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putty/sshbn.c

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26 KiB
C
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/*
* Bignum routines for RSA and DH and stuff.
*/
#include <stdio.h>
#include <assert.h>
#include <stdlib.h>
#include <string.h>
#include "misc.h"
/*
* Usage notes:
* * Do not call the DIVMOD_WORD macro with expressions such as array
* subscripts, as some implementations object to this (see below).
* * Note that none of the division methods below will cope if the
* quotient won't fit into BIGNUM_INT_BITS. Callers should be careful
* to avoid this case.
* If this condition occurs, in the case of the x86 DIV instruction,
* an overflow exception will occur, which (according to a correspondent)
* will manifest on Windows as something like
* 0xC0000095: Integer overflow
* The C variant won't give the right answer, either.
*/
#if defined __GNUC__ && defined __i386__
typedef unsigned long BignumInt;
typedef unsigned long long BignumDblInt;
#define BIGNUM_INT_MASK 0xFFFFFFFFUL
#define BIGNUM_TOP_BIT 0x80000000UL
#define BIGNUM_INT_BITS 32
#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)
#define DIVMOD_WORD(q, r, hi, lo, w) \
__asm__("div %2" : \
"=d" (r), "=a" (q) : \
"r" (w), "d" (hi), "a" (lo))
#elif defined _MSC_VER && defined _M_IX86
typedef unsigned __int32 BignumInt;
typedef unsigned __int64 BignumDblInt;
#define BIGNUM_INT_MASK 0xFFFFFFFFUL
#define BIGNUM_TOP_BIT 0x80000000UL
#define BIGNUM_INT_BITS 32
#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)
/* Note: MASM interprets array subscripts in the macro arguments as
* assembler syntax, which gives the wrong answer. Don't supply them.
* <http://msdn2.microsoft.com/en-us/library/bf1dw62z.aspx> */
#define DIVMOD_WORD(q, r, hi, lo, w) do { \
__asm mov edx, hi \
__asm mov eax, lo \
__asm div w \
__asm mov r, edx \
__asm mov q, eax \
} while(0)
#else
typedef unsigned short BignumInt;
typedef unsigned long BignumDblInt;
#define BIGNUM_INT_MASK 0xFFFFU
#define BIGNUM_TOP_BIT 0x8000U
#define BIGNUM_INT_BITS 16
#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)
#define DIVMOD_WORD(q, r, hi, lo, w) do { \
BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \
q = n / w; \
r = n % w; \
} while (0)
#endif
#define BIGNUM_INT_BYTES (BIGNUM_INT_BITS / 8)
#define BIGNUM_INTERNAL
typedef BignumInt *Bignum;
#include "ssh.h"
BignumInt bnZero[1] = { 0 };
BignumInt bnOne[2] = { 1, 1 };
/*
* The Bignum format is an array of `BignumInt'. The first
* element of the array counts the remaining elements. The
* remaining elements express the actual number, base 2^BIGNUM_INT_BITS, _least_
* significant digit first. (So it's trivial to extract the bit
* with value 2^n for any n.)
*
* All Bignums in this module are positive. Negative numbers must
* be dealt with outside it.
*
* INVARIANT: the most significant word of any Bignum must be
* nonzero.
*/
Bignum Zero = bnZero, One = bnOne;
static Bignum newbn(int length)
{
Bignum b = snewn(length + 1, BignumInt);
if (!b)
abort(); /* FIXME */
memset(b, 0, (length + 1) * sizeof(*b));
b[0] = length;
return b;
}
void bn_restore_invariant(Bignum b)
{
while (b[0] > 1 && b[b[0]] == 0)
b[0]--;
}
Bignum copybn(Bignum orig)
{
Bignum b = snewn(orig[0] + 1, BignumInt);
if (!b)
abort(); /* FIXME */
memcpy(b, orig, (orig[0] + 1) * sizeof(*b));
return b;
}
void freebn(Bignum b)
{
/*
* Burn the evidence, just in case.
