octets.
|
||||
|
||||
|
||||
/*********************** Ephemeral key exchange API ***********************/
|
||||
|
||||
#define SIDH_SECRETKEYBYTES_A 39
|
||||
#define SIDH_SECRETKEYBYTES_B 38
|
||||
#define SIDH_PUBLICKEYBYTES 462
|
||||
#define SIDH_BYTES 154
|
||||
|
||||
// SECURITY NOTE: SIDH supports ephemeral Diffie-Hellman key exchange. It is NOT secure to use it with static keys.
|
||||
// See "On the Security of Supersingular Isogeny Cryptosystems", S.D. Galbraith, C. Petit, B. Shani and Y.B. Ti, in ASIACRYPT 2016, 2016.
|
||||
// Extended version available at: http://eprint.iacr.org/2016/859
|
||||
|
||||
// Generation of Alice's secret key
|
||||
// Outputs random value in [0, 2^305 - 1] to be used as Alice's private key
|
||||
void random_mod_order_A_SIDHp610(unsigned char* random_digits);
|
||||
|
||||
// Generation of Bob's secret key
|
||||
// Outputs random value in [0, 2^Floor(Log(2,3^192)) - 1] to be used as Bob's private key
|
||||
void random_mod_order_B_SIDHp610(unsigned char* random_digits);
|
||||
|
||||
// Alice's ephemeral public key generation
|
||||
// Input: a private key PrivateKeyA in the range [0, 2^305 - 1], stored in 38 bytes.
|
||||
// Output: the public key PublicKeyA consisting of 3 GF(p610^2) elements encoded in 462 bytes.
|
||||
int EphemeralKeyGeneration_A_SIDHp610(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA);
|
||||
|
||||
// Bob's ephemeral key-pair generation
|
||||
// It produces a private key PrivateKeyB and computes the public key PublicKeyB.
|
||||
// The private key is an integer in the range [0, 2^Floor(Log(2,3^192)) - 1], stored in 38 bytes.
|
||||
// The public key consists of 3 GF(p610^2) elements encoded in 462 bytes.
|
||||
int EphemeralKeyGeneration_B_SIDHp610(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB);
|
||||
|
||||
// Alice's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB
|
||||
// Inputs: Alice's PrivateKeyA is an integer in the range [0, 2^305 - 1], stored in 38 bytes.
|
||||
// Bob's PublicKeyB consists of 3 GF(p610^2) elements encoded in 462 bytes.
|
||||
// Output: a shared secret SharedSecretA that consists of one element in GF(p610^2) encoded in 154 bytes.
|
||||
int EphemeralSecretAgreement_A_SIDHp610(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA);
|
||||
|
||||
// Bob's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA
|
||||
// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,3^192)) - 1], stored in 38 bytes.
|
||||
// Alice's PublicKeyA consists of 3 GF(p610^2) elements encoded in 462 bytes.
|
||||
// Output: a shared secret SharedSecretB that consists of one element in GF(p610^2) encoded in 154 bytes.
|
||||
int EphemeralSecretAgreement_B_SIDHp610(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB);
|
||||
|
||||
|
||||
// Encoding of keys for KEX-based isogeny system "SIDHp610" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p610) are encoded in 77 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p610^2), where a and b are defined over GF(p610), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys PrivateKeyA and PrivateKeyB can have values in the range [0, 2^305-1] and [0, 2^Floor(Log(2,3^192)) - 1], resp. In the SIDH API,
|
||||
// Alice's and Bob's private keys are encoded in 39 and 38 octets, resp., in little endian format.
|
||||
// Public keys PublicKeyA and PublicKeyB consist of 3 elements in GF(p610^2). In the SIDH API, they are encoded in 462 octets.
|
||||
// Shared keys SharedSecretA and SharedSecretB consist of one element in GF(p610^2). In the SIDH API, they are encoded in 154 octets.
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,174 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: internal header file for P610
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P610_INTERNAL_H
|
||||
#define P610_INTERNAL_H
|
||||
|
||||
#include "../config.h"
|
||||
|
||||
|
||||
#if (TARGET == TARGET_AMD64) || (TARGET == TARGET_ARM64)
|
||||
#define NWORDS_FIELD 10 // Number of words of a 610-bit field element
|
||||
#define p610_ZERO_WORDS 4 // Number of "0" digits in the least significant part of p610 + 1
|
||||
#elif (TARGET == TARGET_x86)
|
||||
#define NWORDS_FIELD 20
|
||||
#define p610_ZERO_WORDS 9
|
||||
#endif
|
||||
|
||||
|
||||
// Basic constants
|
||||
|
||||
#define NBITS_FIELD 610
|
||||
#define MAXBITS_FIELD 640
|
||||
#define MAXWORDS_FIELD ((MAXBITS_FIELD+RADIX-1)/RADIX) // Max. number of words to represent field elements
|
||||
#define NWORDS64_FIELD ((NBITS_FIELD+63)/64) // Number of 64-bit words of a 610-bit field element
|
||||
#define NBITS_ORDER 320
|
||||
#define NWORDS_ORDER ((NBITS_ORDER+RADIX-1)/RADIX) // Number of words of oA and oB, where oA and oB are the subgroup orders of Alice and Bob, resp.
|
||||
#define NWORDS64_ORDER ((NBITS_ORDER+63)/64) // Number of 64-bit words of a 320-bit element
|
||||
#define MAXBITS_ORDER NBITS_ORDER
|
||||
#define ALICE 0
|
||||
#define BOB 1
|
||||
#define OALICE_BITS 305
|
||||
#define OBOB_BITS 305
|
||||
#define OBOB_EXPON 192
|
||||
#define MASK_ALICE 0x01
|
||||
#define MASK_BOB 0xFF
|
||||
#define PRIME p610
|
||||
#define PARAM_A 6
|
||||
#define PARAM_C 1
|
||||
// Fixed parameters for isogeny tree computation
|
||||
#define MAX_INT_POINTS_ALICE 8
|
||||
#define MAX_INT_POINTS_BOB 10
|
||||
#define MAX_Alice 152
|
||||
#define MAX_Bob 192
|
||||
#define MSG_BYTES 24
|
||||
#define SECRETKEY_A_BYTES ((OALICE_BITS + 7) / 8)
|
||||
#define SECRETKEY_B_BYTES ((OBOB_BITS - 1 + 7) / 8)
|
||||
#define FP2_ENCODED_BYTES 2*((NBITS_FIELD + 7) / 8)
|
||||
|
||||
|
||||
// SIDH's basic element definitions and point representations
|
||||
|
||||
typedef digit_t felm_t[NWORDS_FIELD]; // Datatype for representing 610-bit field elements (640-bit max.)
|
||||
typedef digit_t dfelm_t[2*NWORDS_FIELD]; // Datatype for representing double-precision 2x610-bit field elements (2x640-bit max.)
|
||||
typedef felm_t f2elm_t[2]; // Datatype for representing quadratic extension field elements GF(p610^2)
|
||||
|
||||
typedef struct { f2elm_t X; f2elm_t Z; } point_proj; // Point representation in projective XZ Montgomery coordinates.
|
||||
typedef point_proj point_proj_t[1];
|
||||
|
||||
#ifdef COMPRESS
|
||||
typedef struct { f2elm_t X; f2elm_t Y; f2elm_t Z; } point_full_proj; // Point representation in full projective XYZ Montgomery coordinates
|
||||
typedef point_full_proj point_full_proj_t[1];
|
||||
|
||||
typedef struct { f2elm_t x; f2elm_t y; } point_affine; // Point representation in affine coordinates.
|
||||
typedef point_affine point_t[1];
|
||||
|
||||
typedef f2elm_t publickey_t[3];
|
||||
#endif
|
||||
|
||||
|
||||
/**************** Function prototypes ****************/
|
||||
/************* Multiprecision functions **************/
|
||||
|
||||
// 610-bit multiprecision addition, c = a+b
|
||||
void mp_add610(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_add610_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 610-bit multiprecision subtraction, c = a-b+2p or c = a-b+4p
|
||||
extern void mp_sub610_p2(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void mp_sub610_p4(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub610_p2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub610_p4_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 2x610-bit multiprecision subtraction followed by addition with p610*2^640, c = a-b+(p610*2^640) if a-b < 0, otherwise c=a-b
|
||||
void mp_subaddx2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_subadd610x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Double 2x610-bit multiprecision subtraction, c = c-a-b, where c > a and c > b
|
||||
void mp_dblsub610x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
/************ Field arithmetic functions *************/
|
||||
|
||||
// Copy of a field element, c = a
|
||||
void fpcopy610(const digit_t* a, digit_t* c);
|
||||
|
||||
// Zeroing a field element, a = 0
|
||||
void fpzero610(digit_t* a);
|
||||
|
||||
// Non constant-time comparison of two field elements. If a = b return TRUE, otherwise, return FALSE
|
||||
bool fpequal610_non_constant_time(const digit_t* a, const digit_t* b);
|
||||
|
||||
// Modular addition, c = a+b mod p610
|
||||
extern void fpadd610(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpadd610_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular subtraction, c = a-b mod p610
|
||||
extern void fpsub610(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpsub610_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular negation, a = -a mod p610
|
||||
extern void fpneg610(digit_t* a);
|
||||
|
||||
// Modular division by two, c = a/2 mod p610.
|
||||
void fpdiv2_610(const digit_t* a, digit_t* c);
|
||||
|
||||
// Modular correction to reduce field element a in [0, 2*p610-1] to [0, p610-1].
|
||||
void fpcorrection610(digit_t* a);
|
||||
|
||||
// 610-bit Montgomery reduction, c = a mod p
|
||||
void rdc610_asm(digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field multiplication using Montgomery arithmetic, c = a*b*R^-1 mod p610, where R=2^640
|
||||
void fpmul610_mont(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mul610_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Field squaring using Montgomery arithmetic, c = a*b*R^-1 mod p610, where R=2^640
|
||||
void fpsqr610_mont(const digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field inversion, a = a^-1 in GF(p610)
|
||||
void fpinv610_mont(digit_t* a);
|
||||
|
||||
// Chain to compute (p610-3)/4 using Montgomery arithmetic
|
||||
void fpinv610_chain_mont(digit_t* a);
|
||||
|
||||
/************ GF(p^2) arithmetic functions *************/
|
||||
|
||||
// Copy of a GF(p610^2) element, c = a
|
||||
void fp2copy610(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Zeroing a GF(p610^2) element, a = 0
|
||||
void fp2zero610(f2elm_t a);
|
||||
|
||||
// GF(p610^2) negation, a = -a in GF(p610^2)
|
||||
void fp2neg610(f2elm_t a);
|
||||
|
||||
// GF(p610^2) addition, c = a+b in GF(p610^2)
|
||||
extern void fp2add610(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p610^2) subtraction, c = a-b in GF(p610^2)
|
||||
extern void fp2sub610(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p610^2) division by two, c = a/2 in GF(p610^2)
|
||||
void fp2div2_610(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Modular correction, a = a in GF(p610^2)
|
||||
void fp2correction610(f2elm_t a);
|
||||
|
||||
// GF(p610^2) squaring using Montgomery arithmetic, c = a^2 in GF(p610^2)
|
||||
void fp2sqr610_mont(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// GF(p610^2) multiplication using Montgomery arithmetic, c = a*b in GF(p610^2)
|
||||
void fp2mul610_mont(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p610^2) inversion using Montgomery arithmetic, a = (a0-i*a1)/(a0^2+a1^2)
|
||||
void fp2inv610_mont(f2elm_t a);
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,259 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: portable modular arithmetic for P610
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P610_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p610[NWORDS64_FIELD];
|
||||
extern const uint64_t p610p1[NWORDS64_FIELD];
|
||||
extern const uint64_t p610x2[NWORDS64_FIELD];
|
||||
extern const uint64_t p610x4[NWORDS64_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub610_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p610x2)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub610_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p610x4)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd610(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p610.
|
||||
// Inputs: a, b in [0, 2*p610-1]
|
||||
// Output: c in [0, 2*p610-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p610x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p610x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub610(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p610.
|
||||
// Inputs: a, b in [0, 2*p610-1]
|
||||
// Output: c in [0, 2*p610-1]
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p610x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg610(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p610.
|
||||
// Input/output: a in [0, 2*p610-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p610x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_610(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p610.
|
||||
// Input : a in [0, 2*p610-1]
|
||||
// Output: c in [0, 2*p610-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p610
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p610)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection610(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p610-1] to [0, p610-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p610)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p610)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void digit_x_digit(const digit_t a, const digit_t b, digit_t* c)
|
||||
{ // Digit multiplication, digit * digit -> 2-digit result
|
||||
register digit_t al, ah, bl, bh, temp;
|
||||
digit_t albl, albh, ahbl, ahbh, res1, res2, res3, carry;
|
||||
digit_t mask_low = (digit_t)(-1) >> (sizeof(digit_t)*4), mask_high = (digit_t)(-1) << (sizeof(digit_t)*4);
|
||||
|
||||
al = a & mask_low; // Low part
|
||||
ah = a >> (sizeof(digit_t) * 4); // High part
|
||||
bl = b & mask_low;
|
||||
bh = b >> (sizeof(digit_t) * 4);
|
||||
|
||||
albl = al*bl;
|
||||
albh = al*bh;
|
||||
ahbl = ah*bl;
|
||||
ahbh = ah*bh;
|
||||
c[0] = albl & mask_low; // C00
|
||||
|
||||
res1 = albl >> (sizeof(digit_t) * 4);
|
||||
res2 = ahbl & mask_low;
|
||||
res3 = albh & mask_low;
|
||||
temp = res1 + res2 + res3;
|
||||
carry = temp >> (sizeof(digit_t) * 4);
|
||||
c[0] ^= temp << (sizeof(digit_t) * 4); // C01
|
||||
|
||||
res1 = ahbl >> (sizeof(digit_t) * 4);
|
||||
res2 = albh >> (sizeof(digit_t) * 4);
|
||||
res3 = ahbh & mask_low;
|
||||
temp = res1 + res2 + res3 + carry;
|
||||
c[1] = temp & mask_low; // C10
|
||||
carry = temp & mask_high;
|
||||
c[1] ^= (ahbh & mask_high) + carry; // C11
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
unsigned int i, j;
|
||||
digit_t t = 0, u = 0, v = 0, UV[2];
|
||||
unsigned int carry = 0;
|
||||
|
||||
for (i = 0; i < nwords; i++) {
|
||||
for (j = 0; j <= i; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = nwords; i < 2*nwords-1; i++) {
|
||||
for (j = i-nwords+1; j < nwords; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
c[2*nwords-1] = v;
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Efficient Montgomery reduction using comba and exploiting the special form of the prime p610.
|
||||
// mc = ma*R^-1 mod p610x2, where R = 2^768.
|
||||
// If ma < 2^768*p610, the output mc is in the range [0, 2*p610-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
unsigned int i, j, carry, count = p610_ZERO_WORDS;
|
||||
digit_t UV[2], t = 0, u = 0, v = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
mc[i] = 0;
|
||||
}
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
for (j = 0; j < i; j++) {
|
||||
if (j < (i-p610_ZERO_WORDS+1)) {
|
||||
MUL(mc[j], ((digit_t*)p610p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = NWORDS_FIELD; i < 2*NWORDS_FIELD-1; i++) {
|
||||
if (count > 0) {
|
||||
count -= 1;
|
||||
}
|
||||
for (j = i-NWORDS_FIELD+1; j < NWORDS_FIELD; j++) {
|
||||
if (j < (NWORDS_FIELD-count)) {
|
||||
MUL(mc[j], ((digit_t*)p610p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i-NWORDS_FIELD] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
ADDC(0, v, ma[2*NWORDS_FIELD-1], carry, v);
|
||||
mc[NWORDS_FIELD-1] = v;
|
||||
}
|
||||
|
|
@ -0,0 +1,802 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: modular arithmetic optimized for x64 platforms for P697
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P697_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p697[NWORDS_FIELD];
|
||||
extern const uint64_t p697p1[NWORDS_FIELD];
|
||||
extern const uint64_t p697x2[NWORDS_FIELD];
|
||||
extern const uint64_t p697x4[NWORDS_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub697_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p697x2)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub697_p2_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub697_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p697x4)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub697_p4_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd697(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p697.
|
||||
// Inputs: a, b in [0, 2*p697-1]
|
||||
// Output: c in [0, 2*p697-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p697x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p697x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpadd697_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub697(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p697.
|
||||
// Inputs: a, b in [0, 2*p697-1]
|
||||
// Output: c in [0, 2*p697-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p697x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpsub697_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg697(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p697.
|
||||
// Input/output: a in [0, 2*p697-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p697x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_697(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p697.
|
||||
// Input : a in [0, 2*p697-1]
|
||||
// Output: c in [0, 2*p697-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p697
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p697)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection697(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p697-1] to [0, p697-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p697)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p697)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
|
||||
(void)nwords;
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
unsigned int carry = 0;
|
||||
|
||||
MULADD128(a[0], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[8] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[9] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[10], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[10] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[10], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
c[11] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[10], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
c[12] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[10], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
c[13] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[10], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
c[14] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[10], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
c[15] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[10], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
c[16] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[10], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
c[17] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[10], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
c[18] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[10], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
c[19] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
|
||||
MULADD128(a[10], b[10], uv, carry, uv);
|
||||
c[20] = uv[0];
|
||||
c[21] = uv[1];
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mul697_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Montgomery reduction exploiting special form of the prime.
|
||||
// mc = ma*R^-1 mod p697x2, where R = 2^704.
|
||||
// If ma < 2^704*p697, the output mc is in the range [0, 2*p697-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int carry;
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
|
||||
mc[0] = ma[0];
|
||||
mc[1] = ma[1];
|
||||
mc[2] = ma[2];
|
||||
mc[3] = ma[3];
|
||||
mc[4] = ma[4];
|
||||
MUL128(mc[0], ((digit_t*)p697p1)[5], uv);
|
||||
ADDC(0, uv[0], ma[5], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
mc[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p697p1)[6], uv, carry, uv);
|
||||
MULADD128(mc[1], ((digit_t*)p697p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[6], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p697p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p697p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p697p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[7], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p697p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p697p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p697p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p697p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[8], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[8] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p697p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p697p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p697p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p697p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p697p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[9], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[9] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p697p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p697p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p697p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p697p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p697p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p697p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[10], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[10] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[1], ((digit_t*)p697p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p697p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p697p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p697p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p697p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p697p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[11], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[2], ((digit_t*)p697p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p697p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p697p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p697p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p697p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p697p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[12], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[3], ((digit_t*)p697p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p697p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p697p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p697p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p697p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p697p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[13], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[4], ((digit_t*)p697p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p697p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p697p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p697p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p697p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p697p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[14], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[5], ((digit_t*)p697p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p697p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p697p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p697p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p697p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[10], ((digit_t*)p697p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[15], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[6], ((digit_t*)p697p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p697p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p697p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p697p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[10], ((digit_t*)p697p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[16], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[7], ((digit_t*)p697p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p697p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p697p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[10], ((digit_t*)p697p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[17], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[8], ((digit_t*)p697p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p697p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[10], ((digit_t*)p697p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[18], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[9], ((digit_t*)p697p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[10], ((digit_t*)p697p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[19], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[8] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[10], ((digit_t*)p697p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[20], carry, mc[9]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
ADDC(0, uv[1], ma[21], carry, mc[10]);
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
rdc697_asm(ma, mc);
|
||||
|
||||
#endif
|
||||
}
|
||||
Разница между файлами не показана из-за своего большого размера
Загрузить разницу
|
|
@ -0,0 +1,139 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: supersingular isogeny parameters and generation of functions for P697
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "P697_api.h"
|
||||
#include "P697_internal.h"
|
||||
#include "../internal.h"
|
||||
|
||||
|
||||
// Encoding of field elements, elements over Z_order, elements over GF(p^2) and elliptic curve points:
|
||||
// --------------------------------------------------------------------------------------------------
|
||||
// Elements over GF(p) and Z_order are encoded with the least significant octet (and digit) located at the leftmost position (i.e., little endian format).
|
||||
// Elements (a+b*i) over GF(p^2), where a and b are defined over GF(p), are encoded as {a, b}, with a in the least significant position.
|
||||
// Elliptic curve points P = (x,y) are encoded as {x, y}, with x in the least significant position.
|
||||
// Internally, the number of digits used to represent all these elements is obtained by approximating the number of bits to the immediately greater multiple of 32.
|
||||
// For example, a 697-bit field element is represented with Ceil(697 / 64) = 11 64-bit digits or Ceil(697 / 32) = 22 32-bit digits.
|
||||
|
||||
//
|
||||
// Curve isogeny system "SIDHp697". Base curve: Montgomery curve By^2 = Cx^3 + Ax^2 + Cx defined over GF(p697^2), where A=6, B=1, C=1 and p697 = 2^356*3^215-1
|
||||
//
|
||||
|
||||
const uint64_t p697[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x604054AFFFFFFFFF,
|
||||
0xDF4970CF7313736F, 0x719AEC973BF54225, 0x40E474DA88B90FFE, 0x9A0E279D6CEB3C8E, 0x01B39F97671708CF };
|
||||
const uint64_t p697p1[NWORDS64_FIELD] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x604054B000000000,
|
||||
0xDF4970CF7313736F, 0x719AEC973BF54225, 0x40E474DA88B90FFE, 0x9A0E279D6CEB3C8E, 0x01B39F97671708CF };
|
||||
const uint64_t p697x2[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xC080A95FFFFFFFFF,
|
||||
0xBE92E19EE626E6DE, 0xE335D92E77EA844B, 0x81C8E9B511721FFC, 0x341C4F3AD9D6791C, 0x03673F2ECE2E119F };
|
||||
const uint64_t p697x4[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFC, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x810152BFFFFFFFFF,
|
||||
0x7D25C33DCC4DCDBD, 0xC66BB25CEFD50897, 0x0391D36A22E43FF9, 0x68389E75B3ACF239, 0x06CE7E5D9C5C233E };
|
||||
// Order of Alice's subgroup
|
||||
const uint64_t Alice_order[NWORDS64_ORDER] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000001000000000 };
|
||||
// Order of Bob's subgroup
|
||||
const uint64_t Bob_order[NWORDS64_ORDER] = { 0xF7313736F604054B, 0x73BF54225DF4970C, 0xA88B90FFE719AEC9, 0xD6CEB3C8E40E474D, 0x7671708CF9A0E279, 0x00000000001B39F9 };
|
||||
// Alice's generator values {XPA0 + XPA1*i, XQA0 + XQA1*i, XRA0 + XRA1*i} in GF(p697^2), expressed in Montgomery representation
|
||||
const uint64_t A_gen[6*NWORDS64_FIELD] = { 0xAED913E7D94626F9, 0x6F163E13CE243B16, 0x63211BC832B204DD, 0x35C03D027DA18195, 0x4AC8AE5E92D9A2E0, 0x7901C981FA69E5F6,
|
||||
0xDC074593C4951783, 0xE039A85DA8C4CCCB, 0x238709FB5A391A27, 0x81C303327E8FDA3A, 0x000F36173BC9782E, // XPA0
|
||||
0x266F82DA9F627219, 0xC25C277AD1F10869, 0x947D3148A5C130AB, 0xFC5142FE8F622A88, 0xB5F69FFF2BA5CDB9, 0xA5B6DC9C5B5A65E9,
|
||||
0xD1B526E7169AC83E, 0x0DAD5BA3BDB5F30D, 0xAF70A90042BC2A5E, 0xE55389C1D5AC115F, 0x012EFF54E3702B19, // XPA1
|
||||
0x4C987E2710131A53, 0xC85EBC0B6964FC4E, 0x01064AF42ED201FE, 0x6C7F56903B372893, 0x70D22E68DEE9FB6E, 0x41DBA2F20C3FF934,
|
||||
0x741E3BC447063D35, 0x830A5DA2BB4C3381, 0x1896BD7E957480D5, 0x5FF6ABE18016BD72, 0x015B3A13274C3A5E, // XQA0
|
||||
0xAB9DA605058DB5BD, 0x676326751136B419, 0xA012ED1457E7A8FB, 0x4D2C99E2BCBDBCBF, 0x847DAAAB8AF49694, 0x57E4A8EBEE16077A,
|
||||
0x253098F5145E024F, 0x2834FA2027602D7E, 0x67370BF01ECA39F5, 0xFD1988310BD8B371, 0x006E1C1994AAE711, // XQA1
|
||||
0x388557F6D513BA2E, 0x985FC6241AF2D870, 0xAB4A1A0CB162217E, 0xEFE329C716283B0C, 0x1B8A160873A72DF3, 0xE788A8E93CE9A2BF,
|
||||
0x9208D779576BE635, 0x9F01542376C9CF14, 0xB4C147E4C823B27B, 0x14EBA3D4E36220A2, 0x00B5E9F1B8C6EB1F, // XRA0
|
||||
0x56DA90C58CF6CF46, 0x81618C6931E0A49F, 0xE85EDF7AAA8E245E, 0x3EFAADBA6C218FE5, 0x070BC4D671757F0A, 0x33E57D453747A238,
|
||||
0xA1DE9DC8B2194C11, 0xD5C01615A266F9F3, 0x1FD965E5FB51C6F5, 0x86EA60BF172F4F54, 0x1568A2478263BE4 }; // XRA1
|
||||
// Bob's generator values {XPB0, XQB0, XRB0 + XRB1*i} in GF(p697^2), expressed in Montgomery representation
|
||||
const uint64_t B_gen[6*NWORDS64_FIELD] = { 0x17004B45D6CD5264, 0x2120CCAD6F2560B1, 0x2037B4FC92D82662, 0x64A1CA7B3198E4F9, 0xA049034AC1A0019A, 0xA78FDEEA1525EFC7,
|
||||
0x1235E926EB190D51, 0x20808D93DDDEB13D, 0x4EE5F74BFA19F9E7, 0xB6325316EE6D75DD, 0x016E69166BA0015E, // XPB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XPB1
|
||||
0x6BE584AC7B4EB4F9, 0xF80F2AD8BBBEED51, 0x3681798875177782, 0x50D3F6C3774A2F09, 0xFF3C23A377640B8D, 0x6033D3DF5745A962,
|
||||
0x2FF24E14C9699274, 0x83DA36836A97EB83, 0x25C8EF44B73BD1CD, 0x712062DF86ADEF09, 0x004CF039055BDB65, // XQB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XQB1
|
||||
0x94D7DFC81C1E72E5, 0xE43215CB25F12508, 0x05C2FA2D3F4AE2F9, 0xBB0752FE5CE1746B, 0xA780994FB878A14B, 0x15F6979E08C55016,
|
||||
0xE520E266C3B11912, 0xA857D0496B40DA30, 0xEBACFFF0FDFA0DD2, 0x4C84A4D2485B1E15, 0x00A4F1A9A018A254, // XRB0
|
||||
0x49940C6C65957574, 0xC475B85CD816F0A5, 0x52F4C5971D1E4573, 0xE695F0CD74372CBD, 0x53BC43AA1AFA579E, 0xE02CD95D4A267AE6,
|
||||
0x7B96626EBA6A4ECB, 0xF5E38B098E29F8D0, 0xEAED32068F11ACB9, 0xAFF1F42532675E47, 0x0078655255FA5626 }; // XRB1
|
||||
// Montgomery constant Montgomery_R2 = (2^704)^2 mod p697
|
||||
const uint64_t Montgomery_R2[NWORDS64_FIELD] = { 0x90E8717898EB005C, 0x1DF9EB2CE3B0E597, 0x70EDDE1C2495B71C, 0x441E14E451B09CBC, 0x362ACF49015E62FF, 0x139D92FB72D960C4,
|
||||
0x7840FBE341B9CCE6, 0xFC3D2E62C11AEF2F, 0xE8053C8FF2621C9B, 0x7D2E06601F8D8373, 0x01634C22A8B7316F };
|
||||
// Value one in Montgomery representation
|
||||
const uint64_t Montgomery_one[NWORDS64_FIELD] = { 0x0000000000000096, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x9A4E60E000000000,
|
||||
0x2AF7E672929A5CBD, 0x6F395F62DE4B3DCF, 0xFA2387F3E390A0E9, 0xBBB4C9C22E2A84A5, 0x00C07D499880D65B };
|
||||
|
||||
|
||||
// Fixed parameters for isogeny tree computation
|
||||
const unsigned int strat_Alice[MAX_Alice-1] = {
|
||||
72, 48, 27, 15, 8, 4, 2, 1, 1, 2, 1, 1,
|
||||
4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 12, 7, 4, 2, 1,
|
||||
1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 21, 12, 7, 4, 2,
|
||||
1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 9, 5, 3, 2, 1,
|
||||
1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 33, 17, 9, 5, 4, 2, 1, 1, 2, 1, 1,
|
||||
2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1,
|
||||
1, 16, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1,
|
||||
4, 2, 1, 1, 2, 1, 1 };
|
||||
|
||||
const unsigned int strat_Bob[MAX_Bob-1] = {
|
||||
109, 58, 27, 12, 5, 2, 1, 1, 3, 1, 2, 1,
|
||||
7, 3, 1, 2, 1, 4, 2, 1, 2, 1, 1, 15, 7, 3, 1, 2, 1, 4, 2, 1, 2, 1, 1, 8, 4, 2,
|
||||
1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 31, 15, 7, 3, 1, 2, 1, 4, 2, 1, 2, 1, 1, 8, 4,
|
||||
2, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1,
|
||||
1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 58, 27, 12, 7, 3, 1, 2, 1, 4, 2,
|
||||
1, 2, 1, 1, 7, 3, 1, 2, 1, 4, 2, 1, 2, 1, 1, 15, 7, 3, 1, 2, 1, 4, 2, 1, 2, 1,
|
||||
1, 8, 4, 2, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 31, 15, 7, 3, 1, 2, 1, 4, 2, 1, 2,
|
||||
1, 1, 8, 4, 2, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 2, 1, 1, 4, 2,
|
||||
1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1 };
|
||||
|
||||
// Setting up macro defines and including GF(p), GF(p^2), curve, isogeny and kex functions
|
||||
#define fpcopy fpcopy697
|
||||
#define fpzero fpzero697
|
||||
#define fpadd fpadd697
|
||||
#define fpsub fpsub697
|
||||
#define fpneg fpneg697
|
||||
#define fpdiv2 fpdiv2_697
|
||||
#define fpcorrection fpcorrection697
|
||||
#define fpmul_mont fpmul697_mont
|
||||
#define fpsqr_mont fpsqr697_mont
|
||||
#define fpinv_mont fpinv697_mont
|
||||
#define fpinv_chain_mont fpinv697_chain_mont
|
||||
#define fp2copy fp2copy697
|
||||
#define fp2zero fp2zero697
|
||||
#define fp2add fp2add697
|
||||
#define fp2sub fp2sub697
|
||||
#define mp_sub_p2 mp_sub697_p2
|
||||
#define mp_sub_p4 mp_sub697_p4
|
||||
#define sub_p4 mp_sub_p4
|
||||
#define fp2neg fp2neg697
|
||||
#define fp2div2 fp2div2_697
|
||||
#define fp2correction fp2correction697
|
||||
#define fp2mul_mont fp2mul697_mont
|
||||
#define fp2sqr_mont fp2sqr697_mont
|
||||
#define fp2inv_mont fp2inv697_mont
|
||||
#define fp2inv_mont_ct fp2inv697_mont_ct
|
||||
#define fp2inv_mont_bingcd fp2inv697_mont_bingcd
|
||||
#define mp_add_asm mp_add697_asm
|
||||
#define mp_subaddx2_asm mp_subadd697x2_asm
|
||||
#define mp_dblsubx2_asm mp_dblsub697x2_asm
|
||||
#define crypto_kem_keypair crypto_kem_keypair_SIKEp697
|
||||
#define crypto_kem_enc crypto_kem_enc_SIKEp697
|
||||
#define crypto_kem_dec crypto_kem_dec_SIKEp697
|
||||
#define random_mod_order_A random_mod_order_A_SIDHp697
|
||||
#define random_mod_order_B random_mod_order_B_SIDHp697
|
||||
#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp697
|
||||
#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp697
|
||||
#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp697
|
||||
#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp697
|
||||
|
||||
#include "../fpx.c"
|
||||
#include "../ec_isogeny.c"
|
||||
#include "../sidh.c"
|
||||
#include "../sike.c"
|
||||
|
|
@ -0,0 +1,112 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: API header file for P697
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P697_API_H
|
||||
#define P697_API_H
|
||||
|
||||
|
||||
/*********************** Key encapsulation mechanism API ***********************/
|
||||
|
||||
#define CRYPTO_SECRETKEYBYTES 603 // MSG_BYTES + SECRETKEY_B_BYTES + CRYPTO_PUBLICKEYBYTES bytes
|
||||
#define CRYPTO_PUBLICKEYBYTES 528
|
||||
#define CRYPTO_BYTES 32
|
||||
#define CRYPTO_CIPHERTEXTBYTES 560 // CRYPTO_PUBLICKEYBYTES + MSG_BYTES bytes
|
||||
|
||||
// Algorithm name
|
||||
#define CRYPTO_ALGNAME "SIKEp697"
|
||||
|
||||
// SIKE's key generation
|
||||
// It produces a private key sk and computes the public key pk.
