libtommath/bn_fast_mp_montgomery_reduce.c

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#include <tommath.h>
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
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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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* The library was designed directly after the MPI library by
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* 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
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*/
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/* computes xR**-1 == x (mod N) via Montgomery Reduction
*
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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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*
* Based on Algorithm 14.32 on pp.601 of HAC.
*/
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int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
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{
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int ix, res, olduse;
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mp_word W[MP_WARRAY];
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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) {
if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
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return res;
}
}
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/* first we have to get the digits of the input into
* an array of double precision words W[...]
*/
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{
register mp_word *_W;
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register mp_digit *tmpx;
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/* alias for the W[] array */
_W = W;
/* 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++) {
*_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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for (; ix < n->used * 2 + 1; ix++) {
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*_W++ = 0;
}
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}
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/* now we proceed to zero successive digits
* from the least significant upwards
*/
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for (ix = 0; ix < n->used; ix++) {
/* mu = ai * m' mod b
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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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register mp_digit mu;
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mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
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/* a = a + mu * m * b**i
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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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* 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
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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
* 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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*/
{
register int iy;
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register mp_digit *tmpn;
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register 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;
/* 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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}
}
/* now fix carry for next digit, W[ix+1] */
W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
}
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/* now we have to propagate the carries and
* shift the words downward [all those least
* significant digits we zeroed].
*/
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{
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register mp_digit *tmpx;
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register mp_word *_W, *_W1;
/* 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) DIGIT_BIT);
}
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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
* 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++ = (mp_digit)(*_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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for (; ix < olduse; ix++) {
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*tmpx++ = 0;
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}
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}
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/* set the max used and clamp */
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x->used = n->used + 1;
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) {
return s_mp_sub (x, n, x);
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}
return MP_OKAY;
}
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#endif
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/* $Source$ */
/* $Revision$ */
/* $Date$ */