158 строки
3.3 KiB
C
158 строки
3.3 KiB
C
/* mpi-mod.c - Modular reduction
|
|
* Copyright (C) 1998, 1999, 2001, 2002, 2003,
|
|
* 2007 Free Software Foundation, Inc.
|
|
*
|
|
* This file is part of Libgcrypt.
|
|
*/
|
|
|
|
|
|
#include "mpi-internal.h"
|
|
#include "longlong.h"
|
|
|
|
/* Context used with Barrett reduction. */
|
|
struct barrett_ctx_s {
|
|
MPI m; /* The modulus - may not be modified. */
|
|
int m_copied; /* If true, M needs to be released. */
|
|
int k;
|
|
MPI y;
|
|
MPI r1; /* Helper MPI. */
|
|
MPI r2; /* Helper MPI. */
|
|
MPI r3; /* Helper MPI allocated on demand. */
|
|
};
|
|
|
|
|
|
|
|
void mpi_mod(MPI rem, MPI dividend, MPI divisor)
|
|
{
|
|
mpi_fdiv_r(rem, dividend, divisor);
|
|
}
|
|
|
|
/* This function returns a new context for Barrett based operations on
|
|
* the modulus M. This context needs to be released using
|
|
* _gcry_mpi_barrett_free. If COPY is true M will be transferred to
|
|
* the context and the user may change M. If COPY is false, M may not
|
|
* be changed until gcry_mpi_barrett_free has been called.
|
|
*/
|
|
mpi_barrett_t mpi_barrett_init(MPI m, int copy)
|
|
{
|
|
mpi_barrett_t ctx;
|
|
MPI tmp;
|
|
|
|
mpi_normalize(m);
|
|
ctx = kcalloc(1, sizeof(*ctx), GFP_KERNEL);
|
|
if (!ctx)
|
|
return NULL;
|
|
|
|
if (copy) {
|
|
ctx->m = mpi_copy(m);
|
|
ctx->m_copied = 1;
|
|
} else
|
|
ctx->m = m;
|
|
|
|
ctx->k = mpi_get_nlimbs(m);
|
|
tmp = mpi_alloc(ctx->k + 1);
|
|
|
|
/* Barrett precalculation: y = floor(b^(2k) / m). */
|
|
mpi_set_ui(tmp, 1);
|
|
mpi_lshift_limbs(tmp, 2 * ctx->k);
|
|
mpi_fdiv_q(tmp, tmp, m);
|
|
|
|
ctx->y = tmp;
|
|
ctx->r1 = mpi_alloc(2 * ctx->k + 1);
|
|
ctx->r2 = mpi_alloc(2 * ctx->k + 1);
|
|
|
|
return ctx;
|
|
}
|
|
|
|
void mpi_barrett_free(mpi_barrett_t ctx)
|
|
{
|
|
if (ctx) {
|
|
mpi_free(ctx->y);
|
|
mpi_free(ctx->r1);
|
|
mpi_free(ctx->r2);
|
|
if (ctx->r3)
|
|
mpi_free(ctx->r3);
|
|
if (ctx->m_copied)
|
|
mpi_free(ctx->m);
|
|
kfree(ctx);
|
|
}
|
|
}
|
|
|
|
|
|
/* R = X mod M
|
|
*
|
|
* Using Barrett reduction. Before using this function
|
|
* _gcry_mpi_barrett_init must have been called to do the
|
|
* precalculations. CTX is the context created by this precalculation
|
|
* and also conveys M. If the Barret reduction could no be done a
|
|
* straightforward reduction method is used.
|
|
*
|
|
* We assume that these conditions are met:
|
|
* Input: x =(x_2k-1 ...x_0)_b
|
|
* m =(m_k-1 ....m_0)_b with m_k-1 != 0
|
|
* Output: r = x mod m
|
|
*/
|
|
void mpi_mod_barrett(MPI r, MPI x, mpi_barrett_t ctx)
|
|
{
|
|
MPI m = ctx->m;
|
|
int k = ctx->k;
|
|
MPI y = ctx->y;
|
|
MPI r1 = ctx->r1;
|
|
MPI r2 = ctx->r2;
|
|
int sign;
|
|
|
|
mpi_normalize(x);
|
|
if (mpi_get_nlimbs(x) > 2*k) {
|
|
mpi_mod(r, x, m);
|
|
return;
|
|
}
|
|
|
|
sign = x->sign;
|
|
x->sign = 0;
|
|
|
|
/* 1. q1 = floor( x / b^k-1)
|
|
* q2 = q1 * y
|
|
* q3 = floor( q2 / b^k+1 )
|
|
* Actually, we don't need qx, we can work direct on r2
|
|
*/
|
|
mpi_set(r2, x);
|
|
mpi_rshift_limbs(r2, k-1);
|
|
mpi_mul(r2, r2, y);
|
|
mpi_rshift_limbs(r2, k+1);
|
|
|
|
/* 2. r1 = x mod b^k+1
|
|
* r2 = q3 * m mod b^k+1
|
|
* r = r1 - r2
|
|
* 3. if r < 0 then r = r + b^k+1
|
|
*/
|
|
mpi_set(r1, x);
|
|
if (r1->nlimbs > k+1) /* Quick modulo operation. */
|
|
r1->nlimbs = k+1;
|
|
mpi_mul(r2, r2, m);
|
|
if (r2->nlimbs > k+1) /* Quick modulo operation. */
|
|
r2->nlimbs = k+1;
|
|
mpi_sub(r, r1, r2);
|
|
|
|
if (mpi_has_sign(r)) {
|
|
if (!ctx->r3) {
|
|
ctx->r3 = mpi_alloc(k + 2);
|
|
mpi_set_ui(ctx->r3, 1);
|
|
mpi_lshift_limbs(ctx->r3, k + 1);
|
|
}
|
|
mpi_add(r, r, ctx->r3);
|
|
}
|
|
|
|
/* 4. while r >= m do r = r - m */
|
|
while (mpi_cmp(r, m) >= 0)
|
|
mpi_sub(r, r, m);
|
|
|
|
x->sign = sign;
|
|
}
|
|
|
|
|
|
void mpi_mul_barrett(MPI w, MPI u, MPI v, mpi_barrett_t ctx)
|
|
{
|
|
mpi_mul(w, u, v);
|
|
mpi_mod_barrett(w, w, ctx);
|
|
}
|