|
||||
// Outputs: secret key sk (CRYPTO_SECRETKEYBYTES = 603 bytes)
|
||||
// public key pk (CRYPTO_PUBLICKEYBYTES = 528 bytes)
|
||||
int crypto_kem_keypair_SIKEp697(unsigned char *pk, unsigned char *sk);
|
||||
|
||||
// SIKE's encapsulation
|
||||
// Input: public key pk (CRYPTO_PUBLICKEYBYTES = 528 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 32 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 560 bytes)
|
||||
int crypto_kem_enc_SIKEp697(unsigned char *ct, unsigned char *ss, const unsigned char *pk);
|
||||
|
||||
// SIKE's decapsulation
|
||||
// Input: secret key sk (CRYPTO_SECRETKEYBYTES = 603 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 560 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 32 bytes)
|
||||
int crypto_kem_dec_SIKEp697(unsigned char *ss, const unsigned char *ct, const unsigned char *sk);
|
||||
|
||||
|
||||
// Encoding of keys for KEM-based isogeny system "SIKEp697" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p697) are encoded in 63 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p697^2), where a and b are defined over GF(p697), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys sk consist of the concatenation of a 32-byte random value, a value in the range [0, 2^Floor(Log(2,3^215))-1] and the public key pk. In the SIKE API,
|
||||
// private keys are encoded in 603 octets in little endian format.
|
||||
// Public keys pk consist of 3 elements in GF(p697^2). In the SIKE API, pk is encoded in 528 octets.
|
||||
// Ciphertexts ct consist of the concatenation of a public key value and a 32-byte value. In the SIKE API, ct is encoded in 528 + 32 = 560 octets.
|
||||
// Shared keys ss consist of a value of 32 octets.
|
||||
|
||||
|
||||
/*********************** Ephemeral key exchange API ***********************/
|
||||
|
||||
#define SIDH_SECRETKEYBYTES_A 45
|
||||
#define SIDH_SECRETKEYBYTES_B 43
|
||||
#define SIDH_PUBLICKEYBYTES 528
|
||||
#define SIDH_BYTES 176
|
||||
|
||||
// SECURITY NOTE: SIDH supports ephemeral Diffie-Hellman key exchange. It is NOT secure to use it with static keys.
|
||||
// See "On the Security of Supersingular Isogeny Cryptosystems", S.D. Galbraith, C. Petit, B. Shani and Y.B. Ti, in ASIACRYPT 2016, 2016.
|
||||
// Extended version available at: http://eprint.iacr.org/2016/859
|
||||
|
||||
// Generation of Alice's secret key
|
||||
// Outputs random value in [0, 2^356 - 1] to be used as Alice's private key
|
||||
void random_mod_order_A_SIDHp697(unsigned char* random_digits);
|
||||
|
||||
// Generation of Bob's secret key
|
||||
// Outputs random value in [0, 2^Floor(Log(2,3^215)) - 1] to be used as Bob's private key
|
||||
void random_mod_order_B_SIDHp697(unsigned char* random_digits);
|
||||
|
||||
// Alice's ephemeral public key generation
|
||||
// Input: a private key PrivateKeyA in the range [0, 2^356 - 1], stored in 45 bytes.
|
||||
// Output: the public key PublicKeyA consisting of 3 GF(p697^2) elements encoded in 528 bytes.
|
||||
int EphemeralKeyGeneration_A_SIDHp697(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA);
|
||||
|
||||
// Bob's ephemeral key-pair generation
|
||||
// It produces a private key PrivateKeyB and computes the public key PublicKeyB.
|
||||
// The private key is an integer in the range [0, 2^Floor(Log(2,3^215)) - 1], stored in 43 bytes.
|
||||
// The public key consists of 3 GF(p697^2) elements encoded in 528 bytes.
|
||||
int EphemeralKeyGeneration_B_SIDHp697(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB);
|
||||
|
||||
// Alice's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB
|
||||
// Inputs: Alice's PrivateKeyA is an integer in the range [0, 2^356 - 1], stored in 45 bytes.
|
||||
// Bob's PublicKeyB consists of 3 GF(p697^2) elements encoded in 528 bytes.
|
||||
// Output: a shared secret SharedSecretA that consists of one element in GF(p697^2) encoded in 176 bytes.
|
||||
int EphemeralSecretAgreement_A_SIDHp697(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA);
|
||||
|
||||
// Bob's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA
|
||||
// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,3^215)) - 1], stored in 43 bytes.
|
||||
// Alice's PublicKeyA consists of 3 GF(p697^2) elements encoded in 528 bytes.
|
||||
// Output: a shared secret SharedSecretB that consists of one element in GF(p697^2) encoded in 176 bytes.
|
||||
int EphemeralSecretAgreement_B_SIDHp697(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB);
|
||||
|
||||
|
||||
// Encoding of keys for KEX-based isogeny system "SIDHp697" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p697) are encoded in 63 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p697^2), where a and b are defined over GF(p697), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys PrivateKeyA and PrivateKeyB can have values in the range [0, 2^356-1] and [0, 2^Floor(Log(2,3^215)) - 1], resp. In the SIDH API,
|
||||
// Alice's and Bob's private keys are encoded in 45 and 43 octets, resp., in little endian format.
|
||||
// Public keys PublicKeyA and PublicKeyB consist of 3 elements in GF(p697^2). In the SIDH API, they are encoded in 528 octets.
|
||||
// Shared keys SharedSecretA and SharedSecretB consist of one element in GF(p697^2). In the SIDH API, they are encoded in 176 octets.
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,175 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: internal header file for P697
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P697_INTERNAL_H
|
||||
#define P697_INTERNAL_H
|
||||
|
||||
#include "../config.h"
|
||||
|
||||
|
||||
#if (TARGET == TARGET_AMD64) || (TARGET == TARGET_ARM64)
|
||||
#define NWORDS_FIELD 11 // Number of words of a 697-bit field element
|
||||
#define p697_ZERO_WORDS 5 // Number of "0" digits in the least significant part of p697 + 1
|
||||
#elif (TARGET == TARGET_x86)
|
||||
#define NWORDS_FIELD 22
|
||||
#define p697_ZERO_WORDS 11
|
||||
#endif
|
||||
|
||||
|
||||
// Basic constants
|
||||
|
||||
#define NBITS_FIELD 697
|
||||
#define MAXBITS_FIELD 704
|
||||
#define MAXWORDS_FIELD ((MAXBITS_FIELD+RADIX-1)/RADIX) // Max. number of words to represent field elements
|
||||
#define NWORDS64_FIELD ((NBITS_FIELD+63)/64) // Number of 64-bit words of a 697-bit field element
|
||||
#define NBITS_ORDER 384
|
||||
#define NWORDS_ORDER ((NBITS_ORDER+RADIX-1)/RADIX) // Number of words of oA and oB, where oA and oB are the subgroup orders of Alice and Bob, resp.
|
||||
#define NWORDS64_ORDER ((NBITS_ORDER+63)/64) // Number of 64-bit words of a 256-bit element
|
||||
#define MAXBITS_ORDER NBITS_ORDER
|
||||
#define ALICE 0
|
||||
#define BOB 1
|
||||
#define OALICE_BITS 356
|
||||
#define OBOB_BITS 341
|
||||
#define OBOB_EXPON 215
|
||||
#define MASK_ALICE 0x0F
|
||||
#define MASK_BOB 0x0F
|
||||
#define PRIME p697
|
||||
#define PARAM_A 6
|
||||
#define PARAM_C 1
|
||||
// Fixed parameters for isogeny tree computation
|
||||
#define MAX_INT_POINTS_ALICE 8
|
||||
#define MAX_INT_POINTS_BOB 9
|
||||
#define MAX_Alice 178
|
||||
#define MAX_Bob 215
|
||||
#define MSG_BYTES 32
|
||||
#define SECRETKEY_A_BYTES ((OALICE_BITS + 7) / 8)
|
||||
#define SECRETKEY_B_BYTES ((OBOB_BITS - 1 + 7) / 8)
|
||||
#define FP2_ENCODED_BYTES 2*((NBITS_FIELD + 7) / 8)
|
||||
|
||||
|
||||
// SIDH's basic element definitions and point representations
|
||||
|
||||
typedef digit_t felm_t[NWORDS_FIELD]; // Datatype for representing 697-bit field elements (704-bit max.)
|
||||
typedef digit_t dfelm_t[2*NWORDS_FIELD]; // Datatype for representing double-precision 2x697-bit field elements (2x704-bit max.)
|
||||
typedef felm_t f2elm_t[2]; // Datatype for representing quadratic extension field elements GF(p697^2)
|
||||
|
||||
typedef struct { f2elm_t X; f2elm_t Z; } point_proj; // Point representation in projective XZ Montgomery coordinates.
|
||||
typedef point_proj point_proj_t[1];
|
||||
|
||||
#ifdef COMPRESS
|
||||
typedef struct { f2elm_t X; f2elm_t Y; f2elm_t Z; } point_full_proj; // Point representation in full projective XYZ Montgomery coordinates
|
||||
typedef point_full_proj point_full_proj_t[1];
|
||||
|
||||
typedef struct { f2elm_t x; f2elm_t y; } point_affine; // Point representation in affine coordinates.
|
||||
typedef point_affine point_t[1];
|
||||
|
||||
typedef f2elm_t publickey_t[3];
|
||||
#endif
|
||||
|
||||
|
||||
|
||||
/**************** Function prototypes ****************/
|
||||
/************* Multiprecision functions **************/
|
||||
|
||||
// 697-bit multiprecision addition, c = a+b
|
||||
void mp_add697(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_add697_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 697-bit multiprecision subtraction, c = a-b+2p or c = a-b+4p
|
||||
extern void mp_sub697_p2(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void mp_sub697_p4(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub697_p2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub697_p4_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 2x697-bit multiprecision subtraction followed by addition with p697*2^704, c = a-b+(p697*2^704) if a-b < 0, otherwise c=a-b
|
||||
void mp_subaddx2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_subadd697x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Double 2x697-bit multiprecision subtraction, c = c-a-b, where c > a and c > b
|
||||
void mp_dblsub697x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
/************ Field arithmetic functions *************/
|
||||
|
||||
// Copy of a field element, c = a
|
||||
void fpcopy697(const digit_t* a, digit_t* c);
|
||||
|
||||
// Zeroing a field element, a = 0
|
||||
void fpzero697(digit_t* a);
|
||||
|
||||
// Non constant-time comparison of two field elements. If a = b return TRUE, otherwise, return FALSE
|
||||
bool fpequal697_non_constant_time(const digit_t* a, const digit_t* b);
|
||||
|
||||
// Modular addition, c = a+b mod p697
|
||||
extern void fpadd697(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpadd697_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular subtraction, c = a-b mod p697
|
||||
extern void fpsub697(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpsub697_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular negation, a = -a mod p697
|
||||
extern void fpneg697(digit_t* a);
|
||||
|
||||
// Modular division by two, c = a/2 mod p697.
|
||||
void fpdiv2_697(const digit_t* a, digit_t* c);
|
||||
|
||||
// Modular correction to reduce field element a in [0, 2*p697-1] to [0, p697-1].
|
||||
void fpcorrection697(digit_t* a);
|
||||
|
||||
// 697-bit Montgomery reduction, c = a mod p
|
||||
void rdc697_asm(digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field multiplication using Montgomery arithmetic, c = a*b*R^-1 mod p697, where R=2^768
|
||||
void fpmul697_mont(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mul697_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Field squaring using Montgomery arithmetic, c = a*b*R^-1 mod p697, where R=2^768
|
||||
void fpsqr697_mont(const digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field inversion, a = a^-1 in GF(p697)
|
||||
void fpinv697_mont(digit_t* a);
|
||||
|
||||
// Chain to compute (p697-3)/4 using Montgomery arithmetic
|
||||
void fpinv697_chain_mont(digit_t* a);
|
||||
|
||||
/************ GF(p^2) arithmetic functions *************/
|
||||
|
||||
// Copy of a GF(p697^2) element, c = a
|
||||
void fp2copy697(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Zeroing a GF(p697^2) element, a = 0
|
||||
void fp2zero697(f2elm_t a);
|
||||
|
||||
// GF(p697^2) negation, a = -a in GF(p697^2)
|
||||
void fp2neg697(f2elm_t a);
|
||||
|
||||
// GF(p697^2) addition, c = a+b in GF(p697^2)
|
||||
extern void fp2add697(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p697^2) subtraction, c = a-b in GF(p697^2)
|
||||
extern void fp2sub697(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p697^2) division by two, c = a/2 in GF(p697^2)
|
||||
void fp2div2_697(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Modular correction, a = a in GF(p697^2)
|
||||
void fp2correction697(f2elm_t a);
|
||||
|
||||
// GF(p697^2) squaring using Montgomery arithmetic, c = a^2 in GF(p697^2)
|
||||
void fp2sqr697_mont(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// GF(p697^2) multiplication using Montgomery arithmetic, c = a*b in GF(p697^2)
|
||||
void fp2mul697_mont(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p697^2) inversion using Montgomery arithmetic, a = (a0-i*a1)/(a0^2+a1^2)
|
||||
void fp2inv697_mont(f2elm_t a);
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,259 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: portable modular arithmetic for P697
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P697_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p697[NWORDS64_FIELD];
|
||||
extern const uint64_t p697p1[NWORDS64_FIELD];
|
||||
extern const uint64_t p697x2[NWORDS64_FIELD];
|
||||
extern const uint64_t p697x4[NWORDS64_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub697_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p697x2)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub697_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p697x4)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd697(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p697.
|
||||
// Inputs: a, b in [0, 2*p697-1]
|
||||
// Output: c in [0, 2*p697-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p697x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p697x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub697(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p697.
|
||||
// Inputs: a, b in [0, 2*p697-1]
|
||||
// Output: c in [0, 2*p697-1]
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p697x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg697(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p697.
|
||||
// Input/output: a in [0, 2*p697-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p697x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_697(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p697.
|
||||
// Input : a in [0, 2*p697-1]
|
||||
// Output: c in [0, 2*p697-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p697
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p697)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection697(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p697-1] to [0, p697-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p697)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p697)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void digit_x_digit(const digit_t a, const digit_t b, digit_t* c)
|
||||
{ // Digit multiplication, digit * digit -> 2-digit result
|
||||
register digit_t al, ah, bl, bh, temp;
|
||||
digit_t albl, albh, ahbl, ahbh, res1, res2, res3, carry;
|
||||
digit_t mask_low = (digit_t)(-1) >> (sizeof(digit_t)*4), mask_high = (digit_t)(-1) << (sizeof(digit_t)*4);
|
||||
|
||||
al = a & mask_low; // Low part
|
||||
ah = a >> (sizeof(digit_t) * 4); // High part
|
||||
bl = b & mask_low;
|
||||
bh = b >> (sizeof(digit_t) * 4);
|
||||
|
||||
albl = al*bl;
|
||||
albh = al*bh;
|
||||
ahbl = ah*bl;
|
||||
ahbh = ah*bh;
|
||||
c[0] = albl & mask_low; // C00
|
||||
|
||||
res1 = albl >> (sizeof(digit_t) * 4);
|
||||
res2 = ahbl & mask_low;
|
||||
res3 = albh & mask_low;
|
||||
temp = res1 + res2 + res3;
|
||||
carry = temp >> (sizeof(digit_t) * 4);
|
||||
c[0] ^= temp << (sizeof(digit_t) * 4); // C01
|
||||
|
||||
res1 = ahbl >> (sizeof(digit_t) * 4);
|
||||
res2 = albh >> (sizeof(digit_t) * 4);
|
||||
res3 = ahbh & mask_low;
|
||||
temp = res1 + res2 + res3 + carry;
|
||||
c[1] = temp & mask_low; // C10
|
||||
carry = temp & mask_high;
|
||||
c[1] ^= (ahbh & mask_high) + carry; // C11
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
unsigned int i, j;
|
||||
digit_t t = 0, u = 0, v = 0, UV[2];
|
||||
unsigned int carry = 0;
|
||||
|
||||
for (i = 0; i < nwords; i++) {
|
||||
for (j = 0; j <= i; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = nwords; i < 2*nwords-1; i++) {
|
||||
for (j = i-nwords+1; j < nwords; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
c[2*nwords-1] = v;
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Efficient Montgomery reduction using comba and exploiting the special form of the prime p697.
|
||||
// mc = ma*R^-1 mod p697x2, where R = 2^704.
|
||||
// If ma < 2^704*p697, the output mc is in the range [0, 2*p697-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
unsigned int i, j, carry, count = p697_ZERO_WORDS;
|
||||
digit_t UV[2], t = 0, u = 0, v = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
mc[i] = 0;
|
||||
}
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
for (j = 0; j < i; j++) {
|
||||
if (j < (i-p697_ZERO_WORDS+1)) {
|
||||
MUL(mc[j], ((digit_t*)p697p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = NWORDS_FIELD; i < 2*NWORDS_FIELD-1; i++) {
|
||||
if (count > 0) {
|
||||
count -= 1;
|
||||
}
|
||||
for (j = i-NWORDS_FIELD+1; j < NWORDS_FIELD; j++) {
|
||||
if (j < (NWORDS_FIELD-count)) {
|
||||
MUL(mc[j], ((digit_t*)p697p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i-NWORDS_FIELD] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
ADDC(0, v, ma[2*NWORDS_FIELD-1], carry, v);
|
||||
mc[NWORDS_FIELD-1] = v;
|
||||
}
|
||||
|
|
@ -0,0 +1,910 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: modular arithmetic optimized for x64 platforms for P751
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P751_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p751[NWORDS_FIELD];
|
||||
extern const uint64_t p751p1[NWORDS_FIELD];
|
||||
extern const uint64_t p751x2[NWORDS_FIELD];
|
||||
extern const uint64_t p751x4[NWORDS_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub751_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p751x2)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub751_p2_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub751_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p751x4)[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mp_sub751_p4_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd751(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p751.
|
||||
// Inputs: a, b in [0, 2*p751-1]
|
||||
// Output: c in [0, 2*p751-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p751x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p751x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpadd751_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub751(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p751.
|
||||
// Inputs: a, b in [0, 2*p751-1]
|
||||
// Output: c in [0, 2*p751-1]
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p751x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
fpsub751_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg751(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p751.
|
||||
// Input/output: a in [0, 2*p751-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p751x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_751(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p751.
|
||||
// Input : a in [0, 2*p751-1]
|
||||
// Output: c in [0, 2*p751-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p751
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p751)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection751(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p751-1] to [0, p751-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p751)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p751)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
|
||||
(void)nwords;
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
unsigned int carry = 0;
|
||||
|
||||
MULADD128(a[0], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[8] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[9] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[10], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[10] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[0], b[11], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[10], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[1], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[11], b[0], uv, carry, uv);
|
||||
t += carry;
|
||||
c[11] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[1], b[11], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[10], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[11], b[1], uv, carry, uv);
|
||||
t += carry;
|
||||
c[12] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[11], b[2], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[10], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[2], b[11], uv, carry, uv);
|
||||
t += carry;
|
||||
c[13] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[11], b[3], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[10], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[3], b[11], uv, carry, uv);
|
||||
t += carry;
|
||||
c[14] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[11], b[4], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[10], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[4], b[11], uv, carry, uv);
|
||||
t += carry;
|
||||
c[15] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[11], b[5], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[10], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[5], b[11], uv, carry, uv);
|
||||
t += carry;
|
||||
c[16] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[11], b[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[10], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[6], b[11], uv, carry, uv);
|
||||
t += carry;
|
||||
c[17] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[11], b[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[10], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[7], b[11], uv, carry, uv);
|
||||
t += carry;
|
||||
c[18] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[11], b[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[10], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[8], b[11], uv, carry, uv);
|
||||
t += carry;
|
||||
c[19] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[11], b[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[10], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[9], b[11], uv, carry, uv);
|
||||
t += carry;
|
||||
c[20] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(a[11], b[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(a[10], b[11], uv, carry, uv);
|
||||
t += carry;
|
||||
c[21] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
|
||||
MULADD128(a[11], b[11], uv, carry, uv);
|
||||
c[22] = uv[0];
|
||||
c[23] = uv[1];
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
mul751_asm(a, b, c);
|
||||
|
||||
#endif
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Montgomery reduction exploiting special form of the prime.
|
||||
// mc = ma*R^-1 mod p751x2, where R = 2^768.