*/
memset(b, 0, sizeof(b[0]) * (b[0] + 1));
sfree(b);
}
Bignum bn_power_2(int n)
{
Bignum ret = newbn(n / BIGNUM_INT_BITS + 1);
bignum_set_bit(ret, n, 1);
return ret;
}
/*
* Compute c = a * b.
* Input is in the first len words of a and b.
* Result is returned in the first 2*len words of c.
*/
static void internal_mul(BignumInt *a, BignumInt *b,
BignumInt *c, int len)
{
int i, j;
BignumDblInt t;
for (j = 0; j < 2 * len; j++)
c[j] = 0;
for (i = len - 1; i >= 0; i--) {
t = 0;
for (j = len - 1; j >= 0; j--) {
t += MUL_WORD(a[i], (BignumDblInt) b[j]);
t += (BignumDblInt) c[i + j + 1];
c[i + j + 1] = (BignumInt) t;
t = t >> BIGNUM_INT_BITS;
}
c[i] = (BignumInt) t;
}
}
static void internal_add_shifted(BignumInt *number,
unsigned n, int shift)
{
int word = 1 + (shift / BIGNUM_INT_BITS);
int bshift = shift % BIGNUM_INT_BITS;
BignumDblInt addend;
addend = (BignumDblInt)n << bshift;
while (addend) {
addend += number[word];
number[word] = (BignumInt) addend & BIGNUM_INT_MASK;
addend >>= BIGNUM_INT_BITS;
word++;
}
}
/*
* Compute a = a % m.
* Input in first alen words of a and first mlen words of m.
* Output in first alen words of a
* (of which first alen-mlen words will be zero).
* The MSW of m MUST have its high bit set.
* Quotient is accumulated in the `quotient' array, which is a Bignum
* rather than the internal bigendian format. Quotient parts are shifted
* left by `qshift' before adding into quot.
*/
static void internal_mod(BignumInt *a, int alen,
BignumInt *m, int mlen,
BignumInt *quot, int qshift)
{
BignumInt m0, m1;
unsigned int h;
int i, k;
m0 = m[0];
if (mlen > 1)
m1 = m[1];
else
m1 = 0;
for (i = 0; i <= alen - mlen; i++) {
BignumDblInt t;
unsigned int q, r, c, ai1;
if (i == 0) {
h = 0;
} else {
h = a[i - 1];
a[i - 1] = 0;
}
if (i == alen - 1)
ai1 = 0;
else
ai1 = a[i + 1];
/* Find q = h:a[i] / m0 */
if (h >= m0) {
/*
* Special case.
*
* To illustrate it, suppose a BignumInt is 8 bits, and
* we are dividing (say) A1:23:45:67 by A1:B2:C3. Then
* our initial division will be 0xA123 / 0xA1, which
* will give a quotient of 0x100 and a divide overflow.
* However, the invariants in this division algorithm
* are not violated, since the full number A1:23:... is
* _less_ than the quotient prefix A1:B2:... and so the
* following correction loop would have sorted it out.
*
* In this situation we set q to be the largest
* quotient we _can_ stomach (0xFF, of course).
*/
q = BIGNUM_INT_MASK;
} else {
/* Macro doesn't want an array subscript expression passed
* into it (see definition), so use a temporary. */
BignumInt tmplo = a[i];
DIVMOD_WORD(q, r, h, tmplo, m0);
/* Refine our estimate of q by looking at
h:a[i]:a[i+1] / m0:m1 */
t = MUL_WORD(m1, q);
if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) {
q--;
t -= m1;
r = (r + m0) & BIGNUM_INT_MASK; /* overflow? */
if (r >= (BignumDblInt) m0 &&
t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) q--;
}
}
/* Subtract q * m from a[i...] */
c = 0;
for (k = mlen - 1; k >= 0; k--) {
t = MUL_WORD(q, m[k]);
t += c;
c = (unsigned)(t >> BIGNUM_INT_BITS);
if ((BignumInt) t > a[i + k])
c++;
a[i + k] -= (BignumInt) t;
}
/* Add back m in case of borrow */
if (c != h) {
t = 0;
for (k = mlen - 1; k >= 0; k--) {
t += m[k];
t += a[i + k];
a[i + k] = (BignumInt) t;
t = t >> BIGNUM_INT_BITS;
}
q--;
}
if (quot)
internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i));
}
}
/*
* Compute (base ^ exp) % mod.
