#include "tommath_private.h"
#ifdef BN_S_MP_EXPTMOD_FAST_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
/* SPDX-License-Identifier: Unlicense */
/* 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
# define MAX_WINSIZE 5
#else
# define TAB_SIZE 256
# define MAX_WINSIZE 0
#endif
mp_err s_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 bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
mp_err err;
/* 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.
*/
mp_err(*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;
}
winsize = MAX_WINSIZE ? MP_MIN(MAX_WINSIZE, winsize) : winsize;
/* 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) {
if (MP_HAS(MP_MONTGOMERY_SETUP)) {
/* now setup montgomery */
if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) goto LBL_M;
} else {
err = MP_VAL;
goto LBL_M;
}
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
if (MP_HAS(S_MP_MONTGOMERY_REDUCE_FAST) &&
(((P->used * 2) + 1) < MP_WARRAY) &&
(P->used < MP_MAXFAST)) {
redux = s_mp_montgomery_reduce_fast;
} else if (MP_HAS(MP_MONTGOMERY_REDUCE)) {
/* use slower baseline Montgomery method */
redux = mp_montgomery_reduce;
} else {
err = MP_VAL;
goto LBL_M;
}
} else if (redmode == 1) {
if (MP_HAS(MP_DR_SETUP) && MP_HAS(MP_DR_REDUCE)) {
/* 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;
}
} else if (MP_HAS(MP_REDUCE_2K_SETUP) && MP_HAS(MP_REDUCE_2K)) {
/* 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;
}
/* 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) {
if (MP_HAS(MP_MONTGOMERY_CALC_NORMALIZATION)) {
/* 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;
}
} 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)MP_DIGIT_BIT;
}
/* grab the next msb from the exponent */
y = (mp_digit)(buf >> (MP_DIGIT_BIT - 1)) & 1uL;
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