|
||||
// If ma < 2^768*p751, the output mc is in the range [0, 2*p751-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
|
||||
#if (OS_TARGET == OS_WIN)
|
||||
unsigned int carry;
|
||||
digit_t t = 0;
|
||||
uint128_t uv = {0};
|
||||
|
||||
mc[0] = ma[0];
|
||||
mc[1] = ma[1];
|
||||
mc[2] = ma[2];
|
||||
mc[3] = ma[3];
|
||||
mc[4] = ma[4];
|
||||
MUL128(mc[0], ((digit_t*)p751p1)[5], uv);
|
||||
ADDC(0, uv[0], ma[5], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
mc[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p751p1)[6], uv, carry, uv);
|
||||
MULADD128(mc[1], ((digit_t*)p751p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[6], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p751p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p751p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p751p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[7], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p751p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p751p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p751p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p751p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[8], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[8] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p751p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p751p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p751p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p751p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p751p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[9], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[9] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p751p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p751p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p751p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p751p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p751p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p751p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[10], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[10] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[0], ((digit_t*)p751p1)[11], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[1], ((digit_t*)p751p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p751p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p751p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p751p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p751p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p751p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[11], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[11] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[1], ((digit_t*)p751p1)[11], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[2], ((digit_t*)p751p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p751p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p751p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p751p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p751p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p751p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[12], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[0] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[2], ((digit_t*)p751p1)[11], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[3], ((digit_t*)p751p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p751p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p751p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p751p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p751p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p751p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[13], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[1] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[3], ((digit_t*)p751p1)[11], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[4], ((digit_t*)p751p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p751p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p751p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p751p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p751p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p751p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[14], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[2] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[4], ((digit_t*)p751p1)[11], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[5], ((digit_t*)p751p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p751p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p751p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p751p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p751p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[10], ((digit_t*)p751p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[15], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[3] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[5], ((digit_t*)p751p1)[11], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[6], ((digit_t*)p751p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p751p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p751p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p751p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[10], ((digit_t*)p751p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[11], ((digit_t*)p751p1)[5], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[16], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[4] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[6], ((digit_t*)p751p1)[11], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[7], ((digit_t*)p751p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p751p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p751p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[10], ((digit_t*)p751p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[11], ((digit_t*)p751p1)[6], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[17], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[5] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[7], ((digit_t*)p751p1)[11], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[8], ((digit_t*)p751p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p751p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[10], ((digit_t*)p751p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[11], ((digit_t*)p751p1)[7], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[18], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[6] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[8], ((digit_t*)p751p1)[11], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[9], ((digit_t*)p751p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[10], ((digit_t*)p751p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[11], ((digit_t*)p751p1)[8], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[19], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[7] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[9], ((digit_t*)p751p1)[11], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[10], ((digit_t*)p751p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[11], ((digit_t*)p751p1)[9], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[20], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[8] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[10], ((digit_t*)p751p1)[11], uv, carry, uv);
|
||||
t += carry;
|
||||
MULADD128(mc[11], ((digit_t*)p751p1)[10], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[21], carry, uv[0]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
t += carry;
|
||||
mc[9] = uv[0];
|
||||
uv[0] = uv[1];
|
||||
uv[1] = t;
|
||||
t = 0;
|
||||
|
||||
MULADD128(mc[11], ((digit_t*)p751p1)[11], uv, carry, uv);
|
||||
t += carry;
|
||||
ADDC(0, uv[0], ma[22], carry, mc[10]);
|
||||
ADDC(carry, uv[1], 0, carry, uv[1]);
|
||||
ADDC(0, uv[1], ma[23], carry, mc[11]);
|
||||
|
||||
#elif (OS_TARGET == OS_LINUX)
|
||||
|
||||
rdc751_asm(ma, mc);
|
||||
|
||||
#endif
|
||||
}
|
||||
Разница между файлами не показана из-за своего большого размера
Загрузить разницу
|
|
@ -0,0 +1,142 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: supersingular isogeny parameters and generation of functions for P751
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "P751_api.h"
|
||||
#include "P751_internal.h"
|
||||
#include "../internal.h"
|
||||
|
||||
|
||||
// Encoding of field elements, elements over Z_order, elements over GF(p^2) and elliptic curve points:
|
||||
// --------------------------------------------------------------------------------------------------
|
||||
// Elements over GF(p) and Z_order are encoded with the least significant octet (and digit) located at the leftmost position (i.e., little endian format).
|
||||
// Elements (a+b*i) over GF(p^2), where a and b are defined over GF(p), are encoded as {a, b}, with a in the least significant position.
|
||||
// Elliptic curve points P = (x,y) are encoded as {x, y}, with x in the least significant position.
|
||||
// Internally, the number of digits used to represent all these elements is obtained by approximating the number of bits to the immediately greater multiple of 32.
|
||||
// For example, a 751-bit field element is represented with Ceil(751 / 64) = 12 64-bit digits or Ceil(751 / 32) = 24 32-bit digits.
|
||||
|
||||
//
|
||||
// Curve isogeny system "SIDHp751". Base curve: Montgomery curve By^2 = Cx^3 + Ax^2 + Cx defined over GF(p751^2), where A=6, B=1, C=1 and p751 = 2^372*3^239-1
|
||||
//
|
||||
|
||||
const uint64_t p751[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xEEAFFFFFFFFFFFFF,
|
||||
0xE3EC968549F878A8, 0xDA959B1A13F7CC76, 0x084E9867D6EBE876, 0x8562B5045CB25748, 0x0E12909F97BADC66, 0x00006FE5D541F71C };
|
||||
const uint64_t p751p1[NWORDS64_FIELD] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xEEB0000000000000,
|
||||
0xE3EC968549F878A8, 0xDA959B1A13F7CC76, 0x084E9867D6EBE876, 0x8562B5045CB25748, 0x0E12909F97BADC66, 0x00006FE5D541F71C };
|
||||
const uint64_t p751x2[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xDD5FFFFFFFFFFFFF,
|
||||
0xC7D92D0A93F0F151, 0xB52B363427EF98ED, 0x109D30CFADD7D0ED, 0x0AC56A08B964AE90, 0x1C25213F2F75B8CD, 0x0000DFCBAA83EE38 };
|
||||
const uint64_t p751x4[NWORDS64_FIELD] = { 0xFFFFFFFFFFFFFFFC, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xBABFFFFFFFFFFFFF,
|
||||
0x8FB25A1527E1E2A3, 0x6A566C684FDF31DB, 0x213A619F5BAFA1DB, 0x158AD41172C95D20, 0x384A427E5EEB719A, 0x0001BF975507DC70 };
|
||||
const uint64_t p751x16p[2*NWORDS64_FIELD] = { 0x0000000000000010, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x2A00000000000000,
|
||||
0x826D2F56C0F0EAE2, 0xAD4C9CBD81067123, 0xF62CF3052282F124, 0x53A95F7469B516FE, 0x3DADEC0D08A4732F, 0x58AD934557C11C7E,
|
||||
0x7F731B89B2DA43F2, 0x51AE9F5F5F6AFF3B, 0xD74319A6C9BCA375, 0x5BAB790796CF84D4, 0xA421554FE2E49CA8, 0x20AD617C8DF437CF,
|
||||
0x3AB06E7A12F5FF7B, 0x70A25E037E40347E, 0x51F1D323FB4C1151, 0xAE0D99AA4835FED9, 0xDF5429960D2536B6, 0x000000030E91D466 };
|
||||
// Order of Alice's subgroup
|
||||
const uint64_t Alice_order[NWORDS64_ORDER] = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0010000000000000 };
|
||||
// Order of Bob's subgroup
|
||||
const uint64_t Bob_order[NWORDS64_ORDER] = { 0xC968549F878A8EEB, 0x59B1A13F7CC76E3E, 0xE9867D6EBE876DA9, 0x2B5045CB25748084, 0x2909F97BADC66856, 0x06FE5D541F71C0E1 };
|
||||
// Alice's generator values {XPA0 + XPA1*i, XQA0 + xQA1*i, XRA0 + XRA1*i} in GF(p751^2), expressed in Montgomery representation
|
||||
const uint64_t A_gen[6 * NWORDS64_FIELD] = { 0x884F46B74000BAA8, 0xBA52630F939DEC20, 0xC16FB97BA714A04D, 0x082536745B1AB3DB, 0x1117157F446F9E82, 0xD2F27D621A018490,
|
||||
0x6B24AB523D544BCD, 0x9307D6AA2EA85C94, 0xE1A096729528F20F, 0x896446F868F3255C, 0x2401D996B1BFF8A5, 0x00000EF8786A5C0A, // XPA0
|
||||
0xAEB78B3B96F59394, 0xAB26681E29C90B74, 0xE520AC30FDC4ACF1, 0x870AAAE3A4B8111B, 0xF875BDB738D64EFF, 0x50109A7ECD7ED6BC,
|
||||
0x4CC64848FF0C56FB, 0xE617CB6C519102C9, 0x9C74B3835921E609, 0xC91DDAE4A35A7146, 0x7FC82A155C1B9129, 0x0000214FA6B980B3, // XPA1
|
||||
0x0F93CC38680A8CA9, 0x762E733822E7FED7, 0xE549F005AC0ADB67, 0x94A71FDD2C43A4ED, 0xD48645C2B04721C5, 0x432DA1FE4D4CA4DC,
|
||||
0xBC99655FAA7A80E8, 0xB2C6D502BCFD4823, 0xEE92F40CA2EC8BDB, 0x7B074132EFB6D16C, 0x3340B46FA38A7633, 0x0000215749657F6C, // XQA0
|
||||
0xECFF375BF3079F4C, 0xFBFE74B043E80EF3, 0x17376CBE3C5C7AD1, 0xC06327A7E29CDBF2, 0x2111649C438BF3D4, 0xC1F9298261BA2E97,
|
||||
0x1F9FECE869CFD1C2, 0x01A39B4FC9346D62, 0x147CD1D3E82A3C9F, 0xDE84E9D249E533EE, 0x1C48A5ADFB7C578D, 0x000061ACA0B82E1D, // XQA1
|
||||
0x1600C525D41059F1, 0xA596899A0A1D83F7, 0x6BFDEED6D2B23F35, 0x5C7E707270C23910, 0x276CA1A4E8369411, 0xB193651A602925A0,
|
||||
0x243D239F1CA1F04A, 0x543DC6DA457860AD, 0xCDA590F325181DE9, 0xD3AB7ACFDA80B395, 0x6C97468580FDDF7B, 0x0000352A3E5C4C77, // XRA0
|
||||
0x9B794F9FD1CC3EE8, 0xDB32E40A9B2FD23E, 0x26192A2542E42B67, 0xA18E94FCA045BCE7, 0x96DC1BC38E7CDA2D, 0x9A1D91B752487DE2,
|
||||
0xCC63763987436DA3, 0x1316717AACCC551D, 0xC4C368A4632AFE72, 0x4B6EA85C9CCD5710, 0x7A12CAD582C7BC9A, 0x00001C7E240149BF }; // XRA1
|
||||
// Bob's generator values {XPB0, XQB0, XRB0 + XRB1*i} in GF(p751^2), expressed in Montgomery representation
|
||||
const uint64_t B_gen[6 * NWORDS64_FIELD] = { 0x85691AAF4015F88C, 0x7478C5B8C36E9631, 0x7EF2A185DE4DD6E2, 0x943BBEE46BEB9DC7, 0x1A3EC62798792D22, 0x791BC4B084B31D69,
|
||||
0x03DBE6522CEA17C4, 0x04749AA65D665D83, 0x3D52B5C45EF450F3, 0x0B4219848E36947D, 0xA4CF7070466BDE27, 0x0000334B1FA6D193, // XPB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XPB1
|
||||
0x8E7CB3FA53211340, 0xD67CE54F7A05EEE0, 0xFDDC2C8BCE46FC38, 0x08587FAE3110DF1E, 0xD6B8246FA22B058B, 0x4DAC3ACC905A5DBD,
|
||||
0x51D0BF2FADCED3E8, 0xE5A2406DF6484425, 0x907F177584F671B8, 0x4738A2FFCCED051C, 0x2B0067B4177E4853, 0x00002806AC948D3D, // XQB0
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
|
||||
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, // XQB1
|
||||
0xB56457016D1D6D1C, 0x03DECCB38F39C491, 0xDFB910AC8A559452, 0xA9D0F17D1FF24883, 0x8562BBAF515C248C, 0x249B2A6DDB1CB67D,
|
||||
0x3131AF96FB46835C, 0xE10258398480C3E1, 0xEAB5E2B872D4FAB1, 0xB71E63875FAEB1DF, 0xF8384D4F13757CF6, 0x0000361EC9B09912, // XRB0
|
||||
0x58C967899ED16EF4, 0x81998376DC622A4B, 0x3D1C1DCFE0B12681, 0x9347DEBB953E1730, 0x9ABB344D3A82C2D7, 0xE4881BD2820552B2,
|
||||
0x0037247923D90266, 0x2E3156EDB157E5A5, 0xF86A46A7506823F7, 0x8FE5523A7B7F1CFC, 0xFA3CFFA38372F67B, 0x0000692DCE85FFBD }; // XRB1
|
||||
// Montgomery constant Montgomery_R2 = (2^768)^2 mod p751
|
||||
const uint64_t Montgomery_R2[NWORDS64_FIELD] = { 0x233046449DAD4058, 0xDB010161A696452A, 0x5E36941472E3FD8E, 0xF40BFE2082A2E706, 0x4932CCA8904F8751 ,0x1F735F1F1EE7FC81,
|
||||
0xA24F4D80C1048E18, 0xB56C383CCDB607C5, 0x441DD47B735F9C90, 0x5673ED2C6A6AC82A, 0x06C905261132294B, 0x000041AD830F1F35 };
|
||||
// Value one in Montgomery representation
|
||||
const uint64_t Montgomery_one[NWORDS64_FIELD] = { 0x00000000000249ad, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x8310000000000000,
|
||||
0x5527b1e4375c6c66, 0x697797bf3f4f24d0, 0xc89db7b2ac5c4e2e, 0x4ca4b439d2076956, 0x10f7926c7512c7e9, 0x00002d5b24bce5e2 };
|
||||
|
||||
|
||||
// Fixed parameters for isogeny tree computation
|
||||
const unsigned int strat_Alice[MAX_Alice-1] = {
|
||||
80, 48, 27, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1,
|
||||
1, 3, 2, 1, 1, 1, 1, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1,
|
||||
1, 1, 2, 1, 1, 1, 21, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1,
|
||||
1, 1, 1, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1,
|
||||
33, 20, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1,
|
||||
1, 1, 8, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1,
|
||||
1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1 };
|
||||
|
||||
const unsigned int strat_Bob[MAX_Bob-1] = {
|
||||
112, 63, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1,
|
||||
1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2,
|
||||
1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 31, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2,
|
||||
1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4,
|
||||
2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 49, 31, 16, 8, 4, 2,
|
||||
1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1,
|
||||
15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1,
|
||||
1, 1, 1, 21, 12, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 5, 3, 2, 1, 1, 1, 1,
|
||||
2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1 };
|
||||
|
||||
// Setting up macro defines and including GF(p), GF(p^2), curve, isogeny and kex functions
|
||||
#define fpcopy fpcopy751
|
||||
#define fpzero fpzero751
|
||||
#define fpadd fpadd751
|
||||
#define fpsub fpsub751
|
||||
#define fpneg fpneg751
|
||||
#define fpdiv2 fpdiv2_751
|
||||
#define fpcorrection fpcorrection751
|
||||
#define fpmul_mont fpmul751_mont
|
||||
#define fpsqr_mont fpsqr751_mont
|
||||
#define fpinv_mont fpinv751_mont
|
||||
#define fpinv_chain_mont fpinv751_chain_mont
|
||||
#define fp2copy fp2copy751
|
||||
#define fp2zero fp2zero751
|
||||
#define fp2add fp2add751
|
||||
#define fp2sub fp2sub751
|
||||
#define mp_sub_p2 mp_sub751_p2
|
||||
#define mp_sub_p4 mp_sub751_p4
|
||||
#define sub_p4 mp_sub_p4
|
||||
#define fp2neg fp2neg751
|
||||
#define fp2div2 fp2div2_751
|
||||
#define fp2correction fp2correction751
|
||||
#define fp2mul_mont fp2mul751_mont
|
||||
#define fp2sqr_mont fp2sqr751_mont
|
||||
#define fp2inv_mont fp2inv751_mont
|
||||
#define fp2inv_mont_ct fp2inv751_mont_ct
|
||||
#define fp2inv_mont_bingcd fp2inv751_mont_bingcd
|
||||
#define mp_add_asm mp_add751_asm
|
||||
#define mp_subaddx2_asm mp_subadd751x2_asm
|
||||
#define mp_dblsubx2_asm mp_dblsub751x2_asm
|
||||
#define crypto_kem_keypair crypto_kem_keypair_SIKEp751
|
||||
#define crypto_kem_enc crypto_kem_enc_SIKEp751
|
||||
#define crypto_kem_dec crypto_kem_dec_SIKEp751
|
||||
#define random_mod_order_A random_mod_order_A_SIDHp751
|
||||
#define random_mod_order_B random_mod_order_B_SIDHp751
|
||||
#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp751
|
||||
#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp751
|
||||
#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp751
|
||||
#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp751
|
||||
|
||||
#include "../fpx.c"
|
||||
#include "../ec_isogeny.c"
|
||||
#include "../sidh.c"
|
||||
#include "../sike.c"
|
||||
|
|
@ -0,0 +1,112 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: API header file for P751
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P751_API_H
|
||||
#define P751_API_H
|
||||
|
||||
|
||||
/*********************** Key encapsulation mechanism API ***********************/
|
||||
|
||||
#define CRYPTO_SECRETKEYBYTES 644 // MSG_BYTES + SECRETKEY_B_BYTES + CRYPTO_PUBLICKEYBYTES bytes
|
||||
#define CRYPTO_PUBLICKEYBYTES 564
|
||||
#define CRYPTO_BYTES 32
|
||||
#define CRYPTO_CIPHERTEXTBYTES 596 // CRYPTO_PUBLICKEYBYTES + MSG_BYTES bytes
|
||||
|
||||
// Algorithm name
|
||||
#define CRYPTO_ALGNAME "SIKEp751"
|
||||
|
||||
// SIKE's key generation
|
||||
// It produces a private key sk and computes the public key pk.
|
||||
// Outputs: secret key sk (CRYPTO_SECRETKEYBYTES = 644 bytes)
|
||||
// public key pk (CRYPTO_PUBLICKEYBYTES = 564 bytes)
|
||||
int crypto_kem_keypair_SIKEp751(unsigned char *pk, unsigned char *sk);
|
||||
|
||||
// SIKE's encapsulation
|
||||
// Input: public key pk (CRYPTO_PUBLICKEYBYTES = 564 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 32 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 596 bytes)
|
||||
int crypto_kem_enc_SIKEp751(unsigned char *ct, unsigned char *ss, const unsigned char *pk);
|
||||
|
||||
// SIKE's decapsulation
|
||||
// Input: secret key sk (CRYPTO_SECRETKEYBYTES = 644 bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = 596 bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES = 32 bytes)
|
||||
int crypto_kem_dec_SIKEp751(unsigned char *ss, const unsigned char *ct, const unsigned char *sk);
|
||||
|
||||
|
||||
// Encoding of keys for KEM-based isogeny system "SIKEp751" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p751) are encoded in 94 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p751^2), where a and b are defined over GF(p751), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys sk consist of the concatenation of a 32-byte random value, a value in the range [0, 2^Floor(Log(2,3^239))-1] and the public key pk. In the SIKE API,
|
||||
// private keys are encoded in 644 octets in little endian format.
|
||||
// Public keys pk consist of 3 elements in GF(p751^2). In the SIKE API, pk is encoded in 564 octets.
|
||||
// Ciphertexts ct consist of the concatenation of a public key value and a 32-byte value. In the SIKE API, ct is encoded in 564 + 32 = 596 octets.
|
||||
// Shared keys ss consist of a value of 32 octets.
|
||||
|
||||
|
||||
/*********************** Ephemeral key exchange API ***********************/
|
||||
|
||||
#define SIDH_SECRETKEYBYTES_A 47
|
||||
#define SIDH_SECRETKEYBYTES_B 48
|
||||
#define SIDH_PUBLICKEYBYTES 564
|
||||
#define SIDH_BYTES 188
|
||||
|
||||
// SECURITY NOTE: SIDH supports ephemeral Diffie-Hellman key exchange. It is NOT secure to use it with static keys.
|
||||
// See "On the Security of Supersingular Isogeny Cryptosystems", S.D. Galbraith, C. Petit, B. Shani and Y.B. Ti, in ASIACRYPT 2016, 2016.
|
||||
// Extended version available at: http://eprint.iacr.org/2016/859
|
||||
|
||||
// Generation of Alice's secret key
|
||||
// Outputs random value in [0, 2^372 - 1] to be used as Alice's private key
|
||||
void random_mod_order_A_SIDHp751(unsigned char* random_digits);
|
||||
|
||||
// Generation of Bob's secret key
|
||||
// Outputs random value in [0, 2^Floor(Log(2,3^239)) - 1] to be used as Bob's private key
|
||||
void random_mod_order_B_SIDHp751(unsigned char* random_digits);
|
||||
|
||||
// Alice's ephemeral public key generation
|
||||
// Input: a private key PrivateKeyA in the range [0, 2^372 - 1], stored in 47 bytes.
|
||||
// Output: the public key PublicKeyA consisting of 3 GF(p751^2) elements encoded in 564 bytes.
|
||||
int EphemeralKeyGeneration_A_SIDHp751(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA);
|
||||
|
||||
// Bob's ephemeral key-pair generation
|
||||
// It produces a private key PrivateKeyB and computes the public key PublicKeyB.
|
||||
// The private key is an integer in the range [0, 2^Floor(Log(2,3^239)) - 1], stored in 48 bytes.
|
||||
// The public key consists of 3 GF(p751^2) elements encoded in 564 bytes.
|
||||
int EphemeralKeyGeneration_B_SIDHp751(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB);
|
||||
|
||||
// Alice's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB
|
||||
// Inputs: Alice's PrivateKeyA is an integer in the range [0, 2^372 - 1], stored in 47 bytes.
|
||||
// Bob's PublicKeyB consists of 3 GF(p751^2) elements encoded in 564 bytes.
|
||||
// Output: a shared secret SharedSecretA that consists of one element in GF(p751^2) encoded in 188 bytes.
|
||||
int EphemeralSecretAgreement_A_SIDHp751(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA);
|
||||
|
||||
// Bob's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA
|
||||
// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,3^239)) - 1], stored in 48 bytes.
|
||||
// Alice's PublicKeyA consists of 3 GF(p751^2) elements encoded in 564 bytes.
|
||||
// Output: a shared secret SharedSecretB that consists of one element in GF(p751^2) encoded in 188 bytes.
|
||||
int EphemeralSecretAgreement_B_SIDHp751(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB);
|
||||
|
||||
|
||||
// Encoding of keys for KEX-based isogeny system "SIDHp751" (wire format):
|
||||
// ----------------------------------------------------------------------
|
||||
// Elements over GF(p751) are encoded in 94 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
|
||||
// Elements (a+b*i) over GF(p751^2), where a and b are defined over GF(p751), are encoded as {a, b}, with a in the lowest memory portion.
|
||||
//
|
||||
// Private keys PrivateKeyA and PrivateKeyB can have values in the range [0, 2^372-1] and [0, 2^Floor(Log(2,3^239)) - 1], resp. In the SIDH API,
|
||||
// Alice's and Bob's private keys are encoded in 47 and 48 octets, resp., in little endian format.
|
||||
// Public keys PublicKeyA and PublicKeyB consist of 3 elements in GF(p751^2). In the SIDH API, they are encoded in 564 octets.
|
||||
// Shared keys SharedSecretA and SharedSecretB consist of one element in GF(p751^2). In the SIDH API, they are encoded in 188 octets.
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,175 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: internal header file for P751
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef P751_INTERNAL_H
|
||||
#define P751_INTERNAL_H
|
||||
|
||||
#include "../config.h"
|
||||
|
||||
|
||||
#if (TARGET == TARGET_AMD64) || (TARGET == TARGET_ARM64)
|
||||
#define NWORDS_FIELD 12 // Number of words of a 751-bit field element
|
||||
#define p751_ZERO_WORDS 5 // Number of "0" digits in the least significant part of p751 + 1
|
||||
#elif (TARGET == TARGET_x86)
|
||||
#define NWORDS_FIELD 24
|
||||
#define p751_ZERO_WORDS 11
|
||||
#endif
|
||||
|
||||
|
||||
// Basic constants
|
||||
|
||||
#define NBITS_FIELD 751
|
||||
#define MAXBITS_FIELD 768
|
||||
#define MAXWORDS_FIELD ((MAXBITS_FIELD+RADIX-1)/RADIX) // Max. number of words to represent field elements
|
||||
#define NWORDS64_FIELD ((NBITS_FIELD+63)/64) // Number of 64-bit words of a 751-bit field element
|
||||
#define NBITS_ORDER 384
|
||||
#define NWORDS_ORDER ((NBITS_ORDER+RADIX-1)/RADIX) // Number of words of oA and oB, where oA and oB are the subgroup orders of Alice and Bob, resp.
|
||||
#define NWORDS64_ORDER ((NBITS_ORDER+63)/64) // Number of 64-bit words of a 384-bit element
|
||||
#define MAXBITS_ORDER NBITS_ORDER
|
||||
#define ALICE 0
|
||||
#define BOB 1
|
||||
#define OALICE_BITS 372
|
||||
#define OBOB_BITS 379
|
||||
#define OBOB_EXPON 239
|
||||
#define MASK_ALICE 0x0F
|
||||
#define MASK_BOB 0x03
|
||||
#define PRIME p751
|
||||
#define PARAM_A 6
|
||||
#define PARAM_C 1
|
||||
// Fixed parameters for isogeny tree computation
|
||||
#define MAX_INT_POINTS_ALICE 8
|
||||
#define MAX_INT_POINTS_BOB 10
|
||||
#define MAX_Alice 186
|
||||
#define MAX_Bob 239
|
||||
#define MSG_BYTES 32
|
||||
#define SECRETKEY_A_BYTES ((OALICE_BITS + 7) / 8)
|
||||
#define SECRETKEY_B_BYTES ((OBOB_BITS - 1 + 7) / 8)
|
||||
#define FP2_ENCODED_BYTES 2*((NBITS_FIELD + 7) / 8)
|
||||
|
||||
|
||||
// SIDH's basic element definitions and point representations
|
||||
|
||||
typedef digit_t felm_t[NWORDS_FIELD]; // Datatype for representing 751-bit field elements (768-bit max.)
|
||||
typedef digit_t dfelm_t[2*NWORDS_FIELD]; // Datatype for representing double-precision 2x751-bit field elements (2x768-bit max.)
|
||||
typedef felm_t f2elm_t[2]; // Datatype for representing quadratic extension field elements GF(p751^2)
|
||||
|
||||
typedef struct { f2elm_t X; f2elm_t Z; } point_proj; // Point representation in projective XZ Montgomery coordinates.
|
||||
typedef point_proj point_proj_t[1];
|
||||
|
||||
#ifdef COMPRESS
|
||||
typedef struct { f2elm_t X; f2elm_t Y; f2elm_t Z; } point_full_proj; // Point representation in full projective XYZ Montgomery coordinates
|
||||
typedef point_full_proj point_full_proj_t[1];
|
||||
|
||||
typedef struct { f2elm_t x; f2elm_t y; } point_affine; // Point representation in affine coordinates.