*/
Bignum modpow(Bignum base_in, Bignum exp, Bignum mod)
{
BignumInt *a, *b, *n, *m;
int mshift;
int mlen, i, j;
Bignum base, result;
/*
* The most significant word of mod needs to be non-zero. It
* should already be, but let's make sure.
*/
assert(mod[mod[0]] != 0);
/*
* Make sure the base is smaller than the modulus, by reducing
* it modulo the modulus if not.
*/
base = bigmod(base_in, mod);
/* Allocate m of size mlen, copy mod to m */
/* We use big endian internally */
mlen = mod[0];
m = snewn(mlen, BignumInt);
for (j = 0; j < mlen; j++)
m[j] = mod[mod[0] - j];
/* Shift m left to make msb bit set */
for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
if ((m[0] << mshift) & BIGNUM_TOP_BIT)
break;
if (mshift) {
for (i = 0; i < mlen - 1; i++)
m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));
m[mlen - 1] = m[mlen - 1] << mshift;
}
/* Allocate n of size mlen, copy base to n */
n = snewn(mlen, BignumInt);
i = mlen - base[0];
for (j = 0; j < i; j++)
n[j] = 0;
for (j = 0; j < (int)base[0]; j++)
n[i + j] = base[base[0] - j];
/* Allocate a and b of size 2*mlen. Set a = 1 */
a = snewn(2 * mlen, BignumInt);
b = snewn(2 * mlen, BignumInt);
for (i = 0; i < 2 * mlen; i++)
a[i] = 0;
a[2 * mlen - 1] = 1;
/* Skip leading zero bits of exp. */
i = 0;
j = BIGNUM_INT_BITS-1;
while (i < (int)exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) {
j--;
if (j < 0) {
i++;
j = BIGNUM_INT_BITS-1;
}
}
/* Main computation */
while (i < (int)exp[0]) {
while (j >= 0) {
internal_mul(a + mlen, a + mlen, b, mlen);
internal_mod(b, mlen * 2, m, mlen, NULL, 0);
if ((exp[exp[0] - i] & (1 << j)) != 0) {
internal_mul(b + mlen, n, a, mlen);
internal_mod(a, mlen * 2, m, mlen, NULL, 0);
} else {
BignumInt *t;
t = a;
a = b;
b = t;
}
j--;
}
i++;
j = BIGNUM_INT_BITS-1;
}
/* Fixup result in case the modulus was shifted */
if (mshift) {
for (i = mlen - 1; i < 2 * mlen - 1; i++)
a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));
a[2 * mlen - 1] = a[2 * mlen - 1] << mshift;
internal_mod(a, mlen * 2, m, mlen, NULL, 0);
for (i = 2 * mlen - 1; i >= mlen; i--)
a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));
}
/* Copy result to buffer */
result = newbn(mod[0]);
for (i = 0; i < mlen; i++)
result[result[0] - i] = a[i + mlen];
while (result[0] > 1 && result[result[0]] == 0)
result[0]--;
/* Free temporary arrays */
for (i = 0; i < 2 * mlen; i++)
a[i] = 0;
sfree(a);
for (i = 0; i < 2 * mlen; i++)
b[i] = 0;
sfree(b);
for (i = 0; i < mlen; i++)
m[i] = 0;
sfree(m);
for (i = 0; i < mlen; i++)
n[i] = 0;
sfree(n);
freebn(base);
return result;
}
/*
* Compute (p * q) % mod.
