#include "tommath_private.h"
#ifdef BN_S_MP_MONTGOMERY_REDUCE_FAST_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
/* SPDX-License-Identifier: Unlicense */
/* 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.
*/
mp_err s_mp_montgomery_reduce_fast(mp_int *x, const mp_int *n, mp_digit rho)
{
int ix, olduse;
mp_err err;
mp_word W[MP_WARRAY];
if (x->used > MP_WARRAY) {
return MP_VAL;
}
/* get old used count */
olduse = x->used;
/* grow a as required */
if (x->alloc < (n->used + 1)) {
if ((err = mp_grow(x, n->used + 1)) != MP_OKAY) {
return err;
}
}
/* first we have to get the digits of the input into
* an array of double precision words W[...]
*/
{
mp_word *_W;
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] */
if (ix < ((n->used * 2) + 1)) {
MP_ZERO_BUFFER(_W, sizeof(mp_word) * (size_t)(((n->used * 2) + 1) - ix));
}
}
/* 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)
*/
mp_digit mu;
mu = ((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
*/
{
int iy;
mp_digit *tmpn;
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)MP_DIGIT_BIT;
}
/* now we have to propagate the carries and
* shift the words downward [all those least
* significant digits we zeroed].
*/
{
mp_digit *tmpx;
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)MP_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++ = *_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
*/
MP_ZERO_DIGITS(tmpx, olduse - ix);
}
/* 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
