321 lines
8.3 KiB
C
Executable File
321 lines
8.3 KiB
C
Executable File
#include "tommath_private.h"
|
|
#ifdef BN_MP_EXPTMOD_FAST_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis
|
|
*
|
|
* LibTomMath is a library that provides multiple-precision
|
|
* integer arithmetic as well as number theoretic functionality.
|
|
*
|
|
* The library was designed directly after the MPI library by
|
|
* Michael Fromberger but has been written from scratch with
|
|
* additional optimizations in place.
|
|
*
|
|
* The library is free for all purposes without any express
|
|
* guarantee it works.
|
|
*/
|
|
|
|
/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
|
|
*
|
|
* Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
|
|
* The value of k changes based on the size of the exponent.
|
|
*
|
|
* Uses Montgomery or Diminished Radix reduction [whichever appropriate]
|
|
*/
|
|
|
|
#ifdef MP_LOW_MEM
|
|
# define TAB_SIZE 32
|
|
#else
|
|
# define TAB_SIZE 256
|
|
#endif
|
|
|
|
int mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode)
|
|
{
|
|
mp_int M[TAB_SIZE], res;
|
|
mp_digit buf, mp;
|
|
int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
|
|
|
/* use a pointer to the reduction algorithm. This allows us to use
|
|
* one of many reduction algorithms without modding the guts of
|
|
* the code with if statements everywhere.
|
|
*/
|
|
int (*redux)(mp_int *x, const mp_int *n, mp_digit rho);
|
|
|
|
/* find window size */
|
|
x = mp_count_bits(X);
|
|
if (x <= 7) {
|
|
winsize = 2;
|
|
} else if (x <= 36) {
|
|
winsize = 3;
|
|
} else if (x <= 140) {
|
|
winsize = 4;
|
|
} else if (x <= 450) {
|
|
winsize = 5;
|
|
} else if (x <= 1303) {
|
|
winsize = 6;
|
|
} else if (x <= 3529) {
|
|
winsize = 7;
|
|
} else {
|
|
winsize = 8;
|
|
}
|
|
|
|
#ifdef MP_LOW_MEM
|
|
if (winsize > 5) {
|
|
winsize = 5;
|
|
}
|
|
#endif
|
|
|
|
/* init M array */
|
|
/* init first cell */
|
|
if ((err = mp_init_size(&M[1], P->alloc)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* now init the second half of the array */
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
if ((err = mp_init_size(&M[x], P->alloc)) != MP_OKAY) {
|
|
for (y = 1<<(winsize-1); y < x; y++) {
|
|
mp_clear(&M[y]);
|
|
}
|
|
mp_clear(&M[1]);
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* determine and setup reduction code */
|
|
if (redmode == 0) {
|
|
#ifdef BN_MP_MONTGOMERY_SETUP_C
|
|
/* now setup montgomery */
|
|
if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) {
|
|
goto LBL_M;
|
|
}
|
|
#else
|
|
err = MP_VAL;
|
|
goto LBL_M;
|
|
#endif
|
|
|
|
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
|
|
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
|
|
if ((((P->used * 2) + 1) < (int)MP_WARRAY) &&
|
|
(P->used < (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
|
|
redux = fast_mp_montgomery_reduce;
|
|
} else
|
|
#endif
|
|
{
|
|
#ifdef BN_MP_MONTGOMERY_REDUCE_C
|
|
/* use slower baseline Montgomery method */
|
|
redux = mp_montgomery_reduce;
|
|
#else
|
|
err = MP_VAL;
|
|
goto LBL_M;
|
|
#endif
|
|
}
|
|
} else if (redmode == 1) {
|
|
#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
|
|
/* setup DR reduction for moduli of the form B**k - b */
|
|
mp_dr_setup(P, &mp);
|
|
redux = mp_dr_reduce;
|
|
#else
|
|
err = MP_VAL;
|
|
goto LBL_M;
|
|
#endif
|
|
} else {
|
|
#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
|
|
/* setup DR reduction for moduli of the form 2**k - b */
|
|
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
|
|
goto LBL_M;
|
|
}
|
|
redux = mp_reduce_2k;
|
|
#else
|
|
err = MP_VAL;
|
|
goto LBL_M;
|
|
#endif
|
|
}
|
|
|
|
/* setup result */
|
|
if ((err = mp_init_size(&res, P->alloc)) != MP_OKAY) {
|
|
goto LBL_M;
|
|
}
|
|
|
|
/* create M table
|
|
*
|
|
|
|
*
|
|
* The first half of the table is not computed though accept for M[0] and M[1]
|
|
*/
|
|
|
|
