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#include <tommath_private.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, tstdenis82@gmail.com, http://libtom.org
*/
/* 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[...]
*/
{
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] */
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)
*/
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
*/
{
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) 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) 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
/* ref: HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
/* git commit: e8c27ba7df0efb90708029115c94d681dfa7812f */
/* commit time: 2017-08-29 10:48:46 +0200 */
|
