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#include "tommath_private.h"
#ifdef BN_S_MP_EXPTMOD_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.
*
* SPDX-License-Identifier: Unlicense
*/
#ifdef MP_LOW_MEM
# define TAB_SIZE 32
#else
# define TAB_SIZE 256
#endif
int s_mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode)
{
mp_int M[TAB_SIZE], res, mu;
mp_digit buf;
int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
int (*redux)(mp_int *x, const mp_int *m, const mp_int *mu);
/* 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(&M[1])) != 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(&M[x])) != MP_OKAY) {
for (y = 1<<(winsize-1); y < x; y++) {
mp_clear(&M[y]);
}
mp_clear(&M[1]);
return err;
}
}
/* create mu, used for Barrett reduction */
if ((err = mp_init(&mu)) != MP_OKAY) {
goto LBL_M;
}
if (redmode == 0) {
if ((err = mp_reduce_setup(&mu, P)) != MP_OKAY) {
goto LBL_MU;
}
redux = mp_reduce;
} else {
if ((err = mp_reduce_2k_setup_l(P, &mu)) != MP_OKAY) {
goto LBL_MU;
}
redux = mp_reduce_2k_l;
}
/* create M table
*
* The M table contains powers of the base,
* e.g. M[x] = G**x mod P
*
* The first half of the table is not
* computed though accept for M[0] and M[1]
*/
if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
goto LBL_MU;
}
/* 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_MU;
}
for (x = 0; x < (winsize - 1); x++) {
/* square it */
if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)],
&M[(size_t)1 << (winsize - 1)])) != MP_OKAY) {
goto LBL_MU;
}
/* reduce modulo P */
if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
goto LBL_MU;
}
}
/* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
* for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
*/
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_MU;
}
if ((err = redux(&M[x], P, &mu)) != MP_OKAY) {
goto LBL_MU;
}
}
/* setup result */
if ((err = mp_init(&res)) != MP_OKAY) {
goto LBL_MU;
}
mp_set(&res, 1uL);
/* 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 */
if (digidx == -1) {
break;
}
/* read next digit and reset the bitcnt */
buf = X->dp[digidx--];
bitcnt = (int)DIGIT_BIT;
}
/* grab the next msb from the exponent */
y = (buf >> (mp_digit)(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, &mu)) != 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, &mu)) != 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, &mu)) != 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, &mu)) != MP_OKAY) {
goto LBL_RES;
}
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, &mu)) != MP_OKAY) {
goto LBL_RES;
}
}
}
}
mp_exch(&res, Y);
err = MP_OKAY;
LBL_RES:
mp_clear(&res);
LBL_MU:
mp_clear(&mu);
LBL_M:
mp_clear(&M[1]);
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
mp_clear(&M[x]);
}
return err;
}
#endif
/* ref: HEAD -> master, tag: v1.1.0 */
/* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
/* commit time: 2019-01-28 20:32:32 +0100 */
|