if (redmode == 0) {
|
|
#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
|
|
/* now we need R mod m */
|
|
if ((err = mp_montgomery_calc_normalization(&res, P)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
/* now set M[1] to G * R mod m */
|
|
if ((err = mp_mulmod(G, &res, P, &M[1])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
#else
|
|
err = MP_VAL;
|
|
goto LBL_RES;
|
|
#endif
|
|
} else {
|
|
mp_set(&res, 1uL);
|
|
if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
|
|
if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
for (x = 0; x < (winsize - 1); x++) {
|
|
if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* create upper table */
|
|
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
|
if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux(&M[x], P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* set initial mode and bit cnt */
|
|
mode = 0;
|
|
bitcnt = 1;
|
|
buf = 0;
|
|
digidx = X->used - 1;
|
|
bitcpy = 0;
|
|
bitbuf = 0;
|
|
|
|
for (;;) {
|
|
/* grab next digit as required */
|
|
if (--bitcnt == 0) {
|
|
/* if digidx == -1 we are out of digits so break */
|
|
if (digidx == -1) {
|
|
break;
|
|
}
|
|
/* read next digit and reset bitcnt */
|
|
buf = X->dp[digidx--];
|
|
bitcnt = (int)DIGIT_BIT;
|
|
}
|
|
|
|
/* grab the next msb from the exponent */
|
|
y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
|
|
buf <<= (mp_digit)1;
|
|
|
|
/* if the bit is zero and mode == 0 then we ignore it
|
|
* These represent the leading zero bits before the first 1 bit
|
|
* in the exponent. Technically this opt is not required but it
|
|
* does lower the # of trivial squaring/reductions used
|
|
*/
|
|
if ((mode == 0) && (y == 0)) {
|
|
continue;
|
|
}
|
|
|
|
/* if the bit is zero and mode == 1 then we square */
|
|
if ((mode == 1) && (y == 0)) {
|
|
if ((err = mp_sqr(&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux(&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
continue;
|
|
}
|
|
|
|
/* else we add it to the window */
|
|
bitbuf |= (y << (winsize - ++bitcpy));
|
|
mode = 2;
|
|
|
|
if (bitcpy == winsize) {
|
|
/* ok window is filled so square as required and multiply */
|
|
/* square first */
|
|
for (x = 0; x < winsize; x++) {
|
|
if ((err = mp_sqr(&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux(&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* then multiply */
|
|
if ((err = mp_mul(&res, &M[bitbuf], &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux(&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
/* empty window and reset */
|
|
bitcpy = 0;
|
|
bitbuf = 0;
|
|
mode = 1;
|
|
}
|
|
}
|
|
|
|
/* if bits remain then square/multiply */
|
|
if ((mode == 2) && (bitcpy > 0)) {
|
|
/* square then multiply if the bit is set */
|
|
for (x = 0; x < bitcpy; x++) {
|
|
if ((err = mp_sqr(&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux(&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
/* get next bit of the window */
|
|
bitbuf <<= 1;
|
|
if ((bitbuf & (1 << winsize)) != 0) {
|
|
/* then multiply */
|
|
if ((err = mp_mul(&res, &M[1], &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux(&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
if (redmode == 0) {
|
|
/* fixup result if Montgomery reduction is used
|
|
* recall that any value in a Montgomery system is
|
|
* actually multiplied by R mod n. So we have
|
|
* to reduce one more time to cancel out the factor
|
|
* of R.
|
|
*/
|
|
if ((err = redux(&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* swap res with Y */
|
|
mp_exch(&res, Y);
|
|
err = MP_OKAY;
|
|
LBL_RES:
|
|
mp_clear(&res);
|
|
LBL_M:
|
|
mp_clear(&M[1]);
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
mp_clear(&M[x]);
|
|
}
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* ref: $Format:%D$ */
|
|
/* git commit: $Format:%H$ */
|
|
/* commit time: $Format:%ai$ */
|