* The most significant word of mod MUST be non-zero.
* We assume that the result array is the same size as the mod array.
*/
Bignum modmul(Bignum p, Bignum q, Bignum mod)
{
BignumInt *a, *n, *m, *o;
int mshift;
int pqlen, mlen, rlen, i, j;
Bignum result;
/* Allocate m of size mlen, copy mod to m */
/* We use big endian internally */
mlen = mod[0];
m = snewn(mlen, BignumInt);
for (j = 0; j < mlen; j++)
m[j] = mod[mod[0] - j];
/* Shift m left to make msb bit set */
for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
if ((m[0] << mshift) & BIGNUM_TOP_BIT)
break;
if (mshift) {
for (i = 0; i < mlen - 1; i++)
m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));
m[mlen - 1] = m[mlen - 1] << mshift;
}
pqlen = (p[0] > q[0] ? p[0] : q[0]);
/* Allocate n of size pqlen, copy p to n */
n = snewn(pqlen, BignumInt);
i = pqlen - p[0];
for (j = 0; j < i; j++)
n[j] = 0;
for (j = 0; j < (int)p[0]; j++)
n[i + j] = p[p[0] - j];
/* Allocate o of size pqlen, copy q to o */
o = snewn(pqlen, BignumInt);
i = pqlen - q[0];
for (j = 0; j < i; j++)
o[j] = 0;
for (j = 0; j < (int)q[0]; j++)
o[i + j] = q[q[0] - j];
/* Allocate a of size 2*pqlen for result */
a = snewn(2 * pqlen, BignumInt);
/* Main computation */
internal_mul(n, o, a, pqlen);
internal_mod(a, pqlen * 2, m, mlen, NULL, 0);
/* Fixup result in case the modulus was shifted */
if (mshift) {
for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++)
a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));
a[2 * pqlen - 1] = a[2 * pqlen - 1] << mshift;
internal_mod(a, pqlen * 2, m, mlen, NULL, 0);
for (i = 2 * pqlen - 1; i >= 2 * pqlen - mlen; i--)
a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));
}
/* Copy result to buffer */
rlen = (mlen < pqlen * 2 ? mlen : pqlen * 2);
result = newbn(rlen);
for (i = 0; i < rlen; i++)
result[result[0] - i] = a[i + 2 * pqlen - rlen];
while (result[0] > 1 && result[result[0]] == 0)
result[0]--;
/* Free temporary arrays */
for (i = 0; i < 2 * pqlen; i++)
a[i] = 0;
sfree(a);
for (i = 0; i < mlen; i++)
m[i] = 0;
sfree(m);
for (i = 0; i < pqlen; i++)
n[i] = 0;
sfree(n);
for (i = 0; i < pqlen; i++)
o[i] = 0;
sfree(o);
return result;
}
/*
* Compute p % mod.
* The most significant word of mod MUST be non-zero.
* We assume that the result array is the same size as the mod array.
* We optionally write out a quotient if `quotient' is non-NULL.
* We can avoid writing out the result if `result' is NULL.