|
||||
typedef point_affine point_t[1];
|
||||
|
||||
typedef f2elm_t publickey_t[3];
|
||||
#endif
|
||||
|
||||
|
||||
|
||||
/**************** Function prototypes ****************/
|
||||
/************* Multiprecision functions **************/
|
||||
|
||||
// 751-bit multiprecision addition, c = a+b
|
||||
void mp_add751(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_add751_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 751-bit multiprecision subtraction, c = a-b+2p or c = a-b+4p
|
||||
extern void mp_sub751_p2(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void mp_sub751_p4(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub751_p2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_sub751_p4_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// 2x751-bit multiprecision subtraction followed by addition with p751*2^768, c = a-b+(p751*2^768) if a-b < 0, otherwise c=a-b
|
||||
void mp_subaddx2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mp_subadd751x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Double 2x751-bit multiprecision subtraction, c = c-a-b, where c > a and c > b
|
||||
void mp_dblsub751x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
/************ Field arithmetic functions *************/
|
||||
|
||||
// Copy of a field element, c = a
|
||||
void fpcopy751(const digit_t* a, digit_t* c);
|
||||
|
||||
// Zeroing a field element, a = 0
|
||||
void fpzero751(digit_t* a);
|
||||
|
||||
// Non constant-time comparison of two field elements. If a = b return TRUE, otherwise, return FALSE
|
||||
bool fpequal751_non_constant_time(const digit_t* a, const digit_t* b);
|
||||
|
||||
// Modular addition, c = a+b mod p751
|
||||
extern void fpadd751(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpadd751_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular subtraction, c = a-b mod p751
|
||||
extern void fpsub751(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
extern void fpsub751_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Modular negation, a = -a mod p751
|
||||
extern void fpneg751(digit_t* a);
|
||||
|
||||
// Modular division by two, c = a/2 mod p751.
|
||||
void fpdiv2_751(const digit_t* a, digit_t* c);
|
||||
|
||||
// Modular correction to reduce field element a in [0, 2*p751-1] to [0, p751-1].
|
||||
void fpcorrection751(digit_t* a);
|
||||
|
||||
// 751-bit Montgomery reduction, c = a mod p
|
||||
void rdc751_asm(digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field multiplication using Montgomery arithmetic, c = a*b*R^-1 mod p751, where R=2^768
|
||||
void fpmul751_mont(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
void mul751_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Field squaring using Montgomery arithmetic, c = a*b*R^-1 mod p751, where R=2^768
|
||||
void fpsqr751_mont(const digit_t* ma, digit_t* mc);
|
||||
|
||||
// Field inversion, a = a^-1 in GF(p751)
|
||||
void fpinv751_mont(digit_t* a);
|
||||
|
||||
// Chain to compute (p751-3)/4 using Montgomery arithmetic
|
||||
void fpinv751_chain_mont(digit_t* a);
|
||||
|
||||
/************ GF(p^2) arithmetic functions *************/
|
||||
|
||||
// Copy of a GF(p751^2) element, c = a
|
||||
void fp2copy751(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Zeroing a GF(p751^2) element, a = 0
|
||||
void fp2zero751(f2elm_t a);
|
||||
|
||||
// GF(p751^2) negation, a = -a in GF(p751^2)
|
||||
void fp2neg751(f2elm_t a);
|
||||
|
||||
// GF(p751^2) addition, c = a+b in GF(p751^2)
|
||||
extern void fp2add751(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p751^2) subtraction, c = a-b in GF(p751^2)
|
||||
extern void fp2sub751(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p751^2) division by two, c = a/2 in GF(p751^2)
|
||||
void fp2div2_751(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// Modular correction, a = a in GF(p751^2)
|
||||
void fp2correction751(f2elm_t a);
|
||||
|
||||
// GF(p751^2) squaring using Montgomery arithmetic, c = a^2 in GF(p751^2)
|
||||
void fp2sqr751_mont(const f2elm_t a, f2elm_t c);
|
||||
|
||||
// GF(p751^2) multiplication using Montgomery arithmetic, c = a*b in GF(p751^2)
|
||||
void fp2mul751_mont(const f2elm_t a, const f2elm_t b, f2elm_t c);
|
||||
|
||||
// GF(p751^2) inversion using Montgomery arithmetic, a = (a0-i*a1)/(a0^2+a1^2)
|
||||
void fp2inv751_mont(f2elm_t a);
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,259 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: portable modular arithmetic for P751
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../P751_internal.h"
|
||||
#include "../../internal.h"
|
||||
|
||||
// Global constants
|
||||
extern const uint64_t p751[NWORDS64_FIELD];
|
||||
extern const uint64_t p751p1[NWORDS64_FIELD];
|
||||
extern const uint64_t p751x2[NWORDS64_FIELD];
|
||||
extern const uint64_t p751x4[NWORDS64_FIELD];
|
||||
|
||||
|
||||
__inline void mp_sub751_p2(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 2*p, c = a-b+2p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p751x2)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void mp_sub751_p4(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Multiprecision subtraction with correction with 4*p, c = a-b+4p.
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p751x4)[i], borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpadd751(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular addition, c = a+b mod p751.
|
||||
// Inputs: a, b in [0, 2*p751-1]
|
||||
// Output: c in [0, 2*p751-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], b[i], carry, c[i]);
|
||||
}
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(carry, c[i], ((digit_t*)p751x2)[i], carry, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)carry;
|
||||
|
||||
carry = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, c[i], ((digit_t*)p751x2)[i] & mask, carry, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpsub751(const digit_t* a, const digit_t* b, digit_t* c)
|
||||
{ // Modular subtraction, c = a-b mod p751.
|
||||
// Inputs: a, b in [0, 2*p751-1]
|
||||
// Output: c in [0, 2*p751-1]
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], b[i], borrow, c[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, c[i], ((digit_t*)p751x2)[i] & mask, borrow, c[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
__inline void fpneg751(digit_t* a)
|
||||
{ // Modular negation, a = -a mod p751.
|
||||
// Input/output: a in [0, 2*p751-1]
|
||||
unsigned int i, borrow = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, ((digit_t*)p751x2)[i], a[i], borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void fpdiv2_751(const digit_t* a, digit_t* c)
|
||||
{ // Modular division by two, c = a/2 mod p751.
|
||||
// Input : a in [0, 2*p751-1]
|
||||
// Output: c in [0, 2*p751-1]
|
||||
unsigned int i, carry = 0;
|
||||
digit_t mask;
|
||||
|
||||
mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p751
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(carry, a[i], ((digit_t*)p751)[i] & mask, carry, c[i]);
|
||||
}
|
||||
|
||||
mp_shiftr1(c, NWORDS_FIELD);
|
||||
}
|
||||
|
||||
|
||||
void fpcorrection751(digit_t* a)
|
||||
{ // Modular correction to reduce field element a in [0, 2*p751-1] to [0, p751-1].
|
||||
unsigned int i, borrow = 0;
|
||||
digit_t mask;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
SUBC(borrow, a[i], ((digit_t*)p751)[i], borrow, a[i]);
|
||||
}
|
||||
mask = 0 - (digit_t)borrow;
|
||||
|
||||
borrow = 0;
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
ADDC(borrow, a[i], ((digit_t*)p751)[i] & mask, borrow, a[i]);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void digit_x_digit(const digit_t a, const digit_t b, digit_t* c)
|
||||
{ // Digit multiplication, digit * digit -> 2-digit result
|
||||
register digit_t al, ah, bl, bh, temp;
|
||||
digit_t albl, albh, ahbl, ahbh, res1, res2, res3, carry;
|
||||
digit_t mask_low = (digit_t)(-1) >> (sizeof(digit_t)*4), mask_high = (digit_t)(-1) << (sizeof(digit_t)*4);
|
||||
|
||||
al = a & mask_low; // Low part
|
||||
ah = a >> (sizeof(digit_t) * 4); // High part
|
||||
bl = b & mask_low;
|
||||
bh = b >> (sizeof(digit_t) * 4);
|
||||
|
||||
albl = al*bl;
|
||||
albh = al*bh;
|
||||
ahbl = ah*bl;
|
||||
ahbh = ah*bh;
|
||||
c[0] = albl & mask_low; // C00
|
||||
|
||||
res1 = albl >> (sizeof(digit_t) * 4);
|
||||
res2 = ahbl & mask_low;
|
||||
res3 = albh & mask_low;
|
||||
temp = res1 + res2 + res3;
|
||||
carry = temp >> (sizeof(digit_t) * 4);
|
||||
c[0] ^= temp << (sizeof(digit_t) * 4); // C01
|
||||
|
||||
res1 = ahbl >> (sizeof(digit_t) * 4);
|
||||
res2 = albh >> (sizeof(digit_t) * 4);
|
||||
res3 = ahbh & mask_low;
|
||||
temp = res1 + res2 + res3 + carry;
|
||||
c[1] = temp & mask_low; // C10
|
||||
carry = temp & mask_high;
|
||||
c[1] ^= (ahbh & mask_high) + carry; // C11
|
||||
}
|
||||
|
||||
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
|
||||
{ // Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
unsigned int i, j;
|
||||
digit_t t = 0, u = 0, v = 0, UV[2];
|
||||
unsigned int carry = 0;
|
||||
|
||||
for (i = 0; i < nwords; i++) {
|
||||
for (j = 0; j <= i; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = nwords; i < 2*nwords-1; i++) {
|
||||
for (j = i-nwords+1; j < nwords; j++) {
|
||||
MUL(a[j], b[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
c[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
c[2*nwords-1] = v;
|
||||
}
|
||||
|
||||
|
||||
void rdc_mont(digit_t* ma, digit_t* mc)
|
||||
{ // Efficient Montgomery reduction using comba and exploiting the special form of the prime p751.
|
||||
// mc = ma*R^-1 mod p751x2, where R = 2^768.
|
||||
// If ma < 2^768*p751, the output mc is in the range [0, 2*p751-1].
|
||||
// ma is assumed to be in Montgomery representation.
|
||||
unsigned int i, j, carry, count = p751_ZERO_WORDS;
|
||||
digit_t UV[2], t = 0, u = 0, v = 0;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
mc[i] = 0;
|
||||
}
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
for (j = 0; j < i; j++) {
|
||||
if (j < (i-p751_ZERO_WORDS+1)) {
|
||||
MUL(mc[j], ((digit_t*)p751p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
|
||||
for (i = NWORDS_FIELD; i < 2*NWORDS_FIELD-1; i++) {
|
||||
if (count > 0) {
|
||||
count -= 1;
|
||||
}
|
||||
for (j = i-NWORDS_FIELD+1; j < NWORDS_FIELD; j++) {
|
||||
if (j < (NWORDS_FIELD-count)) {
|
||||
MUL(mc[j], ((digit_t*)p751p1)[i-j], UV+1, UV[0]);
|
||||
ADDC(0, UV[0], v, carry, v);
|
||||
ADDC(carry, UV[1], u, carry, u);
|
||||
t += carry;
|
||||
}
|
||||
}
|
||||
ADDC(0, v, ma[i], carry, v);
|
||||
ADDC(carry, u, 0, carry, u);
|
||||
t += carry;
|
||||
mc[i-NWORDS_FIELD] = v;
|
||||
v = u;
|
||||
u = t;
|
||||
t = 0;
|
||||
}
|
||||
ADDC(0, v, ma[2*NWORDS_FIELD-1], carry, v);
|
||||
mc[NWORDS_FIELD-1] = v;
|
||||
}
|
||||
|
|
@ -0,0 +1,271 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
*
|
||||
* Abstract: configuration file and platform-dependent macros
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef CONFIG_H
|
||||
#define CONFIG_H
|
||||
|
||||
#include <stdint.h>
|
||||
#include <stdbool.h>
|
||||
#include <stddef.h>
|
||||
|
||||
// Definition of operating system
|
||||
|
||||
#define OS_WIN 1
|
||||
#define OS_LINUX 2
|
||||
|
||||
#if defined(__WINDOWS__) // Microsoft Windows OS
|
||||
#define OS_TARGET OS_WIN
|
||||
#elif defined(__LINUX__) // Linux OS
|
||||
#define OS_TARGET OS_LINUX
|
||||
#else
|
||||
#error-- "Unsupported OS"
|
||||
#endif
|
||||
|
||||
#if (OS_TARGET == OS_LINUX)
|
||||
#define ALIGN_FOOTER(N) __attribute__((aligned(N)))
|
||||
#else
|
||||
#define ALIGN_FOOTER(N)
|
||||
#endif
|
||||
|
||||
// Definition of compiler
|
||||
|
||||
#define COMPILER_VC 1
|
||||
#define COMPILER_GCC 2
|
||||
#define COMPILER_CLANG 3
|
||||
|
||||
#if defined(_MSC_VER) // Microsoft Visual C compiler
|
||||
#define COMPILER COMPILER_VC
|
||||
#elif defined(__GNUC__) // GNU GCC compiler
|
||||
#define COMPILER COMPILER_GCC
|
||||
#elif defined(__clang__) // Clang compiler
|
||||
#define COMPILER COMPILER_CLANG
|
||||
#else
|
||||
#error-- "Unsupported COMPILER"
|
||||
#endif
|
||||
|
||||
// Definition of the targeted architecture and basic data types
|
||||
|
||||
#define TARGET_AMD64 1
|
||||
#define TARGET_ARM64 2
|
||||
#define TARGET_x86 3
|
||||
|
||||
#if defined(_AMD64_)
|
||||
#define TARGET TARGET_AMD64
|
||||
#define RADIX 64
|
||||
#define LOG2RADIX 6
|
||||
typedef uint64_t digit_t; // Unsigned 64-bit digit
|
||||
#elif defined(_ARM64_)
|
||||
#define TARGET TARGET_ARM64
|
||||
#define RADIX 64
|
||||
#define LOG2RADIX 6
|
||||
typedef uint64_t digit_t; // Unsigned 64-bit digit
|
||||
#elif defined(_X86_)
|
||||
#define TARGET TARGET_x86
|
||||
#define RADIX 32
|
||||
#define LOG2RADIX 5
|
||||
typedef uint32_t digit_t; // Unsigned 32-bit digit
|
||||
#else
|
||||
#error-- "Unsupported ARCHITECTURE"
|
||||
#endif
|
||||
|
||||
#define RADIX64 64
|
||||
|
||||
// Selection of generic, portable implementation
|
||||
|
||||
#if defined(_GENERIC_)
|
||||
#define GENERIC_IMPLEMENTATION
|
||||
#elif defined(_FAST_)
|
||||
#define FAST_IMPLEMENTATION
|
||||
#endif
|
||||
|
||||
// Extended datatype support
|
||||
|
||||
#if defined(GENERIC_IMPLEMENTATION)
|
||||
typedef uint64_t uint128_t[2];
|
||||
#elif (TARGET == TARGET_AMD64 && OS_TARGET == OS_LINUX) && (COMPILER == COMPILER_GCC || COMPILER == COMPILER_CLANG)
|
||||
#define UINT128_SUPPORT
|
||||
typedef unsigned uint128_t __attribute__((mode(TI)));
|
||||
#elif (TARGET == TARGET_ARM64 && OS_TARGET == OS_LINUX) && (COMPILER == COMPILER_GCC || COMPILER == COMPILER_CLANG)
|
||||
#define UINT128_SUPPORT
|
||||
typedef unsigned uint128_t __attribute__((mode(TI)));
|
||||
#elif (TARGET == TARGET_AMD64) && (OS_TARGET == OS_WIN && COMPILER == COMPILER_VC)
|
||||
#define SCALAR_INTRIN_SUPPORT
|
||||
typedef uint64_t uint128_t[2];
|
||||
#else
|
||||
#error-- "Unsupported configuration"
|
||||
#endif
|
||||
|
||||
// Macro definitions
|
||||
|
||||
#define NBITS_TO_NBYTES(nbits) (((nbits) + 7) / 8) // Conversion macro from number of bits to number of bytes
|
||||
#define NBITS_TO_NWORDS(nbits) (((nbits) + (sizeof(digit_t) * 8) - 1) / (sizeof(digit_t) * 8)) // Conversion macro from number of bits to number of computer words
|
||||
#define NBYTES_TO_NWORDS(nbytes) (((nbytes) + sizeof(digit_t) - 1) / sizeof(digit_t)) // Conversion macro from number of bytes to number of computer words
|
||||
|
||||
|
||||
/********************** Constant-time unsigned comparisons ***********************/
|
||||
|
||||
// The following functions return 1 (TRUE) if condition is true, 0 (FALSE) otherwise
|
||||
|
||||
static __inline unsigned int is_digit_nonzero_ct(digit_t x)
|
||||
{ // Is x != 0?
|
||||
return (unsigned int)((x | (0 - x)) >> (RADIX - 1));
|
||||
}
|
||||
|
||||
static __inline unsigned int is_digit_zero_ct(digit_t x)
|
||||
{ // Is x = 0?
|
||||
return (unsigned int)(1 ^ is_digit_nonzero_ct(x));
|
||||
}
|
||||
|
||||
static __inline unsigned int is_digit_lessthan_ct(digit_t x, digit_t y)
|
||||
{ // Is x < y?
|
||||
return (unsigned int)((x ^ ((x ^ y) | ((x - y) ^ y))) >> (RADIX - 1));
|
||||
}
|
||||
|
||||
/********************** Macros for platform-dependent operations **********************/
|
||||
|
||||
#if defined(GENERIC_IMPLEMENTATION)
|
||||
|
||||
// Digit multiplication
|
||||
#define MUL(multiplier, multiplicand, hi, lo) \
|
||||
digit_x_digit((multiplier), (multiplicand), &(lo));
|
||||
|
||||
// Digit addition with carry
|
||||
#define ADDC(carryIn, addend1, addend2, carryOut, sumOut) \
|
||||
{ \
|
||||
digit_t tempReg = (addend1) + (digit_t)(carryIn); \
|
||||
(sumOut) = (addend2) + tempReg; \
|
||||
(carryOut) = (is_digit_lessthan_ct(tempReg, (digit_t)(carryIn)) | is_digit_lessthan_ct((sumOut), tempReg)); \
|
||||
}
|
||||
|
||||
// Digit subtraction with borrow
|
||||
#define SUBC(borrowIn, minuend, subtrahend, borrowOut, differenceOut) \
|
||||
{ \
|
||||
digit_t tempReg = (minuend) - (subtrahend); \
|
||||
unsigned int borrowReg = (is_digit_lessthan_ct((minuend), (subtrahend)) | ((borrowIn)&is_digit_zero_ct(tempReg))); \
|
||||
(differenceOut) = tempReg - (digit_t)(borrowIn); \
|
||||
(borrowOut) = borrowReg; \
|
||||
}
|
||||
|
||||
// Shift right with flexible datatype
|
||||
#define SHIFTR(highIn, lowIn, shift, shiftOut, DigitSize) \
|
||||
(shiftOut) = ((lowIn) >> (shift)) ^ ((highIn) << (DigitSize - (shift)));
|
||||
|
||||
// Shift left with flexible datatype
|
||||
#define SHIFTL(highIn, lowIn, shift, shiftOut, DigitSize) \
|
||||
(shiftOut) = ((highIn) << (shift)) ^ ((lowIn) >> (DigitSize - (shift)));
|
||||
|
||||
// 64x64-bit multiplication
|
||||
#define MUL128(multiplier, multiplicand, product) \
|
||||
mp_mul((digit_t *)&(multiplier), (digit_t *)&(multiplicand), (digit_t *)&(product), NWORDS_FIELD / 2);
|
||||
|
||||
// 128-bit addition, inputs < 2^127
|
||||
#define ADD128(addend1, addend2, addition) \
|
||||
mp_add((digit_t *)(addend1), (digit_t *)(addend2), (digit_t *)(addition), NWORDS_FIELD);
|
||||
|
||||
// 128-bit addition with output carry
|
||||
#define ADC128(addend1, addend2, carry, addition) \
|
||||
(carry) = mp_add((digit_t *)(addend1), (digit_t *)(addend2), (digit_t *)(addition), NWORDS_FIELD);
|
||||
|
||||
#elif (TARGET == TARGET_AMD64 && OS_TARGET == OS_WIN)
|
||||
|
||||
// Digit multiplication
|
||||
#define MUL(multiplier, multiplicand, hi, lo) \
|
||||
(lo) = _umul128((multiplier), (multiplicand), (hi));
|
||||
|
||||
// Digit addition with carry
|
||||
#define ADDC(carryIn, addend1, addend2, carryOut, sumOut) \
|
||||
(carryOut) = _addcarry_u64((carryIn), (addend1), (addend2), &(sumOut));
|
||||
|
||||
// Digit subtraction with borrow
|
||||
#define SUBC(borrowIn, minuend, subtrahend, borrowOut, differenceOut) \
|
||||
(borrowOut) = _subborrow_u64((borrowIn), (minuend), (subtrahend), &(differenceOut));
|
||||
|
||||
// Digit shift right
|
||||
#define SHIFTR(highIn, lowIn, shift, shiftOut, DigitSize) \
|
||||
(shiftOut) = __shiftright128((lowIn), (highIn), (shift));
|
||||
|
||||
// Digit shift left
|
||||
#define SHIFTL(highIn, lowIn, shift, shiftOut, DigitSize) \
|
||||
(shiftOut) = __shiftleft128((lowIn), (highIn), (shift));
|
||||
|
||||
// 64x64-bit multiplication
|
||||
#define MUL128(multiplier, multiplicand, product) \
|
||||
(product)[0] = _umul128((multiplier), (multiplicand), &(product)[1]);
|
||||
|
||||
// 128-bit addition, inputs < 2^127
|
||||
#define ADD128(addend1, addend2, addition) \
|
||||
{ \
|
||||
unsigned char carry = _addcarry_u64(0, (addend1)[0], (addend2)[0], &(addition)[0]); \
|
||||
_addcarry_u64(carry, (addend1)[1], (addend2)[1], &(addition)[1]); \
|
||||
}
|
||||
|
||||
// 128-bit addition with output carry
|
||||
#define ADC128(addend1, addend2, carry, addition) \
|
||||
(carry) = _addcarry_u64(0, (addend1)[0], (addend2)[0], &(addition)[0]); \
|
||||
(carry) = _addcarry_u64((carry), (addend1)[1], (addend2)[1], &(addition)[1]);
|
||||
|
||||
// 128-bit subtraction, subtrahend < 2^127
|
||||
#define SUB128(minuend, subtrahend, difference) \
|
||||
{ \
|
||||
unsigned char borrow = _subborrow_u64(0, (minuend)[0], (subtrahend)[0], &(difference)[0]); \
|
||||
_subborrow_u64(borrow, (minuend)[1], (subtrahend)[1], &(difference)[1]); \
|
||||
}
|
||||
|
||||
// 128-bit right shift, max. shift value is 64
|
||||
#define SHIFTR128(Input, shift, shiftOut) \
|
||||
(shiftOut)[0] = __shiftright128((Input)[0], (Input)[1], (shift)); \
|
||||
(shiftOut)[1] = (Input)[1] >> (shift);
|
||||
|
||||
// 128-bit left shift, max. shift value is 64
|
||||
#define SHIFTL128(Input, shift, shiftOut) \
|
||||
(shiftOut)[1] = __shiftleft128((Input)[0], (Input)[1], (shift)); \
|
||||
(shiftOut)[0] = (Input)[0] << (shift);
|
||||
|
||||
#define MULADD128(multiplier, multiplicand, addend, carry, result) \
|
||||
; \
|
||||
{ \
|
||||
uint128_t product; \
|
||||
MUL128(multiplier, multiplicand, product); \
|
||||
ADC128(addend, product, carry, result); \
|
||||
}
|
||||
|
||||
#elif ((TARGET == TARGET_AMD64 || TARGET == TARGET_ARM64) && OS_TARGET == OS_LINUX)
|
||||
|
||||
// Digit multiplication
|
||||
#define MUL(multiplier, multiplicand, hi, lo) \
|
||||
{ \
|
||||
uint128_t tempReg = (uint128_t)(multiplier) * (uint128_t)(multiplicand); \
|
||||
*(hi) = (digit_t)(tempReg >> RADIX); \
|
||||
(lo) = (digit_t)tempReg; \
|
||||
}
|
||||
|
||||
// Digit addition with carry
|
||||
#define ADDC(carryIn, addend1, addend2, carryOut, sumOut) \
|
||||
{ \
|
||||
uint128_t tempReg = (uint128_t)(addend1) + (uint128_t)(addend2) + (uint128_t)(carryIn); \
|
||||
(carryOut) = (digit_t)(tempReg >> RADIX); \
|
||||
(sumOut) = (digit_t)tempReg; \
|
||||
}
|
||||
|
||||
// Digit subtraction with borrow
|
||||
#define SUBC(borrowIn, minuend, subtrahend, borrowOut, differenceOut) \
|
||||
{ \
|
||||
uint128_t tempReg = (uint128_t)(minuend) - (uint128_t)(subtrahend) - (uint128_t)(borrowIn); \
|
||||
(borrowOut) = (digit_t)(tempReg >> (sizeof(uint128_t) * 8 - 1)); \
|
||||
(differenceOut) = (digit_t)tempReg; \
|
||||
}
|
||||
|
||||
// Digit shift right
|
||||
#define SHIFTR(highIn, lowIn, shift, shiftOut, DigitSize) \
|
||||
(shiftOut) = ((lowIn) >> (shift)) ^ ((highIn) << (RADIX - (shift)));
|
||||
|
||||
// Digit shift left
|
||||
#define SHIFTL(highIn, lowIn, shift, shiftOut, DigitSize) \
|
||||
(shiftOut) = ((highIn) << (shift)) ^ ((lowIn) >> (RADIX - (shift)));
|
||||
|
||||
#endif
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,416 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: Elliptic curve and isogeny functions
|
||||
*********************************************************************************************/
|
||||
|
||||
|
||||
void xDBL(const point_proj_t P, point_proj_t Q, const f2elm_t A24plus, const f2elm_t C24)
|
||||
{ // Doubling of a Montgomery point in projective coordinates (X:Z).
|
||||
// Input: projective Montgomery x-coordinates P = (X1:Z1), where x1=X1/Z1 and Montgomery curve constants A+2C and 4C.
|
||||
// Output: projective Montgomery x-coordinates Q = 2*P = (X2:Z2).
|
||||
f2elm_t t0, t1;
|
||||
|
||||
mp2_sub_p2(P->X, P->Z, t0); // t0 = X1-Z1
|
||||
mp2_add(P->X, P->Z, t1); // t1 = X1+Z1
|
||||
fp2sqr_mont(t0, t0); // t0 = (X1-Z1)^2
|
||||
fp2sqr_mont(t1, t1); // t1 = (X1+Z1)^2
|
||||
fp2mul_mont(C24, t0, Q->Z); // Z2 = C24*(X1-Z1)^2
|
||||
fp2mul_mont(t1, Q->Z, Q->X); // X2 = C24*(X1-Z1)^2*(X1+Z1)^2
|
||||
mp2_sub_p2(t1, t0, t1); // t1 = (X1+Z1)^2-(X1-Z1)^2
|
||||
fp2mul_mont(A24plus, t1, t0); // t0 = A24plus*[(X1+Z1)^2-(X1-Z1)^2]
|
||||
mp2_add(Q->Z, t0, Q->Z); // Z2 = A24plus*[(X1+Z1)^2-(X1-Z1)^2] + C24*(X1-Z1)^2
|
||||
fp2mul_mont(Q->Z, t1, Q->Z); // Z2 = [A24plus*[(X1+Z1)^2-(X1-Z1)^2] + C24*(X1-Z1)^2]*[(X1+Z1)^2-(X1-Z1)^2]
|
||||
}
|
||||
|
||||
|
||||
void xDBLe(const point_proj_t P, point_proj_t Q, const f2elm_t A24plus, const f2elm_t C24, const int e)
|
||||
{ // Computes [2^e](X:Z) on Montgomery curve with projective constant via e repeated doublings.
