/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* 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]
*/
int
mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
{
mp_int M[256], 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*,mp_int*,mp_digit);
/* 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 G array */
for (x = 0; x < (1 << winsize); x++) {
if ((err = mp_init (&M[x])) != MP_OKAY) {
for (y = 0; y < x; y++) {
mp_clear (&M[y]);
}
return err;
}
}
/* determine and setup reduction code */
if (redmode == 0) {
/* now setup montgomery */
if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
goto __M;
}
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
if (((P->used * 2 + 1) < MP_WARRAY) &&
P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
redux = fast_mp_montgomery_reduce;
} else {
/* use slower baselien method */
redux = mp_montgomery_reduce;
}
} else if (redmode == 1) {
/* setup DR reduction */
mp_dr_setup(P, &mp);
redux = mp_dr_reduce;
} else {
/* setup 2k reduction */
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
goto __M;
}
redux = mp_reduce_2k;
}
/* setup result */
if ((err = mp_init (&res)) != MP_OKAY) {
goto __RES;
}
/* create M table
*
* The M table contains powers of the input 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 (redmode == 0) {
/* now we need R mod m */
if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
goto __RES;
}
/* now set M[1] to G * R mod m */
if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
goto __RES;
}
} else {
mp_set(&res, 1);
if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
goto __RES;
}
}
/* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
goto __RES;
}
for (x = 0; x < (winsize - 1); x++) {
if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
goto __RES;
}
if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
goto __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 __RES;
}
if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
goto __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) {
break;
}
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 __RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
goto __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 __RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
goto __RES;
}
}
/* then multiply */
if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
goto __RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
goto __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 __RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
goto __RES;
}
bitbuf <<= 1;
if ((bitbuf & (1 << winsize)) != 0) {
/* then multiply */
if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
goto __RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
goto __RES;
}
}
}
}
if (redmode == 0) {
/* fixup result if Montgomery reduction is used */
if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
goto __RES;
}
}
mp_exch (&res, Y);
err = MP_OKAY;
__RES:mp_clear (&res);
__M:
for (x = 0; x < (1 << winsize); x++) {
mp_clear (&M[x]);
}
return err;
}
