160 lines
4.3 KiB
C
160 lines
4.3 KiB
C
#include "tommath_private.h"
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#ifdef BN_S_MP_MONTGOMERY_REDUCE_FAST_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis */
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/* SPDX-License-Identifier: Unlicense */
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/* computes xR**-1 == x (mod N) via Montgomery Reduction
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*
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* This is an optimized implementation of montgomery_reduce
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* which uses the comba method to quickly calculate the columns of the
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* reduction.
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*
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* Based on Algorithm 14.32 on pp.601 of HAC.
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*/
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mp_err s_mp_montgomery_reduce_fast(mp_int *x, const mp_int *n, mp_digit rho)
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{
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int ix, olduse;
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mp_err err;
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mp_word W[MP_WARRAY];
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if (x->used > MP_WARRAY) {
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return MP_VAL;
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}
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/* get old used count */
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olduse = x->used;
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/* grow a as required */
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if (x->alloc < (n->used + 1)) {
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if ((err = mp_grow(x, n->used + 1)) != MP_OKAY) {
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return err;
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}
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}
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/* first we have to get the digits of the input into
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* an array of double precision words W[...]
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*/
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{
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mp_word *_W;
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mp_digit *tmpx;
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/* alias for the W[] array */
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_W = W;
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/* alias for the digits of x*/
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tmpx = x->dp;
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/* copy the digits of a into W[0..a->used-1] */
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for (ix = 0; ix < x->used; ix++) {
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*_W++ = *tmpx++;
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}
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/* zero the high words of W[a->used..m->used*2] */
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if (ix < ((n->used * 2) + 1)) {
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MP_ZERO_BUFFER(_W, sizeof(mp_word) * (size_t)(((n->used * 2) + 1) - ix));
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}
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}
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/* now we proceed to zero successive digits
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* from the least significant upwards
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*/
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for (ix = 0; ix < n->used; ix++) {
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/* mu = ai * m' mod b
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*
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* We avoid a double precision multiplication (which isn't required)
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* by casting the value down to a mp_digit. Note this requires
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* that W[ix-1] have the carry cleared (see after the inner loop)
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*/
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mp_digit mu;
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mu = ((W[ix] & MP_MASK) * rho) & MP_MASK;
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/* a = a + mu * m * b**i
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*
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* This is computed in place and on the fly. The multiplication
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* by b**i is handled by offseting which columns the results
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* are added to.
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*
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* Note the comba method normally doesn't handle carries in the
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* inner loop In this case we fix the carry from the previous
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* column since the Montgomery reduction requires digits of the
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* result (so far) [see above] to work. This is
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* handled by fixing up one carry after the inner loop. The
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* carry fixups are done in order so after these loops the
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* first m->used words of W[] have the carries fixed
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*/
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{
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int iy;
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mp_digit *tmpn;
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mp_word *_W;
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/* alias for the digits of the modulus */
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tmpn = n->dp;
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/* Alias for the columns set by an offset of ix */
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_W = W + ix;
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/* inner loop */
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for (iy = 0; iy < n->used; iy++) {
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*_W++ += (mp_word)mu * (mp_word)*tmpn++;
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}
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}
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/* now fix carry for next digit, W[ix+1] */
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W[ix + 1] += W[ix] >> (mp_word)MP_DIGIT_BIT;
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}
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/* now we have to propagate the carries and
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* shift the words downward [all those least
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* significant digits we zeroed].
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*/
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{
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mp_digit *tmpx;
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mp_word *_W, *_W1;
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/* nox fix rest of carries */
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/* alias for current word */
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_W1 = W + ix;
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/* alias for next word, where the carry goes */
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_W = W + ++ix;
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for (; ix < ((n->used * 2) + 1); ix++) {
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*_W++ += *_W1++ >> (mp_word)MP_DIGIT_BIT;
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}
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/* copy out, A = A/b**n
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*
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* The result is A/b**n but instead of converting from an
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* array of mp_word to mp_digit than calling mp_rshd
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* we just copy them in the right order
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*/
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/* alias for destination word */
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tmpx = x->dp;
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/* alias for shifted double precision result */
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_W = W + n->used;
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for (ix = 0; ix < (n->used + 1); ix++) {
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*tmpx++ = *_W++ & (mp_word)MP_MASK;
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}
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/* zero oldused digits, if the input a was larger than
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* m->used+1 we'll have to clear the digits
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*/
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MP_ZERO_DIGITS(tmpx, olduse - ix);
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}
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/* set the max used and clamp */
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x->used = n->used + 1;
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mp_clamp(x);
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/* if A >= m then A = A - m */
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if (mp_cmp_mag(x, n) != MP_LT) {
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return s_mp_sub(x, n, x);
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}
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return MP_OKAY;
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}
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#endif
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