|
||||
// Input: projective Montgomery x-coordinates P = (XP:ZP), such that xP=XP/ZP and Montgomery curve constants A+2C and 4C.
|
||||
// Output: projective Montgomery x-coordinates Q <- (2^e)*P.
|
||||
int i;
|
||||
|
||||
copy_words((digit_t*)P, (digit_t*)Q, 2*2*NWORDS_FIELD);
|
||||
|
||||
for (i = 0; i < e; i++) {
|
||||
xDBL(Q, Q, A24plus, C24);
|
||||
}
|
||||
}
|
||||
|
||||
#if (OALICE_BITS % 2 == 1)
|
||||
|
||||
void get_2_isog(const point_proj_t P, f2elm_t A, f2elm_t C)
|
||||
{ // Computes the corresponding 2-isogeny of a projective Montgomery point (X2:Z2) of order 2.
|
||||
// Input: projective point of order two P = (X2:Z2).
|
||||
// Output: the 2-isogenous Montgomery curve with projective coefficients A/C.
|
||||
|
||||
fp2sqr_mont(P->X, A); // A = X2^2
|
||||
fp2sqr_mont(P->Z, C); // C = Z2^2
|
||||
mp2_sub_p2(C, A, A); // A = Z2^2 - X2^2
|
||||
}
|
||||
|
||||
|
||||
void eval_2_isog(point_proj_t P, point_proj_t Q)
|
||||
{ // Evaluates the isogeny at the point (X:Z) in the domain of the isogeny, given a 2-isogeny phi.
|
||||
// Inputs: the projective point P = (X:Z) and the 2-isogeny kernel projetive point Q = (X2:Z2).
|
||||
// Output: the projective point P = phi(P) = (X:Z) in the codomain.
|
||||
f2elm_t t0, t1, t2, t3;
|
||||
|
||||
mp2_add(Q->X, Q->Z, t0); // t0 = X2+Z2
|
||||
mp2_sub_p2(Q->X, Q->Z, t1); // t1 = X2-Z2
|
||||
mp2_add(P->X, P->Z, t2); // t2 = X+Z
|
||||
mp2_sub_p2(P->X, P->Z, t3); // t3 = X-Z
|
||||
fp2mul_mont(t0, t3, t0); // t0 = (X2+Z2)*(X-Z)
|
||||
fp2mul_mont(t1, t2, t1); // t1 = (X2-Z2)*(X+Z)
|
||||
mp2_add(t0, t1, t2); // t2 = (X2+Z2)*(X-Z) + (X2-Z2)*(X+Z)
|
||||
mp2_sub_p2(t0, t1, t3); // t3 = (X2+Z2)*(X-Z) - (X2-Z2)*(X+Z)
|
||||
fp2mul_mont(P->X, t2, P->X); // Xfinal
|
||||
fp2mul_mont(P->Z, t3, P->Z); // Zfinal
|
||||
}
|
||||
|
||||
#endif
|
||||
|
||||
void get_4_isog(const point_proj_t P, f2elm_t A24plus, f2elm_t C24, f2elm_t* coeff)
|
||||
{ // Computes the corresponding 4-isogeny of a projective Montgomery point (X4:Z4) of order 4.
|
||||
// Input: projective point of order four P = (X4:Z4).
|
||||
// Output: the 4-isogenous Montgomery curve with projective coefficients A+2C/4C and the 3 coefficients
|
||||
// that are used to evaluate the isogeny at a point in eval_4_isog().
|
||||
mp2_sub_p2(P->X, P->Z, coeff[1]); // coeff[1] = X4-Z4
|
||||
mp2_add(P->X, P->Z, coeff[2]); // coeff[2] = X4+Z4
|
||||
fp2sqr_mont(P->Z, coeff[0]); // coeff[0] = Z4^2
|
||||
mp2_add(coeff[0], coeff[0], coeff[0]); // coeff[0] = 2*Z4^2
|
||||
fp2sqr_mont(coeff[0], C24); // C24 = 4*Z4^4
|
||||
mp2_add(coeff[0], coeff[0], coeff[0]); // coeff[0] = 4*Z4^2
|
||||
fp2sqr_mont(P->X, A24plus); // A24plus = X4^2
|
||||
mp2_add(A24plus, A24plus, A24plus); // A24plus = 2*X4^2
|
||||
fp2sqr_mont(A24plus, A24plus); // A24plus = 4*X4^4
|
||||
}
|
||||
|
||||
|
||||
void eval_4_isog(point_proj_t P, f2elm_t* coeff)
|
||||
{ // Evaluates the isogeny at the point (X:Z) in the domain of the isogeny, given a 4-isogeny phi defined
|
||||
// by the 3 coefficients in coeff (computed in the function get_4_isog()).
|
||||
// Inputs: the coefficients defining the isogeny, and the projective point P = (X:Z).
|
||||
// Output: the projective point P = phi(P) = (X:Z) in the codomain.
|
||||
f2elm_t t0, t1;
|
||||
|
||||
mp2_add(P->X, P->Z, t0); // t0 = X+Z
|
||||
mp2_sub_p2(P->X, P->Z, t1); // t1 = X-Z
|
||||
fp2mul_mont(t0, coeff[1], P->X); // X = (X+Z)*coeff[1]
|
||||
fp2mul_mont(t1, coeff[2], P->Z); // Z = (X-Z)*coeff[2]
|
||||
fp2mul_mont(t0, t1, t0); // t0 = (X+Z)*(X-Z)
|
||||
fp2mul_mont(coeff[0], t0, t0); // t0 = coeff[0]*(X+Z)*(X-Z)
|
||||
mp2_add(P->X, P->Z, t1); // t1 = (X-Z)*coeff[2] + (X+Z)*coeff[1]
|
||||
mp2_sub_p2(P->X, P->Z, P->Z); // Z = (X-Z)*coeff[2] - (X+Z)*coeff[1]
|
||||
fp2sqr_mont(t1, t1); // t1 = [(X-Z)*coeff[2] + (X+Z)*coeff[1]]^2
|
||||
fp2sqr_mont(P->Z, P->Z); // Z = [(X-Z)*coeff[2] - (X+Z)*coeff[1]]^2
|
||||
mp2_add(t1, t0, P->X); // X = coeff[0]*(X+Z)*(X-Z) + [(X-Z)*coeff[2] + (X+Z)*coeff[1]]^2
|
||||
mp2_sub_p2(P->Z, t0, t0); // t0 = [(X-Z)*coeff[2] - (X+Z)*coeff[1]]^2 - coeff[0]*(X+Z)*(X-Z)
|
||||
fp2mul_mont(P->X, t1, P->X); // Xfinal
|
||||
fp2mul_mont(P->Z, t0, P->Z); // Zfinal
|
||||
}
|
||||
|
||||
|
||||
void xTPL(const point_proj_t P, point_proj_t Q, const f2elm_t A24minus, const f2elm_t A24plus)
|
||||
{ // Tripling of a Montgomery point in projective coordinates (X:Z).
|
||||
// Input: projective Montgomery x-coordinates P = (X:Z), where x=X/Z and Montgomery curve constants A24plus = A+2C and A24minus = A-2C.
|
||||
// Output: projective Montgomery x-coordinates Q = 3*P = (X3:Z3).
|
||||
f2elm_t t0, t1, t2, t3, t4, t5, t6;
|
||||
|
||||
mp2_sub_p2(P->X, P->Z, t0); // t0 = X-Z
|
||||
fp2sqr_mont(t0, t2); // t2 = (X-Z)^2
|
||||
mp2_add(P->X, P->Z, t1); // t1 = X+Z
|
||||
fp2sqr_mont(t1, t3); // t3 = (X+Z)^2
|
||||
mp2_add(P->X, P->X, t4); // t4 = 2*X
|
||||
mp2_add(P->Z, P->Z, t0); // t0 = 2*Z
|
||||
fp2sqr_mont(t4, t1); // t1 = 4*X^2
|
||||
mp2_sub_p2(t1, t3, t1); // t1 = 4*X^2 - (X+Z)^2
|
||||
mp2_sub_p2(t1, t2, t1); // t1 = 4*X^2 - (X+Z)^2 - (X-Z)^2
|
||||
fp2mul_mont(A24plus, t3, t5); // t5 = A24plus*(X+Z)^2
|
||||
fp2mul_mont(t3, t5, t3); // t3 = A24plus*(X+Z)^4
|
||||
fp2mul_mont(A24minus, t2, t6); // t6 = A24minus*(X-Z)^2
|
||||
fp2mul_mont(t2, t6, t2); // t2 = A24minus*(X-Z)^4
|
||||
mp2_sub_p2(t2, t3, t3); // t3 = A24minus*(X-Z)^4 - A24plus*(X+Z)^4
|
||||
mp2_sub_p2(t5, t6, t2); // t2 = A24plus*(X+Z)^2 - A24minus*(X-Z)^2
|
||||
fp2mul_mont(t1, t2, t1); // t1 = [4*X^2 - (X+Z)^2 - (X-Z)^2]*[A24plus*(X+Z)^2 - A24minus*(X-Z)^2]
|
||||
fp2add(t3, t1, t2); // t2 = [4*X^2 - (X+Z)^2 - (X-Z)^2]*[A24plus*(X+Z)^2 - A24minus*(X-Z)^2] + A24minus*(X-Z)^4 - A24plus*(X+Z)^4
|
||||
fp2sqr_mont(t2, t2); // t2 = t2^2
|
||||
fp2mul_mont(t4, t2, Q->X); // X3 = 2*X*t2
|
||||
fp2sub(t3, t1, t1); // t1 = A24minus*(X-Z)^4 - A24plus*(X+Z)^4 - [4*X^2 - (X+Z)^2 - (X-Z)^2]*[A24plus*(X+Z)^2 - A24minus*(X-Z)^2]
|
||||
fp2sqr_mont(t1, t1); // t1 = t1^2
|
||||
fp2mul_mont(t0, t1, Q->Z); // Z3 = 2*Z*t1
|
||||
}
|
||||
|
||||
|
||||
void xTPLe(const point_proj_t P, point_proj_t Q, const f2elm_t A24minus, const f2elm_t A24plus, const int e)
|
||||
{ // Computes [3^e](X:Z) on Montgomery curve with projective constant via e repeated triplings.
|
||||
// Input: projective Montgomery x-coordinates P = (XP:ZP), such that xP=XP/ZP and Montgomery curve constants A24plus = A+2C and A24minus = A-2C.
|
||||
// Output: projective Montgomery x-coordinates Q <- (3^e)*P.
|
||||
int i;
|
||||
|
||||
copy_words((digit_t*)P, (digit_t*)Q, 2*2*NWORDS_FIELD);
|
||||
|
||||
for (i = 0; i < e; i++) {
|
||||
xTPL(Q, Q, A24minus, A24plus);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void get_3_isog(const point_proj_t P, f2elm_t A24minus, f2elm_t A24plus, f2elm_t* coeff)
|
||||
{ // Computes the corresponding 3-isogeny of a projective Montgomery point (X3:Z3) of order 3.
|
||||
// Input: projective point of order three P = (X3:Z3).
|
||||
// Output: the 3-isogenous Montgomery curve with projective coefficient A/C.
|
||||
f2elm_t t0, t1, t2, t3, t4;
|
||||
|
||||
mp2_sub_p2(P->X, P->Z, coeff[0]); // coeff0 = X-Z
|
||||
fp2sqr_mont(coeff[0], t0); // t0 = (X-Z)^2
|
||||
mp2_add(P->X, P->Z, coeff[1]); // coeff1 = X+Z
|
||||
fp2sqr_mont(coeff[1], t1); // t1 = (X+Z)^2
|
||||
mp2_add(P->X, P->X, t3); // t3 = 2*X
|
||||
fp2sqr_mont(t3, t3); // t3 = 4*X^2
|
||||
fp2sub(t3, t0, t2); // t2 = 4*X^2 - (X-Z)^2
|
||||
fp2sub(t3, t1, t3); // t3 = 4*X^2 - (X+Z)^2
|
||||
mp2_add(t0, t3, t4); // t4 = 4*X^2 - (X+Z)^2 + (X-Z)^2
|
||||
mp2_add(t4, t4, t4); // t4 = 2(4*X^2 - (X+Z)^2 + (X-Z)^2)
|
||||
mp2_add(t1, t4, t4); // t4 = 8*X^2 - (X+Z)^2 + 2*(X-Z)^2
|
||||
fp2mul_mont(t2, t4, A24minus); // A24minus = [4*X^2 - (X-Z)^2]*[8*X^2 - (X+Z)^2 + 2*(X-Z)^2]
|
||||
mp2_add(t1, t2, t4); // t4 = 4*X^2 + (X+Z)^2 - (X-Z)^2
|
||||
mp2_add(t4, t4, t4); // t4 = 2(4*X^2 + (X+Z)^2 - (X-Z)^2)
|
||||
mp2_add(t0, t4, t4); // t4 = 8*X^2 + 2*(X+Z)^2 - (X-Z)^2
|
||||
fp2mul_mont(t3, t4, A24plus); // A24plus = [4*X^2 - (X+Z)^2]*[8*X^2 + 2*(X+Z)^2 - (X-Z)^2]
|
||||
}
|
||||
|
||||
|
||||
void eval_3_isog(point_proj_t Q, const f2elm_t* coeff)
|
||||
{ // Computes the 3-isogeny R=phi(X:Z), given projective point (X3:Z3) of order 3 on a Montgomery curve and
|
||||
// a point P with 2 coefficients in coeff (computed in the function get_3_isog()).
|
||||
// Inputs: projective points P = (X3:Z3) and Q = (X:Z).
|
||||
// Output: the projective point Q <- phi(Q) = (X3:Z3).
|
||||
f2elm_t t0, t1, t2;
|
||||
|
||||
mp2_add(Q->X, Q->Z, t0); // t0 = X+Z
|
||||
mp2_sub_p2(Q->X, Q->Z, t1); // t1 = X-Z
|
||||
fp2mul_mont(coeff[0], t0, t0); // t0 = coeff0*(X+Z)
|
||||
fp2mul_mont(coeff[1], t1, t1); // t1 = coeff1*(X-Z)
|
||||
mp2_add(t0, t1, t2); // t2 = coeff0*(X+Z) + coeff1*(X-Z)
|
||||
mp2_sub_p2(t1, t0, t0); // t0 = coeff1*(X-Z) - coeff0*(X+Z)
|
||||
fp2sqr_mont(t2, t2); // t2 = [coeff0*(X+Z) + coeff1*(X-Z)]^2
|
||||
fp2sqr_mont(t0, t0); // t0 = [coeff1*(X-Z) - coeff0*(X+Z)]^2
|
||||
fp2mul_mont(Q->X, t2, Q->X); // X3final = X*[coeff0*(X+Z) + coeff1*(X-Z)]^2
|
||||
fp2mul_mont(Q->Z, t0, Q->Z); // Z3final = Z*[coeff1*(X-Z) - coeff0*(X+Z)]^2
|
||||
}
|
||||
|
||||
|
||||
void inv_3_way(f2elm_t z1, f2elm_t z2, f2elm_t z3)
|
||||
{ // 3-way simultaneous inversion
|
||||
// Input: z1,z2,z3
|
||||
// Output: 1/z1,1/z2,1/z3 (override inputs).
|
||||
f2elm_t t0, t1, t2;
|
||||
|
||||
fp2mul_mont(z1, z2, t0); // t0 = z1*z2
|
||||
fp2mul_mont(z3, t0, t1); // t1 = z1*z2*z3
|
||||
fp2inv_mont(t1); // t1 = 1/(z1*z2*z3)
|
||||
fp2mul_mont(z3, t1, t2); // t2 = 1/(z1*z2)
|
||||
fp2mul_mont(t0, t1, z3); // z3 = 1/z3
|
||||
fp2mul_mont(t2, z2, t0); // z1 = 1/z1
|
||||
fp2mul_mont(t2, z1, z2); // z2 = 1/z2
|
||||
fp2copy(t0, z1);
|
||||
}
|
||||
|
||||
|
||||
void get_A(const f2elm_t xP, const f2elm_t xQ, const f2elm_t xR, f2elm_t A)
|
||||
{ // Given the x-coordinates of P, Q, and R, returns the value A corresponding to the Montgomery curve E_A: y^2=x^3+A*x^2+x such that R=Q-P on E_A.
|
||||
// Input: the x-coordinates xP, xQ, and xR of the points P, Q and R.
|
||||
// Output: the coefficient A corresponding to the curve E_A: y^2=x^3+A*x^2+x.
|
||||
f2elm_t t0, t1, one = {0};
|
||||
|
||||
fpcopy((digit_t*)&Montgomery_one, one[0]);
|
||||
fp2add(xP, xQ, t1); // t1 = xP+xQ
|
||||
fp2mul_mont(xP, xQ, t0); // t0 = xP*xQ
|
||||
fp2mul_mont(xR, t1, A); // A = xR*t1
|
||||
fp2add(t0, A, A); // A = A+t0
|
||||
fp2mul_mont(t0, xR, t0); // t0 = t0*xR
|
||||
fp2sub(A, one, A); // A = A-1
|
||||
fp2add(t0, t0, t0); // t0 = t0+t0
|
||||
fp2add(t1, xR, t1); // t1 = t1+xR
|
||||
fp2add(t0, t0, t0); // t0 = t0+t0
|
||||
fp2sqr_mont(A, A); // A = A^2
|
||||
fp2inv_mont(t0); // t0 = 1/t0
|
||||
fp2mul_mont(A, t0, A); // A = A*t0
|
||||
fp2sub(A, t1, A); // Afinal = A-t1
|
||||
}
|
||||
|
||||
|
||||
void j_inv(const f2elm_t A, const f2elm_t C, f2elm_t jinv)
|
||||
{ // Computes the j-invariant of a Montgomery curve with projective constant.
|
||||
// Input: A,C in GF(p^2).
|
||||
// Output: j=256*(A^2-3*C^2)^3/(C^4*(A^2-4*C^2)), which is the j-invariant of the Montgomery curve B*y^2=x^3+(A/C)*x^2+x or (equivalently) j-invariant of B'*y^2=C*x^3+A*x^2+C*x.
|
||||
f2elm_t t0, t1;
|
||||
|
||||
fp2sqr_mont(A, jinv); // jinv = A^2
|
||||
fp2sqr_mont(C, t1); // t1 = C^2
|
||||
fp2add(t1, t1, t0); // t0 = t1+t1
|
||||
fp2sub(jinv, t0, t0); // t0 = jinv-t0
|
||||
fp2sub(t0, t1, t0); // t0 = t0-t1
|
||||
fp2sub(t0, t1, jinv); // jinv = t0-t1
|
||||
fp2sqr_mont(t1, t1); // t1 = t1^2
|
||||
fp2mul_mont(jinv, t1, jinv); // jinv = jinv*t1
|
||||
fp2add(t0, t0, t0); // t0 = t0+t0
|
||||
fp2add(t0, t0, t0); // t0 = t0+t0
|
||||
fp2sqr_mont(t0, t1); // t1 = t0^2
|
||||
fp2mul_mont(t0, t1, t0); // t0 = t0*t1
|
||||
fp2add(t0, t0, t0); // t0 = t0+t0
|
||||
fp2add(t0, t0, t0); // t0 = t0+t0
|
||||
fp2inv_mont(jinv); // jinv = 1/jinv
|
||||
fp2mul_mont(jinv, t0, jinv); // jinv = t0*jinv
|
||||
}
|
||||
|
||||
|
||||
void xDBLADD(point_proj_t P, point_proj_t Q, const f2elm_t XPQ, const f2elm_t ZPQ, const f2elm_t A24)
|
||||
{ // Simultaneous doubling and differential addition.
|
||||
// Input: projective Montgomery points P=(XP:ZP) and Q=(XQ:ZQ) such that xP=XP/ZP and xQ=XQ/ZQ, affine difference xPQ=x(P-Q) and Montgomery curve constant A24=(A+2)/4.
|
||||
// Output: projective Montgomery points P <- 2*P = (X2P:Z2P) such that x(2P)=X2P/Z2P, and Q <- P+Q = (XQP:ZQP) such that = x(Q+P)=XQP/ZQP.
|
||||
f2elm_t t0, t1, t2;
|
||||
|
||||
mp2_add(P->X, P->Z, t0); // t0 = XP+ZP
|
||||
mp2_sub_p2(P->X, P->Z, t1); // t1 = XP-ZP
|
||||
fp2sqr_mont(t0, P->X); // XP = (XP+ZP)^2
|
||||
mp2_sub_p2(Q->X, Q->Z, t2); // t2 = XQ-ZQ
|
||||
mp2_add(Q->X, Q->Z, Q->X); // XQ = XQ+ZQ
|
||||
fp2mul_mont(t0, t2, t0); // t0 = (XP+ZP)*(XQ-ZQ)
|
||||
fp2sqr_mont(t1, P->Z); // ZP = (XP-ZP)^2
|
||||
fp2mul_mont(t1, Q->X, t1); // t1 = (XP-ZP)*(XQ+ZQ)
|
||||
mp2_sub_p2(P->X, P->Z, t2); // t2 = (XP+ZP)^2-(XP-ZP)^2
|
||||
fp2mul_mont(P->X, P->Z, P->X); // XP = (XP+ZP)^2*(XP-ZP)^2
|
||||
fp2mul_mont(A24, t2, Q->X); // XQ = A24*[(XP+ZP)^2-(XP-ZP)^2]
|
||||
mp2_sub_p2(t0, t1, Q->Z); // ZQ = (XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ)
|
||||
mp2_add(Q->X, P->Z, P->Z); // ZP = A24*[(XP+ZP)^2-(XP-ZP)^2]+(XP-ZP)^2
|
||||
mp2_add(t0, t1, Q->X); // XQ = (XP+ZP)*(XQ-ZQ)+(XP-ZP)*(XQ+ZQ)
|
||||
fp2mul_mont(P->Z, t2, P->Z); // ZP = [A24*[(XP+ZP)^2-(XP-ZP)^2]+(XP-ZP)^2]*[(XP+ZP)^2-(XP-ZP)^2]
|
||||
fp2sqr_mont(Q->Z, Q->Z); // ZQ = [(XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ)]^2
|
||||
fp2sqr_mont(Q->X, Q->X); // XQ = [(XP+ZP)*(XQ-ZQ)+(XP-ZP)*(XQ+ZQ)]^2
|
||||
fp2mul_mont(Q->Z, XPQ, Q->Z); // ZQ = xPQ*[(XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ)]^2
|
||||
fp2mul_mont(Q->X, ZPQ, Q->X); // XQ = ZPQ*[(XP+ZP)*(XQ-ZQ)+(XP-ZP)*(XQ+ZQ)]^2
|
||||
}
|
||||
|
||||
|
||||
static void swap_points(point_proj_t P, point_proj_t Q, const digit_t option)
|
||||
{ // Swap points.
|
||||
// If option = 0 then P <- P and Q <- Q, else if option = 0xFF...FF then P <- Q and Q <- P
|
||||
digit_t temp;
|
||||
unsigned int i;
|
||||
|
||||
for (i = 0; i < NWORDS_FIELD; i++) {
|
||||
temp = option & (P->X[0][i] ^ Q->X[0][i]);
|
||||
P->X[0][i] = temp ^ P->X[0][i];
|
||||
Q->X[0][i] = temp ^ Q->X[0][i];
|
||||
temp = option & (P->X[1][i] ^ Q->X[1][i]);
|
||||
P->X[1][i] = temp ^ P->X[1][i];
|
||||
Q->X[1][i] = temp ^ Q->X[1][i];
|
||||
temp = option & (P->Z[0][i] ^ Q->Z[0][i]);
|
||||
P->Z[0][i] = temp ^ P->Z[0][i];
|
||||
Q->Z[0][i] = temp ^ Q->Z[0][i];
|
||||
temp = option & (P->Z[1][i] ^ Q->Z[1][i]);
|
||||
P->Z[1][i] = temp ^ P->Z[1][i];
|
||||
Q->Z[1][i] = temp ^ Q->Z[1][i];
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
static void LADDER3PT(const f2elm_t xP, const f2elm_t xQ, const f2elm_t xPQ, const digit_t* m, const unsigned int AliceOrBob, point_proj_t R, const f2elm_t A)
|
||||
{
|
||||
point_proj_t R0 = {0}, R2 = {0};
|
||||
f2elm_t A24 = {0};
|
||||
digit_t mask;
|
||||
int i, nbits, bit, swap, prevbit = 0;
|
||||
|
||||
if (AliceOrBob == ALICE) {
|
||||
nbits = OALICE_BITS;
|
||||
} else {
|
||||
nbits = OBOB_BITS - 1;
|
||||
}
|
||||
|
||||
// Initializing constant
|
||||
fpcopy((digit_t*)&Montgomery_one, A24[0]);
|
||||
mp2_add(A24, A24, A24);
|
||||
mp2_add(A, A24, A24);
|
||||
fp2div2(A24, A24);
|
||||
fp2div2(A24, A24); // A24 = (A+2)/4
|
||||
|
||||
// Initializing points
|
||||
fp2copy(xQ, R0->X);
|
||||
fpcopy((digit_t*)&Montgomery_one, (digit_t*)R0->Z);
|
||||
fp2copy(xPQ, R2->X);
|
||||
fpcopy((digit_t*)&Montgomery_one, (digit_t*)R2->Z);
|
||||
fp2copy(xP, R->X);
|
||||
fpcopy((digit_t*)&Montgomery_one, (digit_t*)R->Z);
|
||||
fpzero((digit_t*)(R->Z)[1]);
|
||||
|
||||
// Main loop
|
||||
for (i = 0; i < nbits; i++) {
|
||||
bit = (m[i >> LOG2RADIX] >> (i & (RADIX-1))) & 1;
|
||||
swap = bit ^ prevbit;
|
||||
prevbit = bit;
|
||||
mask = 0 - (digit_t)swap;
|
||||
|
||||
swap_points(R, R2, mask);
|
||||
xDBLADD(R0, R2, R->X, R->Z, A24);
|
||||
}
|
||||
swap = 0 ^ prevbit;
|
||||
mask = 0 - (digit_t)swap;
|
||||
swap_points(R, R2, mask);
|
||||
}
|
||||
|
||||
|
||||
void TraverseTree(f2elm_t jinv, point_proj_t R, f2elm_t A24plus, f2elm_t C24, const unsigned int *strat, unsigned int lenstrat, bool keygen,
|
||||
point_proj_t phiP, point_proj_t phiQ, point_proj_t phiR)
|
||||
{ // Isogeny tree traversal
|
||||
point_proj_t pts[MAX_INT_POINTS_ALICE];
|
||||
f2elm_t coeff[3];
|
||||
unsigned int i, m, row, ii = 0, index = 0, npts = 0, pts_index[MAX_INT_POINTS_ALICE];
|
||||
|
||||
for (row = 1; row < lenstrat; row++) {
|
||||
while (index < lenstrat - row) {
|
||||
fp2copy(R->X, pts[npts]->X);
|
||||
fp2copy(R->Z, pts[npts]->Z);
|
||||
pts_index[npts++] = index;
|
||||
m = strat[ii++];
|
||||
xDBLe(R, R, A24plus, C24, (int)(2*m));
|
||||
index += m;
|
||||
}
|
||||
get_4_isog(R, A24plus, C24, coeff);
|
||||
if (keygen) {
|
||||
eval_4_isog(phiP, coeff);
|
||||
eval_4_isog(phiQ, coeff);
|
||||
eval_4_isog(phiR, coeff);
|
||||
}
|
||||
|
||||
for (i = 0; i < npts; i++) {
|
||||
eval_4_isog(pts[i], coeff);
|
||||
}
|
||||
|
||||
fp2copy(pts[npts-1]->X, R->X);
|
||||
fp2copy(pts[npts-1]->Z, R->Z);
|
||||
index = pts_index[npts-1];
|
||||
npts -= 1;
|
||||
}
|
||||
get_4_isog(R, A24plus, C24, coeff);
|
||||
if (keygen) {
|
||||
eval_4_isog(phiP, coeff);
|
||||
eval_4_isog(phiQ, coeff);
|
||||
eval_4_isog(phiR, coeff);
|
||||
inv_3_way(phiP->Z, phiQ->Z, phiR->Z);
|
||||
fp2mul_mont(phiP->X, phiP->Z, phiP->X);
|
||||
fp2mul_mont(phiQ->X, phiQ->Z, phiQ->X);
|
||||
fp2mul_mont(phiR->X, phiR->Z, phiR->X);
|
||||
} else {
|
||||
fp2add(A24plus, A24plus, A24plus);
|
||||
fp2sub(A24plus, C24, A24plus);
|
||||
fp2add(A24plus, A24plus, A24plus);
|
||||
j_inv(A24plus, C24, jinv);
|
||||
}
|
||||
}
|
||||
Разница между файлами не показана из-за своего большого размера
Загрузить разницу
|
|
@ -0,0 +1,116 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: internal header file for function definitions
|
||||
*********************************************************************************************/
|
||||
|
||||
#ifndef INTERNAL_H
|
||||
#define INTERNAL_H
|
||||
|
||||
|
||||
/**************** Function prototypes ****************/
|
||||
/************* Multiprecision functions **************/
|
||||
|
||||
// Copy wordsize digits, c = a, where lng(a) = nwords
|
||||
void copy_words(const digit_t* a, digit_t* c, const unsigned int nwords);
|
||||
|
||||
// Compare two byte arrays in constant time
|
||||
int8_t ct_compare(const uint8_t *a, const uint8_t *b, unsigned int len) ;
|
||||
|
||||
// Conditional move in constant time
|
||||
void ct_cmov(uint8_t *r, const uint8_t *a, unsigned int len, int8_t selector);
|
||||
|
||||
// Multiprecision addition, c = a+b, where lng(a) = lng(b) = nwords. Returns the carry bit
|
||||
unsigned int mp_add(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords);
|
||||
|
||||
// Multiprecision subtraction, c = a-b, where lng(a) = lng(b) = nwords. Returns the borrow bit
|
||||
unsigned int mp_sub(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords);
|
||||
|
||||
// 2x434-bit multiprecision subtraction followed by addition with p434*2^448, c = a-b+(p434*2^448) if a-b < 0, otherwise c=a-b
|
||||
void mp_subaddx2_asm(const digit_t* a, const digit_t* b, digit_t* c);
|
||||
|
||||
// Multiprecision left shift
|
||||
void mp_shiftleft(digit_t* x, unsigned int shift, const unsigned int nwords);
|
||||
|
||||
// Multiprecision right shift by one
|
||||
void mp_shiftr1(digit_t* x, const unsigned int nwords);
|
||||
|
||||
// Multiprecision left right shift by one
|
||||
void mp_shiftl1(digit_t* x, const unsigned int nwords);
|
||||
|
||||
// Digit multiplication, digit * digit -> 2-digit result
|
||||
void digit_x_digit(const digit_t a, const digit_t b, digit_t* c);
|
||||
|
||||
// Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = nwords.