*/
static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient)
{
BignumInt *n, *m;
int mshift;
int plen, mlen, i, j;
/* Allocate m of size mlen, copy mod to m */
/* We use big endian internally */
mlen = mod[0];
m = snewn(mlen, BignumInt);
for (j = 0; j < mlen; j++)
m[j] = mod[mod[0] - j];
/* Shift m left to make msb bit set */
for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
if ((m[0] << mshift) & BIGNUM_TOP_BIT)
break;
if (mshift) {
for (i = 0; i < mlen - 1; i++)
m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));
m[mlen - 1] = m[mlen - 1] << mshift;
}
plen = p[0];
/* Ensure plen > mlen */
if (plen <= mlen)
plen = mlen + 1;
/* Allocate n of size plen, copy p to n */
n = snewn(plen, BignumInt);
for (j = 0; j < plen; j++)
n[j] = 0;
for (j = 1; j <= (int)p[0]; j++)
n[plen - j] = p[j];
/* Main computation */
internal_mod(n, plen, m, mlen, quotient, mshift);
/* Fixup result in case the modulus was shifted */
if (mshift) {
for (i = plen - mlen - 1; i < plen - 1; i++)
n[i] = (n[i] << mshift) | (n[i + 1] >> (BIGNUM_INT_BITS - mshift));
n[plen - 1] = n[plen - 1] << mshift;
internal_mod(n, plen, m, mlen, quotient, 0);
for (i = plen - 1; i >= plen - mlen; i--)
n[i] = (n[i] >> mshift) | (n[i - 1] << (BIGNUM_INT_BITS - mshift));
}
/* Copy result to buffer */
if (result) {
for (i = 1; i <= (int)result[0]; i++) {
int j = plen - i;
result[i] = j >= 0 ? n[j] : 0;
}
}
/* Free temporary arrays */
for (i = 0; i < mlen; i++)
m[i] = 0;
sfree(m);
for (i = 0; i < plen; i++)
n[i] = 0;
sfree(n);
}
/*
* Decrement a number.
*/
void decbn(Bignum bn)
{
int i = 1;
while (i < (int)bn[0] && bn[i] == 0)
bn[i++] = BIGNUM_INT_MASK;
bn[i]--;
}
Bignum bignum_from_bytes(const unsigned char *data, int nbytes)
{
Bignum result;
int w, i;
w = (nbytes + BIGNUM_INT_BYTES - 1) / BIGNUM_INT_BYTES; /* bytes->words */
result = newbn(w);
for (i = 1; i <= w; i++)
result[i] = 0;
for (i = nbytes; i--;) {
unsigned char byte = *data++;
result[1 + i / BIGNUM_INT_BYTES] |= byte << (8*i % BIGNUM_INT_BITS);
}
while (result[0] > 1 && result[result[0]] == 0)
result[0]--;
return result;
}
/*
* Read an SSH-1-format bignum from a data buffer. Return the number
* of bytes consumed, or -1 if there wasn't enough data.
*/
int ssh1_read_bignum(const unsigned char *data, int len, Bignum * result)
{
const unsigned char *p = data;
int i;
int w, b;
if (len < 2)
return -1;
w = 0;
for (i = 0; i < 2; i++)
w = (w << 8) + *p++;
b = (w + 7) / 8; /* bits -> bytes */
if (len < b+2)
return -1;
if (!result) /* just return length */
return b + 2;
*result = bignum_from_bytes(p, b);
return p + b - data;
}
/*
* Return the bit count of a bignum, for SSH-1 encoding.
*/
int bignum_bitcount(Bignum bn)
{
int bitcount = bn[0] * BIGNUM_INT_BITS - 1;
while (bitcount >= 0
&& (bn[bitcount / BIGNUM_INT_BITS + 1] >> (bitcount % BIGNUM_INT_BITS)) == 0) bitcount--;
return bitcount + 1;
}
/*
* Return the byte length of a bignum when SSH-1 encoded.
*/
int ssh1_bignum_length(Bignum bn)
{
return 2 + (bignum_bitcount(bn) + 7) / 8;
}
/*
* Return the byte length of a bignum when SSH-2 encoded.
*/
int ssh2_bignum_length(Bignum bn)
{
return 4 + (bignum_bitcount(bn) + 8) / 8;
}
/*
* Return a byte from a bignum; 0 is least significant, etc.
*/
int bignum_byte(Bignum bn, int i)
{
if (i >= (int)(BIGNUM_INT_BYTES * bn[0]))
return 0; /* beyond the end */
else
return (bn[i / BIGNUM_INT_BYTES + 1] >>
((i % BIGNUM_INT_BYTES)*8)) & 0xFF;
}
/*
* Return a bit from a bignum; 0 is least significant, etc.
