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