|
||||
void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords);
|
||||
|
||||
/************ Montgomery reduction and conversion functions *************/
|
||||
|
||||
// Montgomery reduction, c = a mod p
|
||||
void rdc_mont(digit_t* a, digit_t* c);
|
||||
|
||||
// Conversion to Montgomery representation
|
||||
void to_mont(const digit_t* a, digit_t* mc);
|
||||
|
||||
// Conversion from Montgomery representation to standard representation
|
||||
void from_mont(const digit_t* ma, digit_t* c);
|
||||
|
||||
// Conversion of a GF(p^2) element to Montgomery representation
|
||||
void to_fp2mont(const f2elm_t a, f2elm_t mc);
|
||||
|
||||
// Conversion of a GF(p^2) element from Montgomery representation to standard representation
|
||||
void from_fp2mont(const f2elm_t ma, f2elm_t c);
|
||||
|
||||
// n-way Montgomery inversion
|
||||
void mont_n_way_inv(const f2elm_t* vec, const int n, f2elm_t* out);
|
||||
|
||||
/************ Elliptic curve and isogeny functions *************/
|
||||
|
||||
// Computes the j-invariant of a Montgomery curve with projective constant.
|
||||
void j_inv(const f2elm_t A, const f2elm_t C, f2elm_t jinv);
|
||||
|
||||
// Simultaneous doubling and differential addition.
|
||||
void xDBLADD(point_proj_t P, point_proj_t Q, const f2elm_t XPQ, const f2elm_t ZPQ, const f2elm_t A24);
|
||||
|
||||
// Doubling of a Montgomery point in projective coordinates (X:Z).
|
||||
void xDBL(const point_proj_t P, point_proj_t Q, const f2elm_t A24plus, const f2elm_t C24);
|
||||
|
||||
// Computes [2^e](X:Z) on Montgomery curve with projective constant via e repeated doublings.
|
||||
void xDBLe(const point_proj_t P, point_proj_t Q, const f2elm_t A24plus, const f2elm_t C24, const int e);
|
||||
|
||||
// Differential addition.
|
||||
void xADD(point_proj_t P, const point_proj_t Q, const f2elm_t xPQ);
|
||||
|
||||
// Computes the corresponding 4-isogeny of a projective Montgomery point (X4:Z4) of order 4.
|
||||
void get_4_isog(const point_proj_t P, f2elm_t A24plus, f2elm_t C24, f2elm_t* coeff);
|
||||
|
||||
// Evaluates the isogeny at the point (X:Z) in the domain of the isogeny.
|
||||
void eval_4_isog(point_proj_t P, f2elm_t* coeff);
|
||||
|
||||
// Tripling of a Montgomery point in projective coordinates (X:Z).
|
||||
void xTPL(const point_proj_t P, point_proj_t Q, const f2elm_t A24minus, const f2elm_t A24plus);
|
||||
|
||||
// Computes [3^e](X:Z) on Montgomery curve with projective constant via e repeated triplings.
|
||||
void xTPLe(const point_proj_t P, point_proj_t Q, const f2elm_t A24minus, const f2elm_t A24plus, const int e);
|
||||
|
||||
// Computes the corresponding 3-isogeny of a projective Montgomery point (X3:Z3) of order 3.
|
||||
void get_3_isog(const point_proj_t P, f2elm_t A24minus, f2elm_t A24plus, f2elm_t* coeff);
|
||||
|
||||
// Computes the 3-isogeny R=phi(X:Z), given projective point (X3:Z3) of order 3 on a Montgomery curve and a point P with coefficients given in coeff.
|
||||
void eval_3_isog(point_proj_t Q, const f2elm_t* coeff);
|
||||
|
||||
// 3-way simultaneous inversion
|
||||
void inv_3_way(f2elm_t z1, f2elm_t z2, f2elm_t z3);
|
||||
|
||||
// Given the x-coordinates of P, Q, and R, returns the value A corresponding to the Montgomery curve E_A: y^2=x^3+A*x^2+x such that R=Q-P on E_A.
|
||||
void get_A(const f2elm_t xP, const f2elm_t xQ, const f2elm_t xR, f2elm_t A);
|
||||
|
||||
// Isogeny tree traversal
|
||||
void TraverseTree(f2elm_t jinv, point_proj_t R, f2elm_t A24plus, f2elm_t C24, const unsigned int *strat, unsigned int lenstrat, bool keygen, point_proj_t PhiP, point_proj_t PhiQ, point_proj_t PhiR);
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,61 @@
|
|||
/********************************************************************************************
|
||||
* Hardware-based random number generation function
|
||||
*
|
||||
* It uses /dev/urandom in Linux and CNG's BCryptGenRandom function in Windows
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "random.h"
|
||||
#include <stdlib.h>
|
||||
#if defined(__WINDOWS__)
|
||||
#include <windows.h>
|
||||
#include <bcrypt.h>
|
||||
#elif defined(__LINUX__)
|
||||
#include <unistd.h>
|
||||
#include <fcntl.h>
|
||||
static int lock = -1;
|
||||
#endif
|
||||
|
||||
#define passed 0
|
||||
#define failed 1
|
||||
|
||||
|
||||
static __inline void delay(unsigned int count)
|
||||
{
|
||||
while (count--) {}
|
||||
}
|
||||
|
||||
|
||||
int randombytes(unsigned char* random_array, unsigned long long nbytes)
|
||||
{ // Generation of "nbytes" of random values
|
||||
|
||||
#if defined(__WINDOWS__)
|
||||
if (!BCRYPT_SUCCESS(BCryptGenRandom(NULL, random_array, (unsigned long)nbytes, BCRYPT_USE_SYSTEM_PREFERRED_RNG))) {
|
||||
return failed;
|
||||
}
|
||||
|
||||
#elif defined(__LINUX__)
|
||||
int r, n = (int)nbytes, count = 0;
|
||||
|
||||
if (lock == -1) {
|
||||
do {
|
||||
lock = open("/dev/urandom", O_RDONLY);
|
||||
if (lock == -1) {
|
||||
delay(0xFFFFF);
|
||||
}
|
||||
} while (lock == -1);
|
||||
}
|
||||
|
||||
while (n > 0) {
|
||||
do {
|
||||
r = read(lock, random_array+count, n);
|
||||
if (r == -1) {
|
||||
delay(0xFFFF);
|
||||
}
|
||||
} while (r == -1);
|
||||
count += r;
|
||||
n -= r;
|
||||
}
|
||||
#endif
|
||||
|
||||
return passed;
|
||||
}
|
||||
|
|
@ -0,0 +1,9 @@
|
|||
#ifndef RANDOM_H
|
||||
#define RANDOM_H
|
||||
|
||||
|
||||
// Generate random bytes and output the result to random_array
|
||||
int randombytes(unsigned char* random_array, unsigned long long nbytes);
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,573 @@
|
|||
/********************************************************************************************
|
||||
* SHA3-derived functions: SHAKE and cSHAKE
|
||||
*
|
||||
* Based on the public domain implementation in crypto_hash/keccakc512/simple/
|
||||
* from http://bench.cr.yp.to/supercop.html by Ronny Van Keer
|
||||
* and the public domain "TweetFips202" implementation from https://twitter.com/tweetfips202
|
||||
* by Gilles Van Assche, Daniel J. Bernstein, and Peter Schwabe
|
||||
*
|
||||
* See NIST Special Publication 800-185 for more information:
|
||||
* http://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-185.pdf
|
||||
*
|
||||
*********************************************************************************************/
|
||||
|
||||
#include <stdint.h>
|
||||
#include <assert.h>
|
||||
#include "fips202.h"
|
||||
|
||||
#define NROUNDS 24
|
||||
#define ROL(a, offset) ((a << offset) ^ (a >> (64-offset)))
|
||||
|
||||
|
||||
static uint64_t load64(const unsigned char *x)
|
||||
{
|
||||
unsigned long long r = 0, i;
|
||||
|
||||
for (i = 0; i < 8; ++i) {
|
||||
r |= (unsigned long long)x[i] << 8 * i;
|
||||
}
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
static void store64(uint8_t *x, uint64_t u)
|
||||
{
|
||||
unsigned int i;
|
||||
|
||||
for (i = 0; i < 8; ++i) {
|
||||
x[i] = (uint8_t)u;
|
||||
u >>= 8;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
static const uint64_t KeccakF_RoundConstants[NROUNDS] =
|
||||
{
|
||||
(uint64_t)0x0000000000000001ULL,
|
||||
(uint64_t)0x0000000000008082ULL,
|
||||
(uint64_t)0x800000000000808aULL,
|
||||
(uint64_t)0x8000000080008000ULL,
|
||||
(uint64_t)0x000000000000808bULL,
|
||||
(uint64_t)0x0000000080000001ULL,
|
||||
(uint64_t)0x8000000080008081ULL,
|
||||
(uint64_t)0x8000000000008009ULL,
|
||||
(uint64_t)0x000000000000008aULL,
|
||||
(uint64_t)0x0000000000000088ULL,
|
||||
(uint64_t)0x0000000080008009ULL,
|
||||
(uint64_t)0x000000008000000aULL,
|
||||
(uint64_t)0x000000008000808bULL,
|
||||
(uint64_t)0x800000000000008bULL,
|
||||
(uint64_t)0x8000000000008089ULL,
|
||||
(uint64_t)0x8000000000008003ULL,
|
||||
(uint64_t)0x8000000000008002ULL,
|
||||
(uint64_t)0x8000000000000080ULL,
|
||||
(uint64_t)0x000000000000800aULL,
|
||||
(uint64_t)0x800000008000000aULL,
|
||||
(uint64_t)0x8000000080008081ULL,
|
||||
(uint64_t)0x8000000000008080ULL,
|
||||
(uint64_t)0x0000000080000001ULL,
|
||||
(uint64_t)0x8000000080008008ULL
|
||||
};
|
||||
|
||||
|
||||
void KeccakF1600_StatePermute(uint64_t * state)
|
||||
{
|
||||
int round;
|
||||
|
||||
uint64_t Aba, Abe, Abi, Abo, Abu;
|
||||
uint64_t Aga, Age, Agi, Ago, Agu;
|
||||
uint64_t Aka, Ake, Aki, Ako, Aku;
|
||||
uint64_t Ama, Ame, Ami, Amo, Amu;
|
||||
uint64_t Asa, Ase, Asi, Aso, Asu;
|
||||
uint64_t BCa, BCe, BCi, BCo, BCu;
|
||||
uint64_t Da, De, Di, Do, Du;
|
||||
uint64_t Eba, Ebe, Ebi, Ebo, Ebu;
|
||||
uint64_t Ega, Ege, Egi, Ego, Egu;
|
||||
uint64_t Eka, Eke, Eki, Eko, Eku;
|
||||
uint64_t Ema, Eme, Emi, Emo, Emu;
|
||||
uint64_t Esa, Ese, Esi, Eso, Esu;
|
||||
|
||||
//copyFromState(A, state)
|
||||
Aba = state[ 0];
|
||||
Abe = state[ 1];
|
||||
Abi = state[ 2];
|
||||
Abo = state[ 3];
|
||||
Abu = state[ 4];
|
||||
Aga = state[ 5];
|
||||
Age = state[ 6];
|
||||
Agi = state[ 7];
|
||||
Ago = state[ 8];
|
||||
Agu = state[ 9];
|
||||
Aka = state[10];
|
||||
Ake = state[11];
|
||||
Aki = state[12];
|
||||
Ako = state[13];
|
||||
Aku = state[14];
|
||||
Ama = state[15];
|
||||
Ame = state[16];
|
||||
Ami = state[17];
|
||||
Amo = state[18];
|
||||
Amu = state[19];
|
||||
Asa = state[20];
|
||||
Ase = state[21];
|
||||
Asi = state[22];
|
||||
Aso = state[23];
|
||||
Asu = state[24];
|
||||
|
||||
for( round = 0; round < NROUNDS; round += 2 )
|
||||
{
|
||||
// prepareTheta
|
||||
BCa = Aba^Aga^Aka^Ama^Asa;
|
||||
BCe = Abe^Age^Ake^Ame^Ase;
|
||||
BCi = Abi^Agi^Aki^Ami^Asi;
|
||||
BCo = Abo^Ago^Ako^Amo^Aso;
|
||||
BCu = Abu^Agu^Aku^Amu^Asu;
|
||||
|
||||
//thetaRhoPiChiIotaPrepareTheta(round , A, E)
|
||||
Da = BCu^ROL(BCe, 1);
|
||||
De = BCa^ROL(BCi, 1);
|
||||
Di = BCe^ROL(BCo, 1);
|
||||
Do = BCi^ROL(BCu, 1);
|
||||
Du = BCo^ROL(BCa, 1);
|
||||
|
||||
Aba ^= Da;
|
||||
BCa = Aba;
|
||||
Age ^= De;
|
||||
BCe = ROL(Age, 44);
|
||||
Aki ^= Di;
|
||||
BCi = ROL(Aki, 43);
|
||||
Amo ^= Do;
|
||||
BCo = ROL(Amo, 21);
|
||||
Asu ^= Du;
|
||||
BCu = ROL(Asu, 14);
|
||||
Eba = BCa ^((~BCe)& BCi );
|
||||
Eba ^= (uint64_t)KeccakF_RoundConstants[round];
|
||||
Ebe = BCe ^((~BCi)& BCo );
|
||||
Ebi = BCi ^((~BCo)& BCu );
|
||||
Ebo = BCo ^((~BCu)& BCa );
|
||||
Ebu = BCu ^((~BCa)& BCe );
|
||||
|
||||
Abo ^= Do;
|
||||
BCa = ROL(Abo, 28);
|
||||
Agu ^= Du;
|
||||
BCe = ROL(Agu, 20);
|
||||
Aka ^= Da;
|
||||
BCi = ROL(Aka, 3);
|
||||
Ame ^= De;
|
||||
BCo = ROL(Ame, 45);
|
||||
Asi ^= Di;
|
||||
BCu = ROL(Asi, 61);
|
||||
Ega = BCa ^((~BCe)& BCi );
|
||||
Ege = BCe ^((~BCi)& BCo );
|
||||
Egi = BCi ^((~BCo)& BCu );
|
||||
Ego = BCo ^((~BCu)& BCa );
|
||||
Egu = BCu ^((~BCa)& BCe );
|
||||
|
||||
Abe ^= De;
|
||||
BCa = ROL(Abe, 1);
|
||||
Agi ^= Di;
|
||||
BCe = ROL(Agi, 6);
|
||||
Ako ^= Do;
|
||||
BCi = ROL(Ako, 25);
|
||||
Amu ^= Du;
|
||||
BCo = ROL(Amu, 8);
|
||||
Asa ^= Da;
|
||||
BCu = ROL(Asa, 18);
|
||||
Eka = BCa ^((~BCe)& BCi );
|
||||
Eke = BCe ^((~BCi)& BCo );
|
||||
Eki = BCi ^((~BCo)& BCu );
|
||||
Eko = BCo ^((~BCu)& BCa );
|
||||
Eku = BCu ^((~BCa)& BCe );
|
||||
|
||||
Abu ^= Du;
|
||||
BCa = ROL(Abu, 27);
|
||||
Aga ^= Da;
|
||||
BCe = ROL(Aga, 36);
|
||||
Ake ^= De;
|
||||
BCi = ROL(Ake, 10);
|
||||
Ami ^= Di;
|
||||
BCo = ROL(Ami, 15);
|
||||
Aso ^= Do;
|
||||
BCu = ROL(Aso, 56);
|
||||
Ema = BCa ^((~BCe)& BCi );
|
||||
Eme = BCe ^((~BCi)& BCo );
|
||||
Emi = BCi ^((~BCo)& BCu );
|
||||
Emo = BCo ^((~BCu)& BCa );
|
||||
Emu = BCu ^((~BCa)& BCe );
|
||||
|
||||
Abi ^= Di;
|
||||
BCa = ROL(Abi, 62);
|
||||
Ago ^= Do;
|
||||
BCe = ROL(Ago, 55);
|
||||
Aku ^= Du;
|
||||
BCi = ROL(Aku, 39);
|
||||
Ama ^= Da;
|
||||
BCo = ROL(Ama, 41);
|
||||
Ase ^= De;
|
||||
BCu = ROL(Ase, 2);
|
||||
Esa = BCa ^((~BCe)& BCi );
|
||||
Ese = BCe ^((~BCi)& BCo );
|
||||
Esi = BCi ^((~BCo)& BCu );
|
||||
Eso = BCo ^((~BCu)& BCa );
|
||||
Esu = BCu ^((~BCa)& BCe );
|
||||
|
||||
// prepareTheta
|
||||
BCa = Eba^Ega^Eka^Ema^Esa;
|
||||
BCe = Ebe^Ege^Eke^Eme^Ese;
|
||||
BCi = Ebi^Egi^Eki^Emi^Esi;
|
||||
BCo = Ebo^Ego^Eko^Emo^Eso;
|
||||
BCu = Ebu^Egu^Eku^Emu^Esu;
|
||||
|
||||
//thetaRhoPiChiIotaPrepareTheta(round+1, E, A)
|
||||
Da = BCu^ROL(BCe, 1);
|
||||
De = BCa^ROL(BCi, 1);
|
||||
Di = BCe^ROL(BCo, 1);
|
||||
Do = BCi^ROL(BCu, 1);
|
||||
Du = BCo^ROL(BCa, 1);
|
||||
|
||||
Eba ^= Da;
|
||||
BCa = Eba;
|
||||
Ege ^= De;
|
||||
BCe = ROL(Ege, 44);
|
||||
Eki ^= Di;
|
||||
BCi = ROL(Eki, 43);
|
||||
Emo ^= Do;
|
||||
BCo = ROL(Emo, 21);
|
||||
Esu ^= Du;
|
||||
BCu = ROL(Esu, 14);
|
||||
Aba = BCa ^((~BCe)& BCi );
|
||||
Aba ^= (uint64_t)KeccakF_RoundConstants[round+1];
|
||||
Abe = BCe ^((~BCi)& BCo );
|
||||
Abi = BCi ^((~BCo)& BCu );
|
||||
Abo = BCo ^((~BCu)& BCa );
|
||||
Abu = BCu ^((~BCa)& BCe );
|
||||
|
||||
Ebo ^= Do;
|
||||
BCa = ROL(Ebo, 28);
|
||||
Egu ^= Du;
|
||||
BCe = ROL(Egu, 20);
|
||||
Eka ^= Da;
|
||||
BCi = ROL(Eka, 3);
|
||||
Eme ^= De;
|
||||
BCo = ROL(Eme, 45);
|
||||
Esi ^= Di;
|
||||
BCu = ROL(Esi, 61);
|
||||
Aga = BCa ^((~BCe)& BCi );
|
||||
Age = BCe ^((~BCi)& BCo );
|
||||
Agi = BCi ^((~BCo)& BCu );
|
||||
Ago = BCo ^((~BCu)& BCa );
|
||||
Agu = BCu ^((~BCa)& BCe );
|
||||
|
||||
Ebe ^= De;
|
||||
BCa = ROL(Ebe, 1);
|
||||
Egi ^= Di;
|
||||
BCe = ROL(Egi, 6);
|
||||
Eko ^= Do;
|
||||
BCi = ROL(Eko, 25);
|
||||
Emu ^= Du;
|
||||
BCo = ROL(Emu, 8);
|
||||
Esa ^= Da;
|
||||
BCu = ROL(Esa, 18);
|
||||
Aka = BCa ^((~BCe)& BCi );
|
||||
Ake = BCe ^((~BCi)& BCo );
|
||||
Aki = BCi ^((~BCo)& BCu );
|
||||
Ako = BCo ^((~BCu)& BCa );
|
||||
Aku = BCu ^((~BCa)& BCe );
|
||||
|
||||
Ebu ^= Du;
|
||||
BCa = ROL(Ebu, 27);
|
||||
Ega ^= Da;
|
||||
BCe = ROL(Ega, 36);
|
||||
Eke ^= De;
|
||||
BCi = ROL(Eke, 10);
|
||||
Emi ^= Di;
|
||||
BCo = ROL(Emi, 15);
|
||||
Eso ^= Do;
|
||||
BCu = ROL(Eso, 56);
|
||||
Ama = BCa ^((~BCe)& BCi );
|
||||
Ame = BCe ^((~BCi)& BCo );
|
||||
Ami = BCi ^((~BCo)& BCu );
|
||||
Amo = BCo ^((~BCu)& BCa );
|
||||
Amu = BCu ^((~BCa)& BCe );
|
||||
|
||||
Ebi ^= Di;
|
||||
BCa = ROL(Ebi, 62);
|
||||
Ego ^= Do;
|
||||
BCe = ROL(Ego, 55);
|
||||
Eku ^= Du;
|
||||
BCi = ROL(Eku, 39);
|
||||
Ema ^= Da;
|
||||
BCo = ROL(Ema, 41);
|
||||
Ese ^= De;
|
||||
BCu = ROL(Ese, 2);
|
||||
Asa = BCa ^((~BCe)& BCi );
|
||||
Ase = BCe ^((~BCi)& BCo );
|
||||
Asi = BCi ^((~BCo)& BCu );
|
||||
Aso = BCo ^((~BCu)& BCa );
|
||||
Asu = BCu ^((~BCa)& BCe );
|
||||
}
|
||||
|
||||
//copyToState(state, A)
|
||||
state[ 0] = Aba;
|
||||
state[ 1] = Abe;
|
||||
state[ 2] = Abi;
|
||||
state[ 3] = Abo;
|
||||
state[ 4] = Abu;
|
||||
state[ 5] = Aga;
|
||||
state[ 6] = Age;
|
||||
state[ 7] = Agi;
|
||||
state[ 8] = Ago;
|
||||
state[ 9] = Agu;
|
||||
state[10] = Aka;
|
||||
state[11] = Ake;
|
||||
state[12] = Aki;
|
||||
state[13] = Ako;
|
||||
state[14] = Aku;
|
||||
state[15] = Ama;
|
||||
state[16] = Ame;
|
||||
state[17] = Ami;
|
||||
state[18] = Amo;
|
||||
state[19] = Amu;
|
||||
state[20] = Asa;
|
||||
state[21] = Ase;
|
||||
state[22] = Asi;
|
||||
state[23] = Aso;
|
||||
state[24] = Asu;
|
||||
|
||||
#undef round
|
||||
}
|
||||
|
||||
#include <string.h>
|
||||
#define MIN(a, b) ((a) < (b) ? (a) : (b))
|
||||
|
||||
|
||||
static void keccak_absorb(uint64_t *s, unsigned int r, const unsigned char *m, unsigned long long int mlen, unsigned char p)
|
||||
{
|
||||
unsigned long long i;
|
||||
unsigned char t[200];
|
||||
|
||||
while (mlen >= r)
|
||||
{
|
||||
for (i = 0; i < r / 8; ++i)
|
||||
s[i] ^= load64(m + 8 * i);
|
||||
|
||||
KeccakF1600_StatePermute(s);
|
||||
mlen -= r;
|
||||
m += r;
|
||||
}
|
||||
|
||||
for (i = 0; i < r; ++i)
|
||||
t[i] = 0;
|
||||
for (i = 0; i < mlen; ++i)
|
||||
t[i] = m[i];
|
||||
t[i] = p;
|
||||
t[r - 1] |= 128;
|
||||
for (i = 0; i < r / 8; ++i)
|
||||
s[i] ^= load64(t + 8 * i);
|
||||
}
|
||||
|
||||
|
||||
static void keccak_squeezeblocks(unsigned char *h, unsigned long long int nblocks, uint64_t *s, unsigned int r)
|
||||
{
|
||||
unsigned int i;
|
||||
|
||||
