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authorWilliam Joye <wjoye@cfa.harvard.edu>2016-12-21 22:13:18 (GMT)
committerWilliam Joye <wjoye@cfa.harvard.edu>2016-12-21 22:13:18 (GMT)
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-#include <tommath.h>
-#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_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.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
- */
-
-/* computes xR**-1 == x (mod N) via Montgomery Reduction
- *
- * This is an optimized implementation of montgomery_reduce
- * which uses the comba method to quickly calculate the columns of the
- * reduction.
- *
- * Based on Algorithm 14.32 on pp.601 of HAC.
-*/
-int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
-{
- int ix, res, olduse;
- mp_word W[MP_WARRAY];
-
- /* get old used count */
- olduse = x->used;
-
- /* grow a as required */
- if (x->alloc < n->used + 1) {
- if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
- return res;
- }
- }
-
- /* first we have to get the digits of the input into
- * an array of double precision words W[...]
- */
- {
- register mp_word *_W;
- register mp_digit *tmpx;
-
- /* alias for the W[] array */
- _W = W;
-
- /* alias for the digits of x*/
- tmpx = x->dp;
-
- /* copy the digits of a into W[0..a->used-1] */
- for (ix = 0; ix < x->used; ix++) {
- *_W++ = *tmpx++;
- }
-
- /* zero the high words of W[a->used..m->used*2] */
- for (; ix < n->used * 2 + 1; ix++) {
- *_W++ = 0;
- }
- }
-
- /* now we proceed to zero successive digits
- * from the least significant upwards
- */
- for (ix = 0; ix < n->used; ix++) {
- /* mu = ai * m' mod b
- *
- * We avoid a double precision multiplication (which isn't required)
- * by casting the value down to a mp_digit. Note this requires
- * that W[ix-1] have the carry cleared (see after the inner loop)
- */
- register mp_digit mu;
- mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
-
- /* a = a + mu * m * b**i
- *
- * This is computed in place and on the fly. The multiplication
- * by b**i is handled by offseting which columns the results
- * are added to.
- *
- * Note the comba method normally doesn't handle carries in the
- * inner loop In this case we fix the carry from the previous
- * column since the Montgomery reduction requires digits of the
- * result (so far) [see above] to work. This is
- * handled by fixing up one carry after the inner loop. The
- * carry fixups are done in order so after these loops the
- * first m->used words of W[] have the carries fixed
- */
- {
- register int iy;
- register mp_digit *tmpn;
- register mp_word *_W;
-
- /* alias for the digits of the modulus */
- tmpn = n->dp;
-
- /* Alias for the columns set by an offset of ix */
- _W = W + ix;
-
- /* inner loop */
- for (iy = 0; iy < n->used; iy++) {
- *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
- }
- }
-
- /* now fix carry for next digit, W[ix+1] */
- W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
- }
-
- /* now we have to propagate the carries and
- * shift the words downward [all those least
- * significant digits we zeroed].
- */
- {
- register mp_digit *tmpx;
- register mp_word *_W, *_W1;
-
- /* nox fix rest of carries */
-
- /* alias for current word */
- _W1 = W + ix;
-
- /* alias for next word, where the carry goes */
- _W = W + ++ix;
-
- for (; ix <= n->used * 2 + 1; ix++) {
- *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
- }
-
- /* copy out, A = A/b**n
- *
- * The result is A/b**n but instead of converting from an
- * array of mp_word to mp_digit than calling mp_rshd
- * we just copy them in the right order
- */
-
- /* alias for destination word */
- tmpx = x->dp;
-
- /* alias for shifted double precision result */
- _W = W + n->used;
-
- for (ix = 0; ix < n->used + 1; ix++) {
- *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
- }
-
- /* zero oldused digits, if the input a was larger than
- * m->used+1 we'll have to clear the digits
- */
- for (; ix < olduse; ix++) {
- *tmpx++ = 0;
- }
- }
-
- /* set the max used and clamp */
- x->used = n->used + 1;
- mp_clamp (x);
-
- /* if A >= m then A = A - m */
- if (mp_cmp_mag (x, n) != MP_LT) {
- return s_mp_sub (x, n, x);
- }
- return MP_OKAY;
-}
-#endif