*/
int bignum_bit(Bignum bn, int i)
{
if (i >= (int)(BIGNUM_INT_BITS * bn[0]))
return 0; /* beyond the end */
else
return (bn[i / BIGNUM_INT_BITS + 1] >> (i % BIGNUM_INT_BITS)) & 1;
}
/*
* Set a bit in a bignum; 0 is least significant, etc.
*/
void bignum_set_bit(Bignum bn, int bitnum, int value)
{
if (bitnum >= (int)(BIGNUM_INT_BITS * bn[0]))
abort(); /* beyond the end */
else {
int v = bitnum / BIGNUM_INT_BITS + 1;
int mask = 1 << (bitnum % BIGNUM_INT_BITS);
if (value)
bn[v] |= mask;
else
bn[v] &= ~mask;
}
}
/*
* Write a SSH-1-format bignum into a buffer. It is assumed the
* buffer is big enough. Returns the number of bytes used.
*/
int ssh1_write_bignum(void *data, Bignum bn)
{
unsigned char *p = data;
int len = ssh1_bignum_length(bn);
int i;
int bitc = bignum_bitcount(bn);
*p++ = (bitc >> 8) & 0xFF;
*p++ = (bitc) & 0xFF;
for (i = len - 2; i--;)
*p++ = bignum_byte(bn, i);
return len;
}
/*
* Compare two bignums. Returns like strcmp.
*/
int bignum_cmp(Bignum a, Bignum b)
{
int amax = a[0], bmax = b[0];
int i = (amax > bmax ? amax : bmax);
while (i) {
BignumInt aval = (i > amax ? 0 : a[i]);
BignumInt bval = (i > bmax ? 0 : b[i]);
if (aval < bval)
return -1;
if (aval > bval)
return +1;
i--;
}
return 0;
}
/*
* Right-shift one bignum to form another.
*/
Bignum bignum_rshift(Bignum a, int shift)
{
Bignum ret;
int i, shiftw, shiftb, shiftbb, bits;
BignumInt ai, ai1;
bits = bignum_bitcount(a) - shift;
ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS);
if (ret) {
shiftw = shift / BIGNUM_INT_BITS;
shiftb = shift % BIGNUM_INT_BITS;
shiftbb = BIGNUM_INT_BITS - shiftb;
ai1 = a[shiftw + 1];
for (i = 1; i <= (int)ret[0]; i++) {
ai = ai1;
ai1 = (i + shiftw + 1 <= (int)a[0] ? a[i + shiftw + 1] : 0);
ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & BIGNUM_INT_MASK;
}
}
return ret;
}
/*
* Non-modular multiplication and addition.
*/
Bignum bigmuladd(Bignum a, Bignum b, Bignum addend)
{
int alen = a[0], blen = b[0];
int mlen = (alen > blen ? alen : blen);
int rlen, i, maxspot;
BignumInt *workspace;
Bignum ret;
/* mlen space for a, mlen space for b, 2*mlen for result */
workspace = snewn(mlen * 4, BignumInt);
for (i = 0; i < mlen; i++) {
workspace[0 * mlen + i] = (mlen - i <= (int)a[0] ? a[mlen - i] : 0);
workspace[1 * mlen + i] = (mlen - i <= (int)b[0] ? b[mlen - i] : 0);
}
internal_mul(workspace + 0 * mlen, workspace + 1 * mlen,
workspace + 2 * mlen, mlen);
/* now just copy the result back */
rlen = alen + blen + 1;
if (addend && rlen <= (int)addend[0])
rlen = addend[0] + 1;
ret = newbn(rlen);
maxspot = 0;
for (i = 1; i <= (int)ret[0]; i++) {
ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0);
if (ret[i] != 0)
maxspot = i;
}
ret[0] = maxspot;
/* now add in the addend, if any */
if (addend) {
BignumDblInt carry = 0;
for (i = 1; i <= rlen; i++) {
carry += (i <= (int)ret[0] ? ret[i] : 0);
carry += (i <= (int)addend[0] ? addend[i] : 0);
ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;
carry >>= BIGNUM_INT_BITS;
if (ret[i] != 0 && i > maxspot)
maxspot = i;
}
}
ret[0] = maxspot;
sfree(workspace);
return ret;
}
/*
* Non-modular multiplication.