while(nblocks > 0)
|
||||
{
|
||||
KeccakF1600_StatePermute(s);
|
||||
for (i = 0; i < (r>>3); i++)
|
||||
{
|
||||
store64(h+8*i, s[i]);
|
||||
}
|
||||
h += r;
|
||||
nblocks--;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/********** SHAKE128 ***********/
|
||||
|
||||
void shake128_absorb(uint64_t *s, const unsigned char *input, unsigned int inputByteLen)
|
||||
{
|
||||
keccak_absorb(s, SHAKE128_RATE, input, inputByteLen, 0x1F);
|
||||
}
|
||||
|
||||
|
||||
void shake128_squeezeblocks(unsigned char *output, unsigned long long nblocks, uint64_t *s)
|
||||
{
|
||||
keccak_squeezeblocks(output, nblocks, s, SHAKE128_RATE);
|
||||
}
|
||||
|
||||
|
||||
void shake128(unsigned char *output, unsigned long long outlen, const unsigned char *input, unsigned long long inlen)
|
||||
{
|
||||
uint64_t s[25] = {0};
|
||||
unsigned char t[SHAKE128_RATE];
|
||||
unsigned long long nblocks = outlen/SHAKE128_RATE;
|
||||
size_t i;
|
||||
|
||||
/* Absorb input */
|
||||
keccak_absorb(s, SHAKE128_RATE, input, inlen, 0x1F);
|
||||
|
||||
/* Squeeze output */
|
||||
keccak_squeezeblocks(output, nblocks, s, SHAKE128_RATE);
|
||||
|
||||
output += nblocks*SHAKE128_RATE;
|
||||
outlen -= nblocks*SHAKE128_RATE;
|
||||
|
||||
if (outlen)
|
||||
{
|
||||
keccak_squeezeblocks(t, 1, s, SHAKE128_RATE);
|
||||
for (i = 0; i < outlen; i++)
|
||||
output[i] = t[i];
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/********** cSHAKE128 ***********/
|
||||
|
||||
void cshake128_simple_absorb(uint64_t s[25], uint16_t cstm, const unsigned char *in, unsigned long long inlen)
|
||||
{
|
||||
unsigned char *sep = (unsigned char*)s;
|
||||
unsigned int i;
|
||||
|
||||
for (i = 0; i < 25; i++)
|
||||
s[i] = 0;
|
||||
|
||||
/* Absorb customization (domain-separation) string */
|
||||
sep[0] = 0x01;
|
||||
sep[1] = 0xa8;
|
||||
sep[2] = 0x01;
|
||||
sep[3] = 0x00;
|
||||
sep[4] = 0x01;
|
||||
sep[5] = 16; // fixed bitlen of cstm
|
||||
sep[6] = cstm & 0xff;
|
||||
sep[7] = cstm >> 8;
|
||||
|
||||
KeccakF1600_StatePermute(s);
|
||||
|
||||
/* Absorb input */
|
||||
keccak_absorb(s, SHAKE128_RATE, in, inlen, 0x04);
|
||||
}
|
||||
|
||||
|
||||
void cshake128_simple_squeezeblocks(unsigned char *output, unsigned long long nblocks, uint64_t *s)
|
||||
{
|
||||
keccak_squeezeblocks(output, nblocks, s, SHAKE128_RATE);
|
||||
}
|
||||
|
||||
|
||||
void cshake128_simple(unsigned char *output, unsigned long long outlen, uint16_t cstm, const unsigned char *in, unsigned long long inlen)
|
||||
{
|
||||
uint64_t s[25];
|
||||
unsigned char t[SHAKE128_RATE];
|
||||
unsigned int i;
|
||||
|
||||
cshake128_simple_absorb(s, cstm, in, inlen);
|
||||
|
||||
/* Squeeze output */
|
||||
keccak_squeezeblocks(output, outlen/SHAKE128_RATE, s, SHAKE128_RATE);
|
||||
output += (outlen/SHAKE128_RATE)*SHAKE128_RATE;
|
||||
|
||||
if (outlen%SHAKE128_RATE)
|
||||
{
|
||||
keccak_squeezeblocks(t, 1, s, SHAKE128_RATE);
|
||||
for (i = 0; i < outlen%SHAKE128_RATE; i++)
|
||||
output[i] = t[i];
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/********** SHAKE256 ***********/
|
||||
|
||||
void shake256_absorb(uint64_t *s, const unsigned char *input, unsigned int inputByteLen)
|
||||
{
|
||||
keccak_absorb(s, SHAKE256_RATE, input, inputByteLen, 0x1F);
|
||||
}
|
||||
|
||||
|
||||
void shake256_squeezeblocks(unsigned char *output, unsigned long long nblocks, uint64_t *s)
|
||||
{
|
||||
keccak_squeezeblocks(output, nblocks, s, SHAKE256_RATE);
|
||||
}
|
||||
|
||||
|
||||
void shake256(unsigned char *output, unsigned long long outlen, const unsigned char *input, unsigned long long inlen)
|
||||
{
|
||||
uint64_t s[25];
|
||||
unsigned char t[SHAKE256_RATE];
|
||||
unsigned long long nblocks = outlen/SHAKE256_RATE;
|
||||
size_t i;
|
||||
|
||||
for (i = 0; i < 25; ++i)
|
||||
s[i] = 0;
|
||||
|
||||
/* Absorb input */
|
||||
keccak_absorb(s, SHAKE256_RATE, input, inlen, 0x1F);
|
||||
|
||||
/* Squeeze output */
|
||||
keccak_squeezeblocks(output, nblocks, s, SHAKE256_RATE);
|
||||
|
||||
output += nblocks*SHAKE256_RATE;
|
||||
outlen -= nblocks*SHAKE256_RATE;
|
||||
|
||||
if (outlen)
|
||||
{
|
||||
keccak_squeezeblocks(t, 1, s, SHAKE256_RATE);
|
||||
for (i = 0; i < outlen; i++)
|
||||
output[i] = t[i];
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/********** cSHAKE256 ***********/
|
||||
|
||||
void cshake256_simple_absorb(uint64_t s[25], uint16_t cstm, const unsigned char *in, unsigned long long inlen)
|
||||
{
|
||||
unsigned char *sep = (unsigned char*)s;
|
||||
unsigned int i;
|
||||
|
||||
for (i = 0; i < 25; i++)
|
||||
s[i] = 0;
|
||||
|
||||
/* Absorb customization (domain-separation) string */
|
||||
sep[0] = 0x01;
|
||||
sep[1] = 0x88;
|
||||
sep[2] = 0x01;
|
||||
sep[3] = 0x00;
|
||||
sep[4] = 0x01;
|
||||
sep[5] = 16; // fixed bitlen of cstm
|
||||
sep[6] = cstm & 0xff;
|
||||
sep[7] = cstm >> 8;
|
||||
|
||||
KeccakF1600_StatePermute(s);
|
||||
|
||||
/* Absorb input */
|
||||
keccak_absorb(s, SHAKE256_RATE, in, inlen, 0x04);
|
||||
}
|
||||
|
||||
|
||||
void cshake256_simple_squeezeblocks(unsigned char *output, unsigned long long nblocks, uint64_t *s)
|
||||
{
|
||||
keccak_squeezeblocks(output, nblocks, s, SHAKE256_RATE);
|
||||
}
|
||||
|
||||
|
||||
void cshake256_simple(unsigned char *output, unsigned long long outlen, uint16_t cstm, const unsigned char *in, unsigned long long inlen)
|
||||
{
|
||||
uint64_t s[25];
|
||||
unsigned char t[SHAKE256_RATE];
|
||||
unsigned int i;
|
||||
|
||||
cshake256_simple_absorb(s, cstm, in, inlen);
|
||||
|
||||
/* Squeeze output */
|
||||
keccak_squeezeblocks(output, outlen/SHAKE256_RATE, s, SHAKE256_RATE);
|
||||
output += (outlen/SHAKE256_RATE)*SHAKE256_RATE;
|
||||
|
||||
if(outlen%SHAKE256_RATE)
|
||||
{
|
||||
keccak_squeezeblocks(t, 1, s, SHAKE256_RATE);
|
||||
for (i = 0; i < outlen%SHAKE256_RATE; i++)
|
||||
output[i] = t[i];
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,27 @@
|
|||
#ifndef FIPS202_H
|
||||
#define FIPS202_H
|
||||
|
||||
#include <stdint.h>
|
||||
|
||||
|
||||
#define SHAKE128_RATE 168
|
||||
#define SHAKE256_RATE 136
|
||||
|
||||
void shake128_absorb(uint64_t *s, const unsigned char *input, unsigned int inputByteLen);
|
||||
void shake128_squeezeblocks(unsigned char *output, unsigned long long nblocks, uint64_t *s);
|
||||
void shake128(unsigned char *output, unsigned long long outlen, const unsigned char *input, unsigned long long inlen);
|
||||
|
||||
void cshake128_simple_absorb(uint64_t *s, uint16_t cstm, const unsigned char *in, unsigned long long inlen);
|
||||
void cshake128_simple_squeezeblocks(unsigned char *output, unsigned long long nblocks, uint64_t *s);
|
||||
void cshake128_simple(unsigned char *output, unsigned long long outlen, uint16_t cstm, const unsigned char *in, unsigned long long inlen);
|
||||
|
||||
void shake256_absorb(uint64_t *s, const unsigned char *input, unsigned int inputByteLen);
|
||||
void shake256_squeezeblocks(unsigned char *output, unsigned long long nblocks, uint64_t *s);
|
||||
void shake256(unsigned char *output, unsigned long long outlen, const unsigned char *input, unsigned long long inlen);
|
||||
|
||||
void cshake256_simple_absorb(uint64_t *s, uint16_t cstm, const unsigned char *in, unsigned long long inlen);
|
||||
void cshake256_simple_squeezeblocks(unsigned char *output, unsigned long long nblocks, uint64_t *s);
|
||||
void cshake256_simple(unsigned char *output, unsigned long long outlen, uint16_t cstm, const unsigned char *in, unsigned long long inlen);
|
||||
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,263 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: Ephemeral supersingular isogeny Diffie-Hellman key exchange (SIDH)
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "random/random.h"
|
||||
|
||||
|
||||
static void init_basis(digit_t *gen, f2elm_t XP, f2elm_t XQ, f2elm_t XR)
|
||||
{ // Initialization of basis points
|
||||
fpcopy(gen, XP[0]);
|
||||
fpcopy(gen + NWORDS_FIELD, XP[1]);
|
||||
fpcopy(gen + 2*NWORDS_FIELD, XQ[0]);
|
||||
fpcopy(gen + 3*NWORDS_FIELD, XQ[1]);
|
||||
fpcopy(gen + 4*NWORDS_FIELD, XR[0]);
|
||||
fpcopy(gen + 5*NWORDS_FIELD, XR[1]);
|
||||
}
|
||||
|
||||
|
||||
void random_mod_order_A(unsigned char* random_digits)
|
||||
{ // Generation of Alice's secret key
|
||||
// Outputs random value in [0, 2^eA - 1]
|
||||
|
||||
randombytes(random_digits, SECRETKEY_A_BYTES);
|
||||
random_digits[SECRETKEY_A_BYTES-1] &= MASK_ALICE; // Masking last byte
|
||||
}
|
||||
|
||||
|
||||
void random_mod_order_B(unsigned char* random_digits)
|
||||
{ // Generation of Bob's secret key
|
||||
// Outputs random value in [0, 2^Floor(Log(2, oB)) - 1]
|
||||
|
||||
randombytes(random_digits, SECRETKEY_B_BYTES);
|
||||
random_digits[SECRETKEY_B_BYTES-1] &= MASK_BOB; // Masking last byte
|
||||
}
|
||||
|
||||
|
||||
int EphemeralKeyGeneration_A(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA)
|
||||
{ // Alice's ephemeral public key generation
|
||||
// Input: a private key PrivateKeyA in the range [0, 2^eA - 1].
|
||||
// Output: the public key PublicKeyA consisting of 3 elements in GF(p^2) which are encoded by removing leading 0 bytes.
|
||||
point_proj_t R, phiP = {0}, phiQ = {0}, phiR = {0};
|
||||
f2elm_t XPA, XQA, XRA, A24plus = {0}, C24 = {0}, A = {0}, unused;
|
||||
digit_t SecretKeyA[NWORDS_ORDER] = {0};
|
||||
|
||||
// Initialize basis points
|
||||
init_basis((digit_t*)A_gen, XPA, XQA, XRA);
|
||||
init_basis((digit_t*)B_gen, phiP->X, phiQ->X, phiR->X);
|
||||
fpcopy((digit_t*)&Montgomery_one, (phiP->Z)[0]);
|
||||
fpcopy((digit_t*)&Montgomery_one, (phiQ->Z)[0]);
|
||||
fpcopy((digit_t*)&Montgomery_one, (phiR->Z)[0]);
|
||||
|
||||
// Initialize constants: A24plus = A+2C, C24 = 4C, where A=6, C=1
|
||||
fpcopy((digit_t*)&Montgomery_one, A24plus[0]);
|
||||
fp2add(A24plus, A24plus, A24plus);
|
||||
fp2add(A24plus, A24plus, C24);
|
||||
fp2add(A24plus, C24, A);
|
||||
fp2add(C24, C24, A24plus);
|
||||
|
||||
// Retrieve kernel point
|
||||
decode_to_digits(PrivateKeyA, SecretKeyA, SECRETKEY_A_BYTES, NWORDS_ORDER);
|
||||
LADDER3PT(XPA, XQA, XRA, SecretKeyA, ALICE, R, A);
|
||||
|
||||
#if (OALICE_BITS % 2 == 1)
|
||||
point_proj_t S;
|
||||
|
||||
xDBLe(R, S, A24plus, C24, (int)(OALICE_BITS-1));
|
||||
get_2_isog(S, A24plus, C24);
|
||||
eval_2_isog(phiP, S);
|
||||
eval_2_isog(phiQ, S);
|
||||
eval_2_isog(phiR, S);
|
||||
eval_2_isog(R, S);
|
||||
#endif
|
||||
|
||||
// Traverse tree
|
||||
TraverseTree(unused, R, A24plus, C24, strat_Alice, (unsigned int)MAX_Alice, true, phiP, phiQ, phiR);
|
||||
// Format public key
|
||||
fp2_encode(phiP->X, PublicKeyA);
|
||||
fp2_encode(phiQ->X, PublicKeyA + FP2_ENCODED_BYTES);
|
||||
fp2_encode(phiR->X, PublicKeyA + 2*FP2_ENCODED_BYTES);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
int EphemeralKeyGeneration_B(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB)
|
||||
{ // Bob's ephemeral public key generation
|
||||
// Input: a private key PrivateKeyB in the range [0, 2^Floor(Log(2,oB)) - 1].
|
||||
// Output: the public key PublicKeyB consisting of 3 elements in GF(p^2) which are encoded by removing leading 0 bytes.
|
||||
point_proj_t R, phiP = {0}, phiQ = {0}, phiR = {0}, pts[MAX_INT_POINTS_BOB];
|
||||
f2elm_t XPB, XQB, XRB, coeff[3], A24plus = {0}, A24minus = {0}, A = {0};
|
||||
unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_BOB], npts = 0, ii = 0;
|
||||
digit_t SecretKeyB[NWORDS_ORDER] = {0};
|
||||
|
||||
// Initialize basis points
|
||||
init_basis((digit_t*)B_gen, XPB, XQB, XRB);
|
||||
init_basis((digit_t*)A_gen, phiP->X, phiQ->X, phiR->X);
|
||||
fpcopy((digit_t*)&Montgomery_one, (phiP->Z)[0]);
|
||||
fpcopy((digit_t*)&Montgomery_one, (phiQ->Z)[0]);
|
||||
fpcopy((digit_t*)&Montgomery_one, (phiR->Z)[0]);
|
||||
|
||||
// Initialize constants: A24minus = A-2C, A24plus = A+2C, where A=6, C=1
|
||||
fpcopy((digit_t*)&Montgomery_one, A24plus[0]);
|
||||
fp2add(A24plus, A24plus, A24plus);
|
||||
fp2add(A24plus, A24plus, A24minus);
|
||||
fp2add(A24plus, A24minus, A);
|
||||
fp2add(A24minus, A24minus, A24plus);
|
||||
|
||||
// Retrieve kernel point
|
||||
decode_to_digits(PrivateKeyB, SecretKeyB, SECRETKEY_B_BYTES, NWORDS_ORDER);
|
||||
LADDER3PT(XPB, XQB, XRB, SecretKeyB, BOB, R, A);
|
||||
|
||||
// Traverse tree
|
||||
index = 0;
|
||||
for (row = 1; row < MAX_Bob; row++) {
|
||||
while (index < MAX_Bob-row) {
|
||||
fp2copy(R->X, pts[npts]->X);
|
||||
fp2copy(R->Z, pts[npts]->Z);
|
||||
pts_index[npts++] = index;
|
||||
m = strat_Bob[ii++];
|
||||
xTPLe(R, R, A24minus, A24plus, (int)m);
|
||||
index += m;
|
||||
}
|
||||
get_3_isog(R, A24minus, A24plus, coeff);
|
||||
|
||||
for (i = 0; i < npts; i++) {
|
||||
eval_3_isog(pts[i], coeff);
|
||||
}
|
||||
eval_3_isog(phiP, coeff);
|
||||
eval_3_isog(phiQ, coeff);
|
||||
eval_3_isog(phiR, coeff);
|
||||
|
||||
fp2copy(pts[npts-1]->X, R->X);
|
||||
fp2copy(pts[npts-1]->Z, R->Z);
|
||||
index = pts_index[npts-1];
|
||||
npts -= 1;
|
||||
}
|
||||
|
||||
get_3_isog(R, A24minus, A24plus, coeff);
|
||||
eval_3_isog(phiP, coeff);
|
||||
eval_3_isog(phiQ, coeff);
|
||||
eval_3_isog(phiR, coeff);
|
||||
|
||||
inv_3_way(phiP->Z, phiQ->Z, phiR->Z);
|
||||
fp2mul_mont(phiP->X, phiP->Z, phiP->X);
|
||||
fp2mul_mont(phiQ->X, phiQ->Z, phiQ->X);
|
||||
fp2mul_mont(phiR->X, phiR->Z, phiR->X);
|
||||
|
||||
// Format public key
|
||||
fp2_encode(phiP->X, PublicKeyB);
|
||||
fp2_encode(phiQ->X, PublicKeyB + FP2_ENCODED_BYTES);
|
||||
fp2_encode(phiR->X, PublicKeyB + 2*FP2_ENCODED_BYTES);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
int EphemeralSecretAgreement_A(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA)
|
||||
{ // Alice's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB
|
||||
// Inputs: Alice's PrivateKeyA is an integer in the range [0, oA-1].
|
||||
// Bob's PublicKeyB consists of 3 elements in GF(p^2) encoded by removing leading 0 bytes.
|
||||
// Output: a shared secret SharedSecretA that consists of one element in GF(p^2) encoded by removing leading 0 bytes.
|
||||
point_proj_t R, unused1, unused2, unused3;
|
||||
f2elm_t PKB[3], jinv, A24plus = {0}, C24 = {0}, A = {0};
|
||||
digit_t SecretKeyA[NWORDS_ORDER] = {0};
|
||||
|
||||
// Initialize images of Bob's basis
|
||||
fp2_decode(PublicKeyB, PKB[0]);
|
||||
fp2_decode(PublicKeyB + FP2_ENCODED_BYTES, PKB[1]);
|
||||
fp2_decode(PublicKeyB + 2*FP2_ENCODED_BYTES, PKB[2]);
|
||||
|
||||
// Initialize constants: A24plus = A+2C, C24 = 4C, where C=1
|
||||
get_A(PKB[0], PKB[1], PKB[2], A);
|
||||
fpadd((digit_t*)&Montgomery_one, (digit_t*)&Montgomery_one, C24[0]);
|
||||
fp2add(A, C24, A24plus);
|
||||
fpadd(C24[0], C24[0], C24[0]);
|
||||
|
||||
// Retrieve kernel point
|
||||
decode_to_digits(PrivateKeyA, SecretKeyA, SECRETKEY_A_BYTES, NWORDS_ORDER);
|
||||
LADDER3PT(PKB[0], PKB[1], PKB[2], SecretKeyA, ALICE, R, A);
|
||||
|
||||
#if (OALICE_BITS % 2 == 1)
|
||||
point_proj_t S;
|
||||
|
||||
xDBLe(R, S, A24plus, C24, (int)(OALICE_BITS-1));
|
||||
get_2_isog(S, A24plus, C24);
|
||||
eval_2_isog(R, S);
|
||||
#endif
|
||||
|
||||
// Traverse tree
|
||||
TraverseTree(jinv, R, A24plus, C24, strat_Alice, (unsigned int)MAX_Alice, false, unused1, unused2, unused3);
|
||||
// Format shared secret
|
||||
fp2_encode(jinv, SharedSecretA);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
int EphemeralSecretAgreement_B(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB)
|
||||
{ // Bob's ephemeral shared secret computation
|
||||
// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA
|
||||
// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,oB)) - 1].
|
||||
// Alice's PublicKeyA consists of 3 elements in GF(p^2) encoded by removing leading 0 bytes.
|
||||
// Output: a shared secret SharedSecretB that consists of one element in GF(p^2) encoded by removing leading 0 bytes.
|
||||
point_proj_t R, pts[MAX_INT_POINTS_BOB];
|
||||
f2elm_t coeff[3], PKB[3], jinv;
|
||||
f2elm_t A24plus = {0}, A24minus = {0}, A = {0};
|
||||
unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_BOB], npts = 0, ii = 0;
|
||||
digit_t SecretKeyB[NWORDS_ORDER] = {0};
|
||||
|
||||
// Initialize images of Alice's basis
|
||||
fp2_decode(PublicKeyA, PKB[0]);
|
||||
fp2_decode(PublicKeyA + FP2_ENCODED_BYTES, PKB[1]);
|
||||
fp2_decode(PublicKeyA + 2*FP2_ENCODED_BYTES, PKB[2]);
|
||||
|
||||
// Initialize constants: A24plus = A+2C, A24minus = A-2C, where C=1
|
||||
get_A(PKB[0], PKB[1], PKB[2], A);
|
||||
fpadd((digit_t*)&Montgomery_one, (digit_t*)&Montgomery_one, A24minus[0]);
|
||||
fp2add(A, A24minus, A24plus);
|
||||
fp2sub(A, A24minus, A24minus);
|
||||
|
||||
// Retrieve kernel point
|
||||
decode_to_digits(PrivateKeyB, SecretKeyB, SECRETKEY_B_BYTES, NWORDS_ORDER);
|
||||
LADDER3PT(PKB[0], PKB[1], PKB[2], SecretKeyB, BOB, R, A);
|
||||
|
||||
// Traverse tree
|
||||
index = 0;
|
||||
for (row = 1; row < MAX_Bob; row++) {
|
||||
while (index < MAX_Bob-row) {
|
||||
fp2copy(R->X, pts[npts]->X);
|
||||
fp2copy(R->Z, pts[npts]->Z);
|
||||
pts_index[npts++] = index;
|
||||
m = strat_Bob[ii++];
|
||||
xTPLe(R, R, A24minus, A24plus, (int)m);
|
||||
index += m;
|
||||
}
|
||||
get_3_isog(R, A24minus, A24plus, coeff);
|
||||
|
||||
for (i = 0; i < npts; i++) {
|
||||
eval_3_isog(pts[i], coeff);
|
||||
}
|
||||
|
||||
fp2copy(pts[npts-1]->X, R->X);
|
||||
fp2copy(pts[npts-1]->Z, R->Z);
|
||||
index = pts_index[npts-1];
|
||||
npts -= 1;
|
||||
}
|
||||
|
||||
get_3_isog(R, A24minus, A24plus, coeff);
|
||||
fp2add(A24plus, A24minus, A);
|
||||
fp2add(A, A, A);
|
||||
fp2sub(A24plus, A24minus, A24plus);
|
||||
j_inv(A, A24plus, jinv);
|
||||
fp2_encode(jinv, SharedSecretB); // Format shared secret
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -0,0 +1,98 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: supersingular isogeny key encapsulation (SIKE) protocol
|
||||
*********************************************************************************************/
|
||||
|
||||
#include <string.h>
|
||||
#include "sha3/fips202.h"
|
||||
|
||||
|
||||
int crypto_kem_keypair(unsigned char *pk, unsigned char *sk)
|
||||
{ // SIKE's key generation
|
||||
// Outputs: secret key sk (CRYPTO_SECRETKEYBYTES = MSG_BYTES + SECRETKEY_B_BYTES + CRYPTO_PUBLICKEYBYTES bytes)
|
||||
// public key pk (CRYPTO_PUBLICKEYBYTES bytes)
|
||||
|
||||
// Generate lower portion of secret key sk <- s||SK
|
||||
randombytes(sk, MSG_BYTES);
|
||||
random_mod_order_B(sk + MSG_BYTES);
|
||||
|
||||
// Generate public key pk
|
||||
EphemeralKeyGeneration_B(sk + MSG_BYTES, pk);
|
||||
|
||||
// Append public key pk to secret key sk
|
||||
memcpy(&sk[MSG_BYTES + SECRETKEY_B_BYTES], pk, CRYPTO_PUBLICKEYBYTES);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
int crypto_kem_enc(unsigned char *ct, unsigned char *ss, const unsigned char *pk)
|
||||
{ // SIKE's encapsulation
|
||||
// Input: public key pk (CRYPTO_PUBLICKEYBYTES bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = CRYPTO_PUBLICKEYBYTES + MSG_BYTES bytes)
|
||||
unsigned char ephemeralsk[SECRETKEY_A_BYTES];
|
||||
unsigned char jinvariant[FP2_ENCODED_BYTES];
|
||||
unsigned char h[MSG_BYTES];
|
||||
unsigned char temp[CRYPTO_CIPHERTEXTBYTES+MSG_BYTES];
|
||||
|
||||
// Generate ephemeralsk <- G(m||pk) mod oA
|
||||
randombytes(temp, MSG_BYTES);
|
||||
memcpy(&temp[MSG_BYTES], pk, CRYPTO_PUBLICKEYBYTES);
|
||||
shake256(ephemeralsk, SECRETKEY_A_BYTES, temp, CRYPTO_PUBLICKEYBYTES+MSG_BYTES);
|
||||
ephemeralsk[SECRETKEY_A_BYTES - 1] &= MASK_ALICE;
|
||||
|
||||
// Encrypt
|
||||
EphemeralKeyGeneration_A(ephemeralsk, ct);
|
||||
EphemeralSecretAgreement_A(ephemeralsk, pk, jinvariant);
|
||||
shake256(h, MSG_BYTES, jinvariant, FP2_ENCODED_BYTES);
|
||||
for (int i = 0; i < MSG_BYTES; i++) {
|
||||
ct[i + CRYPTO_PUBLICKEYBYTES] = temp[i] ^ h[i];
|
||||
}
|
||||
|
||||
// Generate shared secret ss <- H(m||ct)
|
||||
memcpy(&temp[MSG_BYTES], ct, CRYPTO_CIPHERTEXTBYTES);
|
||||
shake256(ss, CRYPTO_BYTES, temp, CRYPTO_CIPHERTEXTBYTES+MSG_BYTES);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
int crypto_kem_dec(unsigned char *ss, const unsigned char *ct, const unsigned char *sk)
|
||||
{ // SIKE's decapsulation
|
||||
// Input: secret key sk (CRYPTO_SECRETKEYBYTES = MSG_BYTES + SECRETKEY_B_BYTES + CRYPTO_PUBLICKEYBYTES bytes)
|
||||
// ciphertext message ct (CRYPTO_CIPHERTEXTBYTES = CRYPTO_PUBLICKEYBYTES + MSG_BYTES bytes)
|
||||
// Outputs: shared secret ss (CRYPTO_BYTES bytes)
|
||||
unsigned char ephemeralsk_[SECRETKEY_A_BYTES];
|
||||
unsigned char jinvariant_[FP2_ENCODED_BYTES];
|
||||
unsigned char h_[MSG_BYTES];
|
||||
unsigned char c0_[CRYPTO_PUBLICKEYBYTES];
|
||||
unsigned char temp[CRYPTO_CIPHERTEXTBYTES+MSG_BYTES];
|
||||
|
||||
// Decrypt
|
||||
EphemeralSecretAgreement_B(sk + MSG_BYTES, ct, jinvariant_);
|
||||
shake256(h_, MSG_BYTES, jinvariant_, FP2_ENCODED_BYTES);
|
||||
for (int i = 0; i < MSG_BYTES; i++) {
|
||||
temp[i] = ct[i + CRYPTO_PUBLICKEYBYTES] ^ h_[i];
|
||||
}
|
||||
|
||||
// Generate ephemeralsk_ <- G(m||pk) mod oA
|
||||
memcpy(&temp[MSG_BYTES], &sk[MSG_BYTES + SECRETKEY_B_BYTES], CRYPTO_PUBLICKEYBYTES);
|
||||
shake256(ephemeralsk_, SECRETKEY_A_BYTES, temp, CRYPTO_PUBLICKEYBYTES+MSG_BYTES);
|
||||
ephemeralsk_[SECRETKEY_A_BYTES - 1] &= MASK_ALICE;
|
||||
|
||||
// Generate shared secret ss <- H(m||ct), or output ss <- H(s||ct) in case of ct verification failure
|
||||
EphemeralKeyGeneration_A(ephemeralsk_, c0_);
|
||||
// If selector = 0 then do ss = H(m||ct), else if selector = -1 load s to do ss = H(s||ct)
|
||||
int8_t selector = ct_compare(c0_, ct, CRYPTO_PUBLICKEYBYTES);
|
||||
ct_cmov(temp, sk, MSG_BYTES, selector);
|
||||
memcpy(&temp[MSG_BYTES], ct, CRYPTO_CIPHERTEXTBYTES);
|
||||
shake256(ss, CRYPTO_BYTES, temp, CRYPTO_CIPHERTEXTBYTES+MSG_BYTES);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -0,0 +1,616 @@
|
|||
/********************************************************************************************
|
||||
* SIDH: an efficient supersingular isogeny cryptography library
|
||||
* Copyright (c) Microsoft Corporation
|
||||
*
|
||||
* Website: https://github.com/microsoft/PQCrypto-SIDH
|
||||
* Released under MIT license
|
||||
*
|
||||
* Abstract: testing code for field arithmetic, elliptic curve and isogeny functions
|
||||
*********************************************************************************************/
|
||||
|
||||
#include "../src/config.h"
|
||||
#include "../src/P377/P377_internal.h"
|
||||
#include "../src/internal.h"
|
||||
#include "test_extras.h"
|
||||
#include <stdio.h>
|
||||
|
||||
|
||||
// Benchmark and test parameters
|
||||
#if defined(GENERIC_IMPLEMENTATION) || (TARGET == TARGET_ARM)
|
||||
#define BENCH_LOOPS 100 // Number of iterations per bench
|
||||
#define SMALL_BENCH_LOOPS 100 // Number of iterations per bench
|
||||
#define TEST_LOOPS 10 // Number of iterations per test
|
||||
#else
|
||||
#define BENCH_LOOPS 100000
|
||||
#define SMALL_BENCH_LOOPS 10000
|
||||
#define TEST_LOOPS 100
|
||||
#endif
|
||||
|
||||
|
||||
bool fp_test()
|
||||
{ // Tests for the field arithmetic
|
||||
bool OK = true;
|
||||
int n, passed;
|
||||
felm_t a, b, c, d, e, f, ma, mb, mc, md, me, mf;
|
||||
|
||||
printf("\n--------------------------------------------------------------------------------------------------------\n\n");
|
||||
printf("Testing field arithmetic over GF(p377): \n\n");
|
||||
|
||||
// Field addition over the prime p377
|
||||
passed = 1;
|
||||
for (n=0; n<TEST_LOOPS; n++)
|
||||
{
|
||||
fprandom377_test(a); fprandom377_test(b); fprandom377_test(c); fprandom377_test(d); fprandom377_test(e); fprandom377_test(f);
|
||||
|
||||
fpadd377(a, b, d); fpadd377(d, c, e); // e = (a+b)+c
|
||||
fpadd377(b, c, d); fpadd377(d, a, f); // f = a+(b+c)
|
||||
fpcorrection377(e);
|
||||
fpcorrection377(f);
|
||||
if (compare_words(e, f, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fpadd377(a, b, d); // d = a+b
|
||||
fpadd377(b, a, e); // e = b+a
|
||||
fpcorrection377(d);
|
||||
fpcorrection377(e);
|
||||
if (compare_words(d, e, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fpzero377(b);
|
||||
fpadd377(a, b, d); // d = a+0
|
||||
if (compare_words(a, d, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fpzero377(b);
|
||||
fpcopy377(a, d);
|
||||
fpneg377(d);
|
||||
fpadd377(a, d, e); // e = a+(-a)
|
||||
fpcorrection377(e);
|
||||
if (compare_words(e, b, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
}
|
||||
if (passed==1) printf(" GF(p) addition tests ............................................ PASSED");
|
||||
else { printf(" GF(p) addition tests... FAILED"); printf("\n"); return false; }
|
||||
printf("\n");
|
||||
|
||||
// Field subtraction over the prime p377
|
||||
passed = 1;
|
||||
for (n=0; n<TEST_LOOPS; n++)
|
||||
{
|
||||
fprandom377_test(a); fprandom377_test(b); fprandom377_test(c); fprandom377_test(d); fprandom377_test(e); fprandom377_test(f);
|
||||
|
||||
fpsub377(a, b, d); fpsub377(d, c, e); // e = (a-b)-c
|
||||
fpadd377(b, c, d); fpsub377(a, d, f); // f = a-(b+c)
|
||||
fpcorrection377(e);
|
||||
fpcorrection377(f);
|
||||
if (compare_words(e, f, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fpsub377(a, b, d); // d = a-b
|
||||
fpsub377(b, a, e);
|
||||
fpneg377(e); // e = -(b-a)
|
||||
fpcorrection377(d);
|
||||
fpcorrection377(e);
|
||||
if (compare_words(d, e, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fpzero377(b);
|
||||
fpsub377(a, b, d); // d = a-0
|
||||
if (compare_words(a, d, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fpzero377(b);
|
||||
fpcopy377(a, d);
|
||||
fpsub377(a, d, e); // e = a+(-a)
|
||||
fpcorrection377(e);
|
||||
if (compare_words(e, b, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
}
|
||||
if (passed==1) printf(" GF(p) subtraction tests ......................................... PASSED");
|
||||
else { printf(" GF(p) subtraction tests... FAILED"); printf("\n"); return false; }
|
||||
printf("\n");
|
||||
|
||||
// Field multiplication over the prime p377
|
||||
passed = 1;
|
||||
for (n=0; n<TEST_LOOPS; n++)
|
||||
{
|
||||
fprandom377_test(a); fprandom377_test(b); fprandom377_test(c);
|
||||
fprandom377_test(ma); fprandom377_test(mb); fprandom377_test(mc); fprandom377_test(md); fprandom377_test(me); fprandom377_test(mf);
|
||||
|
||||
to_mont(a, ma);
|
||||
fpcopy377(ma, mc);
|
||||
from_mont(mc, c);
|
||||
if (compare_words(a, c, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
to_mont(a, ma); to_mont(b, mb); to_mont(c, mc);
|
||||
fpmul377_mont(ma, mb, md); fpmul377_mont(md, mc, me); // e = (a*b)*c
|
||||
fpmul377_mont(mb, mc, md); fpmul377_mont(md, ma, mf); // f = a*(b*c)
|
||||
from_mont(me, e);
|
||||
from_mont(mf, f);
|
||||
if (compare_words(e, f, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
to_mont(a, ma); to_mont(b, mb); to_mont(c, mc);
|
||||
fpadd377(mb, mc, md); fpmul377_mont(ma, md, me); // e = a*(b+c)
|
||||
fpmul377_mont(ma, mb, md); fpmul377_mont(ma, mc, mf); fpadd377(md, mf, mf); // f = a*b+a*c
|
||||
from_mont(me, e);
|
||||
from_mont(mf, f);
|
||||
if (compare_words(e, f, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
to_mont(a, ma); to_mont(b, mb);
|
||||
fpmul377_mont(ma, mb, md); // d = a*b
|
||||
fpmul377_mont(mb, ma, me); // e = b*a
|
||||
from_mont(md, d);
|
||||
from_mont(me, e);
|
||||
if (compare_words(d, e, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
to_mont(a, ma);
|
||||
fpzero377(b); b[0] = 1; to_mont(b, mb);
|
||||
fpmul377_mont(ma, mb, md); // d = a*1
|
||||
from_mont(ma, a);
|
||||
from_mont(md, d);
|
||||
if (compare_words(a, d, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fpzero377(b); to_mont(b, mb);
|
||||
fpmul377_mont(ma, mb, md); // d = a*0
|
||||
from_mont(mb, b);
|
||||
from_mont(md, d);
|
||||
if (compare_words(b, d, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
}
|
||||
if (passed==1) printf(" GF(p) multiplication tests ...................................... PASSED");
|
||||
else { printf(" GF(p) multiplication tests... FAILED"); printf("\n"); return false; }
|
||||
printf("\n");
|
||||
|
||||
// Field squaring over the prime p377
|
||||
passed = 1;
|
||||
for (n=0; n<TEST_LOOPS; n++)
|
||||
{
|
||||
fprandom377_test(a);
|
||||
|
||||
to_mont(a, ma);
|
||||
fpsqr377_mont(ma, mb); // b = a^2
|
||||
fpmul377_mont(ma, ma, mc); // c = a*a
|
||||
if (compare_words(mb, mc, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fpzero377(a); to_mont(a, ma);
|
||||
fpsqr377_mont(ma, md); // d = 0^2
|
||||
if (compare_words(ma, md, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
}
|
||||
if (passed==1) printf(" GF(p) squaring tests............................................. PASSED");
|
||||
else { printf(" GF(p) squaring tests... FAILED"); printf("\n"); return false; }
|
||||
printf("\n");
|
||||
|
||||
// Field inversion over the prime p377
|
||||
passed = 1;
|
||||
for (n=0; n<TEST_LOOPS; n++)
|
||||
{
|
||||
fprandom377_test(a);
|
||||
to_mont(a, ma);
|
||||
fpzero377(d); d[0]=1; to_mont(d, md);
|
||||
fpcopy377(ma, mb);
|
||||
fpinv377_mont(ma);
|
||||
fpmul377_mont(ma, mb, mc); // c = a*a^-1
|
||||
if (compare_words(mc, md, NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
}
|
||||
if (passed==1) printf(" GF(p) inversion tests............................................ PASSED");
|
||||
else { printf(" GF(p) inversion tests... FAILED"); printf("\n"); return false; }
|
||||
printf("\n");
|
||||
|
||||
return OK;
|
||||
}
|
||||
|
||||
|
||||
bool fp2_test()
|
||||
{ // Tests for the quadratic extension field arithmetic
|
||||
bool OK = true;
|
||||
int n, passed;
|
||||
f2elm_t a, b, c, d, e, f, ma, mb, mc, md, me, mf;
|
||||
|
||||
printf("\n--------------------------------------------------------------------------------------------------------\n\n");
|
||||
printf("Testing quadratic extension arithmetic over GF(p377^2): \n\n");
|
||||
|
||||
// Addition over GF(p377^2)
|
||||
passed = 1;
|
||||
for (n=0; n<TEST_LOOPS; n++)
|
||||
{
|
||||
fp2random377_test((digit_t*)a); fp2random377_test((digit_t*)b); fp2random377_test((digit_t*)c); fp2random377_test((digit_t*)d); fp2random377_test((digit_t*)e); fp2random377_test((digit_t*)f);
|
||||
|
||||
fp2add377(a, b, d); fp2add377(d, c, e); // e = (a+b)+c
|
||||
fp2add377(b, c, d); fp2add377(d, a, f); // f = a+(b+c)
|
||||
if (compare_words((digit_t*)e, (digit_t*)f, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fp2add377(a, b, d); // d = a+b
|
||||
fp2add377(b, a, e); // e = b+a
|
||||
if (compare_words((digit_t*)d, (digit_t*)e, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fp2zero377(b);
|
||||
fp2add377(a, b, d); // d = a+0
|
||||
if (compare_words((digit_t*)a, (digit_t*)d, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fp2zero377(b);
|
||||
fp2copy377(a, d);
|
||||
fp2neg377(d);
|
||||
fp2add377(a, d, e); // e = a+(-a)
|
||||
if (compare_words((digit_t*)e, (digit_t*)b, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
}
|
||||
if (passed==1) printf(" GF(p^2) addition tests .......................................... PASSED");
|
||||
else { printf(" GF(p^2) addition tests... FAILED"); printf("\n"); return false; }
|
||||
printf("\n");
|
||||
|
||||
// Subtraction over GF(p377^2)
|
||||
passed = 1;
|
||||
for (n=0; n<TEST_LOOPS; n++)
|
||||
{
|
||||
fp2random377_test((digit_t*)a); fp2random377_test((digit_t*)b); fp2random377_test((digit_t*)c); fp2random377_test((digit_t*)d); fp2random377_test((digit_t*)e); fp2random377_test((digit_t*)f);
|
||||
|
||||
fp2sub377(a, b, d); fp2sub377(d, c, e); // e = (a-b)-c
|
||||
fp2add377(b, c, d); fp2sub377(a, d, f); // f = a-(b+c)
|
||||
if (compare_words((digit_t*)e, (digit_t*)f, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fp2sub377(a, b, d); // d = a-b
|
||||
fp2sub377(b, a, e);
|
||||
fp2neg377(e); // e = -(b-a)
|
||||
if (compare_words((digit_t*)d, (digit_t*)e, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fp2zero377(b);
|
||||
fp2sub377(a, b, d); // d = a-0
|
||||
if (compare_words((digit_t*)a, (digit_t*)d, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fp2zero377(b);
|
||||
fp2copy377(a, d);
|
||||
fp2sub377(a, d, e); // e = a+(-a)
|
||||
if (compare_words((digit_t*)e, (digit_t*)b, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
}
|
||||
if (passed==1) printf(" GF(p^2) subtraction tests ....................................... PASSED");
|
||||
else { printf(" GF(p^2) subtraction tests... FAILED"); printf("\n"); return false; }
|
||||
printf("\n");
|
||||
|
||||
// Multiplication over GF(p377^2)
|
||||
passed = 1;
|
||||
for (n=0; n<TEST_LOOPS; n++)
|
||||
{
|
||||
fp2random377_test((digit_t*)a); fp2random377_test((digit_t*)b); fp2random377_test((digit_t*)c);
|
||||
fp2random377_test((digit_t*)ma); fp2random377_test((digit_t*)mb); fp2random377_test((digit_t*)mc); fp2random377_test((digit_t*)md); fp2random377_test((digit_t*)me); fp2random377_test((digit_t*)mf);
|
||||
|
||||
to_fp2mont(a, ma);
|
||||
fp2copy377(ma, mc);
|
||||
from_fp2mont(mc, c);
|
||||
if (compare_words((digit_t*)a, (digit_t*)c, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
to_fp2mont(a, ma); to_fp2mont(b, mb); to_fp2mont(c, mc);
|
||||
fp2mul377_mont(ma, mb, md); fp2mul377_mont(md, mc, me); // e = (a*b)*c
|
||||
fp2mul377_mont(mb, mc, md); fp2mul377_mont(md, ma, mf); // f = a*(b*c)
|
||||
from_fp2mont(me, e);
|
||||
from_fp2mont(mf, f);
|
||||
if (compare_words((digit_t*)e, (digit_t*)f, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
to_fp2mont(a, ma); to_fp2mont(b, mb); to_fp2mont(c, mc);
|
||||
fp2add377(mb, mc, md); fp2mul377_mont(ma, md, me); // e = a*(b+c)
|
||||
fp2mul377_mont(ma, mb, md); fp2mul377_mont(ma, mc, mf); fp2add377(md, mf, mf); // f = a*b+a*c
|
||||
from_fp2mont(me, e);
|
||||
from_fp2mont(mf, f);
|
||||
if (compare_words((digit_t*)e, (digit_t*)f, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
to_fp2mont(a, ma); to_fp2mont(b, mb);
|
||||
fp2mul377_mont(ma, mb, md); // d = a*b
|
||||
fp2mul377_mont(mb, ma, me); // e = b*a
|
||||
from_fp2mont(md, d);
|
||||
from_fp2mont(me, e);
|
||||
if (compare_words((digit_t*)d, (digit_t*)e, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
to_fp2mont(a, ma);
|
||||
fp2zero377(b); b[0][0] = 1; to_fp2mont(b, mb);
|
||||
fp2mul377_mont(ma, mb, md); // d = a*1
|
||||
from_fp2mont(md, d);
|
||||
if (compare_words((digit_t*)a, (digit_t*)d, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fp2zero377(b); to_fp2mont(b, mb);
|
||||
fp2mul377_mont(ma, mb, md); // d = a*0
|
||||
from_fp2mont(md, d);
|
||||
if (compare_words((digit_t*)b, (digit_t*)d, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
}
|
||||
if (passed==1) printf(" GF(p^2) multiplication tests .................................... PASSED");
|
||||
else { printf(" GF(p^2) multiplication tests... FAILED"); printf("\n"); return false; }
|
||||
printf("\n");
|
||||
|
||||
// Squaring over GF(p377^2)
|
||||
passed = 1;
|
||||
for (n=0; n<TEST_LOOPS; n++)
|
||||
{
|
||||
fp2random377_test((digit_t*)a);
|
||||
|
||||
to_fp2mont(a, ma);
|
||||
fp2sqr377_mont(ma, mb); // b = a^2
|
||||
fp2mul377_mont(ma, ma, mc); // c = a*a
|
||||
from_fp2mont(mb, b);
|
||||
from_fp2mont(mc, c);
|
||||
if (compare_words((digit_t*)b, (digit_t*)c, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
|
||||
fp2zero377(a); to_fp2mont(a, ma);
|
||||
fp2sqr377_mont(ma, md); // d = 0^2
|
||||
from_fp2mont(md, d);
|
||||
if (compare_words((digit_t*)a, (digit_t*)d, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
}
|
||||
if (passed==1) printf(" GF(p^2) squaring tests........................................... PASSED");
|
||||
else { printf(" GF(p^2) squaring tests... FAILED"); printf("\n"); return false; }
|
||||
printf("\n");
|
||||
|
||||
// Inversion over GF(p377^2)
|
||||
passed = 1;
|
||||
for (n=0; n<TEST_LOOPS; n++)
|
||||
{
|
||||
fp2random377_test((digit_t*)a);
|
||||
|
||||
to_fp2mont(a, ma);
|
||||
fp2zero377(d); d[0][0]=1; to_fp2mont(d, md);
|
||||
fp2copy377(ma, mb);
|
||||
fp2inv377_mont(ma);
|
||||
fp2mul377_mont(ma, mb, mc); // c = a*a^-1
|
||||
from_fp2mont(mc, c);
|
||||
if (compare_words((digit_t*)c, (digit_t*)d, 2*NWORDS_FIELD)!=0) { passed=0; break; }
|
||||
}
|
||||
if (passed==1) printf(" GF(p^2) inversion tests.......................................... PASSED");
|
||||
else { printf(" GF(p^2) inversion tests... FAILED"); printf("\n"); return false; }
|
||||
printf("\n");
|
||||
|
||||
return OK;
|
||||
}
|
||||
|
||||
|
||||
bool fp_run()
|
||||
{
|
||||
bool OK = true;
|
||||
int n;
|
||||
unsigned long long cycles, cycles1, cycles2;
|
||||
felm_t a, b, c;
|
||||
dfelm_t aa;
|
||||
|
||||
printf("\n--------------------------------------------------------------------------------------------------------\n\n");
|
||||
printf("Benchmarking field arithmetic over GF(p377): \n\n");
|
||||
|
||||
fprandom377_test(a); fprandom377_test(b); fprandom377_test(c);
|
||||
|
||||
// GF(p) addition using p377
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
cycles1 = cpucycles();
|
||||
fpadd377(a, b, c);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" GF(p) addition runs in .......................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
// GF(p) subtraction using p377
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
cycles1 = cpucycles();
|
||||
fpsub377(a, b, c);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" GF(p) subtraction runs in ....................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
// GF(p) multiplication using p377
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
cycles1 = cpucycles();
|
||||
fpmul377_mont(a, b, c);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" GF(p) multiplication runs in .................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
// GF(p) reduction using p377
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
mp_mul(a, b, aa, NWORDS_FIELD);
|
||||
|
||||
cycles1 = cpucycles();
|
||||
rdc_mont(aa, c);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" GF(p) reduction runs in ......................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
// GF(p) inversion
|
||||
cycles = 0;
|
||||
for (n=0; n<SMALL_BENCH_LOOPS; n++)
|
||||
{
|
||||
cycles1 = cpucycles();
|
||||
fpinv377_mont(a);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" GF(p) inversion (exponentiation) runs in ........................ %7lld ", cycles/SMALL_BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
return OK;
|
||||
}
|
||||
|
||||
|
||||
bool fp2_run()
|
||||
{
|
||||
bool OK = true;
|
||||
int n;
|
||||
unsigned long long cycles, cycles1, cycles2;
|
||||
f2elm_t a, b, c;
|
||||
|
||||
printf("\n--------------------------------------------------------------------------------------------------------\n\n");
|
||||
printf("Benchmarking quadratic extension arithmetic over GF(p377^2): \n\n");
|
||||
|
||||
fp2random377_test((digit_t*)a); fp2random377_test((digit_t*)b); fp2random377_test((digit_t*)c);
|
||||
|
||||
// GF(p^2) addition
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
cycles1 = cpucycles();
|
||||
fp2add377(a, b, c);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" GF(p^2) addition runs in ........................................ %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
// GF(p^2) subtraction
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
cycles1 = cpucycles();
|
||||
fp2sub377(a, b, c);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" GF(p^2) subtraction runs in ..................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
// GF(p^2) multiplication
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
cycles1 = cpucycles();
|
||||
fp2mul377_mont(a, b, c);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" GF(p^2) multiplication runs in .................................. %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
// GF(p^2) squaring
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
cycles1 = cpucycles();
|
||||
fp2sqr377_mont(a, b);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" GF(p^2) squaring runs in ........................................ %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
// GF(p^2) inversion
|
||||
cycles = 0;
|
||||
for (n=0; n<SMALL_BENCH_LOOPS; n++)
|
||||
{
|
||||
cycles1 = cpucycles();
|
||||
fp2inv377_mont(a);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" GF(p^2) inversion (exponentiation) runs in ...................... %7lld ", cycles/SMALL_BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
return OK;
|
||||
}
|
||||
|
||||
|
||||
bool ecisog_run()
|
||||
{
|
||||
bool OK = true;
|
||||
int n;
|
||||
unsigned long long cycles, cycles1, cycles2;
|
||||
f2elm_t A24, C24, A4, A, C, coeff[5];
|
||||
point_proj_t P, Q;
|
||||
|
||||
printf("\n--------------------------------------------------------------------------------------------------------\n\n");
|
||||
printf("Benchmarking elliptic curve and isogeny functions: \n\n");
|
||||
|
||||
// Point doubling
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
fp2random377_test((digit_t*)A24); fp2random377_test((digit_t*)C24);
|
||||
|
||||
cycles1 = cpucycles();
|
||||
xDBL(P, Q, A24, C24);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" Point doubling runs in .......................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
// 4-isogeny of a projective point
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
fp2random377_test((digit_t*)A); fp2random377_test((digit_t*)coeff[0]); fp2random377_test((digit_t*)coeff[1]); fp2random377_test((digit_t*)coeff[2]);
|
||||
|
||||
cycles1 = cpucycles();
|
||||
get_4_isog(P, A, C, coeff);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" 4-isogeny of projective point runs in ........................... %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
// 4-isogeny evaluation at projective point
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
fp2random377_test((digit_t*)A); fp2random377_test((digit_t*)coeff[0]); fp2random377_test((digit_t*)coeff[1]); fp2random377_test((digit_t*)coeff[2]);
|
||||
|
||||
cycles1 = cpucycles();
|
||||
eval_4_isog(P, coeff);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" 4-isogeny evaluation at projective point runs in ................ %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
// Point tripling
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
fp2random377_test((digit_t*)A4); fp2random377_test((digit_t*)C);
|
||||
|
||||
cycles1 = cpucycles();
|
||||
xTPL(P, Q, A4, C);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" Point tripling runs in .......................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
// 3-isogeny of a projective point
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
fp2random377_test((digit_t*)A); fp2random377_test((digit_t*)C);
|
||||
|
||||
cycles1 = cpucycles();
|
||||
get_3_isog(P, A, C, coeff);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" 3-isogeny of projective point runs in ........................... %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
// 3-isogeny evaluation at projective point
|
||||
cycles = 0;
|
||||
for (n=0; n<BENCH_LOOPS; n++)
|
||||
{
|
||||
cycles1 = cpucycles();
|
||||
eval_3_isog(Q, coeff);
|
||||
cycles2 = cpucycles();
|
||||
cycles = cycles+(cycles2-cycles1);
|
||||
}
|
||||
printf(" 3-isogeny evaluation at projective point runs in ................ %7lld ", cycles/BENCH_LOOPS); print_unit;
|
||||
printf("\n");
|
||||
|
||||
return OK;
|
||||
}
|
||||
|
||||
|
||||
int main()
|
||||
{
|
||||
bool OK = true;
|
||||
|
||||
OK = OK && fp_test(); // Test field operations using p377
|
||||
OK = OK && fp_run(); // Benchmark field operations using p377
|
||||
|
||||
OK = OK && fp2_test(); // Test arithmetic functions over GF(p377^2)
|
||||
OK = OK && fp2_run(); // Benchmark arithmetic functions over GF(p377^2)
|
||||
|
||||
OK = OK && ecisog_run(); // Benchmark elliptic curve and isogeny functions
|
||||
|
||||
return OK;
|
||||
}
|
||||
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