*/
Bignum bigmul(Bignum a, Bignum b)
{
return bigmuladd(a, b, NULL);
}
/*
* Create a bignum which is the bitmask covering another one. That
* is, the smallest integer which is >= N and is also one less than
* a power of two.
*/
Bignum bignum_bitmask(Bignum n)
{
Bignum ret = copybn(n);
int i;
BignumInt j;
i = ret[0];
while (n[i] == 0 && i > 0)
i--;
if (i <= 0)
return ret; /* input was zero */
j = 1;
while (j < n[i])
j = 2 * j + 1;
ret[i] = j;
while (--i > 0)
ret[i] = BIGNUM_INT_MASK;
return ret;
}
/*
* Convert a (max 32-bit) long into a bignum.
*/
Bignum bignum_from_long(unsigned long nn)
{
Bignum ret;
BignumDblInt n = nn;
ret = newbn(3);
ret[1] = (BignumInt)(n & BIGNUM_INT_MASK);
ret[2] = (BignumInt)((n >> BIGNUM_INT_BITS) & BIGNUM_INT_MASK);
ret[3] = 0;
ret[0] = (ret[2] ? 2 : 1);
return ret;
}
/*
* Add a long to a bignum.
*/
Bignum bignum_add_long(Bignum number, unsigned long addendx)
{
Bignum ret = newbn(number[0] + 1);
int i, maxspot = 0;
BignumDblInt carry = 0, addend = addendx;
for (i = 1; i <= (int)ret[0]; i++) {
carry += addend & BIGNUM_INT_MASK;
carry += (i <= (int)number[0] ? number[i] : 0);
addend >>= BIGNUM_INT_BITS;
ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;
carry >>= BIGNUM_INT_BITS;
if (ret[i] != 0)
maxspot = i;
}
ret[0] = maxspot;
return ret;
}
/*
* Compute the residue of a bignum, modulo a (max 16-bit) short.
*/
unsigned short bignum_mod_short(Bignum number, unsigned short modulus)
{
BignumDblInt mod, r;
int i;
r = 0;
mod = modulus;
for (i = number[0]; i > 0; i--)
r = (r * (BIGNUM_TOP_BIT % mod) * 2 + number[i] % mod) % mod;
return (unsigned short) r;
}
#ifdef DEBUG
void diagbn(char *prefix, Bignum md)
{
int i, nibbles, morenibbles;
static const char hex[] = "0123456789ABCDEF";
debug(("%s0x", prefix ? prefix : ""));
nibbles = (3 + bignum_bitcount(md)) / 4;
if (nibbles < 1)
nibbles = 1;
morenibbles = 4 * md[0] - nibbles;
for (i = 0; i < morenibbles; i++)
debug(("-"));
for (i = nibbles; i--;)
debug(("%c",
hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF]));
if (prefix)
debug(("\n"));
}
#endif
/*
* Simple division.
*/
Bignum bigdiv(Bignum a, Bignum b)
{
Bignum q = newbn(a[0]);
bigdivmod(a, b, NULL, q);
return q;
}
/*
* Simple remainder.
*/
Bignum bigmod(Bignum a, Bignum b)
{
Bignum r = newbn(b[0]);
bigdivmod(a, b, r, NULL);
return r;
}
/*
* Greatest common divisor.
*/
Bignum biggcd(Bignum av, Bignum bv)
{
Bignum a = copybn(av);
Bignum b = copybn(bv);
while (bignum_cmp(b, Zero) != 0) {
Bignum t = newbn(b[0]);
bigdivmod(a, b, t, NULL);
while (t[0] > 1 && t[t[0]] == 0)
t[0]--;
freebn(a);
a = b;
b = t;
}
freebn(b);
return a;
}
/*
* Modular inverse, using Euclid's extended algorithm.
*/
Bignum modinv(Bignum number, Bignum modulus)
{
Bignum a = copybn(modulus);
Bignum b = copybn(number);
Bignum xp = copybn(Zero);
Bignum x = copybn(One);
int sign = +1;
while (bignum_cmp(b, One) != 0) {
Bignum t = newbn(b[0]);
Bignum q = newbn(a[0]);
bigdivmod(a, b, t, q);
while (t[0] > 1 && t[t[0]] == 0)
t[0]--;
freebn(a);
a = b;
b = t;
t = xp;
xp = x;
x = bigmuladd(q, xp, t);
sign = -sign;
freebn(t);
freebn(q);
}
freebn(b);
freebn(a);
freebn(xp);
/* now we know that sign * x == 1, and that x < modulus */
if (sign < 0) {
/* set a new x to be modulus - x */
Bignum newx = newbn(modulus[0]);
BignumInt carry = 0;
int maxspot = 1;
int i;
for (i = 1; i <= (int)newx[0]; i++) {
BignumInt aword = (i <= (int)modulus[0] ? modulus[i] : 0);
BignumInt bword = (i <= (int)x[0] ? x[i] : 0);
newx[i] = aword - bword - carry;
bword = ~bword;
carry = carry ? (newx[i] >= bword) : (newx[i] > bword);
if (newx[i] != 0)
maxspot = i;
}
newx[0] = maxspot;
freebn(x);
x = newx;
}
/* and return. */
return x;
}
/*
* Render a bignum into decimal. Return a malloced string holding
* the decimal representation.
*/
char *bignum_decimal(Bignum x)
{
int ndigits, ndigit;
int i, iszero;
BignumDblInt carry;
char *ret;
BignumInt *workspace;
/*
* First, estimate the number of digits. Since log(10)/log(2)
* is just greater than 93/28 (the joys of continued fraction
* approximations...) we know that for every 93 bits, we need
* at most 28 digits. This will tell us how much to malloc.
*
* Formally: if x has i bits, that means x is strictly less
* than 2^i. Since 2 is less than 10^(28/93), this is less than
* 10^(28i/93). We need an integer power of ten, so we must
* round up (rounding down might make it less than x again).
* Therefore if we multiply the bit count by 28/93, rounding
* up, we will have enough digits.
*
* i=0 (i.e., x=0) is an irritating special case.
*/
i = bignum_bitcount(x);
if (!i)
ndigits = 1; /* x = 0 */
else
ndigits = (28 * i + 92) / 93; /* multiply by 28/93 and round up */
ndigits++; /* allow for trailing \0 */
ret = snewn(ndigits, char);
/*
* Now allocate some workspace to hold the binary form as we
* repeatedly divide it by ten. Initialise this to the
* big-endian form of the number.
*/
workspace = snewn(x[0], BignumInt);
for (i = 0; i < (int)x[0]; i++)
workspace[i] = x[x[0] - i];
/*
* Next, write the decimal number starting with the last digit.
* We use ordinary short division, dividing 10 into the
* workspace.
*/
ndigit = ndigits - 1;
ret[ndigit] = '\0';
do {
iszero = 1;
carry = 0;
for (i = 0; i < (int)x[0]; i++) {
carry = (carry << BIGNUM_INT_BITS) + workspace[i];
workspace[i] = (BignumInt) (carry / 10);
if (workspace[i])
iszero = 0;
carry %= 10;
}
ret[--ndigit] = (char) (carry + '0');
} while (!iszero);
/*
* There's a chance we've fallen short of the start of the
* string. Correct if so.
*/
if (ndigit > 0)
memmove(ret, ret + ndigit, ndigits - ndigit);
/*
* Done.
*/
sfree(workspace);
return ret;
}
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