-/* -*-c-*-
- *
- * $Id$
- *
- * Montgomery reduction
- *
- * (c) 1999 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "mp.h"
-#include "mpmont.h"
-
-/*----- Tweakables --------------------------------------------------------*/
-
-/* --- @MPMONT_DISABLE@ --- *
- *
- * Replace all the clever Montgomery reduction with good old-fashioned long
- * division.
- */
-
-/* #define MPMONT_DISABLE */
-
-/*----- Reduction and multiplication --------------------------------------*/
-
-/* --- @mpmont_create@ --- *
- *
- * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
- * @mp *m@ = modulus to use
- *
- * Returns: Zero on success, nonzero on error.
- *
- * Use: Initializes a Montgomery reduction context ready for use.
- * The argument @m@ must be a positive odd integer.
- */
-
-#ifdef MPMONT_DISABLE
-
-int mpmont_create(mpmont *mm, mp *m)
-{
- mp_shrink(m);
- mm->m = MP_COPY(m);
- mm->r = MP_ONE;
- mm->r2 = MP_ONE;
- mm->mi = MP_ONE;
- return (0);
-}
-
-#else
-
-int mpmont_create(mpmont *mm, mp *m)
-{
- size_t n = MP_LEN(m);
- mp *r2 = mp_new(2 * n + 1, 0);
- mp r;
-
- /* --- Take a copy of the modulus --- */
-
- if (!MP_POSP(m) || !MP_ODDP(m))
- return (-1);
- mm->m = MP_COPY(m);
-
- /* --- Determine %$R^2$% --- */
-
- mm->n = n;
- MPX_ZERO(r2->v, r2->vl - 1);
- r2->vl[-1] = 1;
-
- /* --- Find the magic value @mi@ --- */
-
- mp_build(&r, r2->v + n, r2->vl);
- mm->mi = mp_modinv(MP_NEW, m, &r);
- mm->mi = mp_sub(mm->mi, &r, mm->mi);
-
- /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
-
- mm->r2 = MP_NEW;
- mp_div(0, &mm->r2, r2, m);
- mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
- MP_DROP(r2);
- return (0);
-}
-
-#endif
-
-/* --- @mpmont_destroy@ --- *
- *
- * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
- *
- * Returns: ---
- *
- * Use: Disposes of a context when it's no longer of any use to
- * anyone.
- */
-
-void mpmont_destroy(mpmont *mm)
-{
- MP_DROP(mm->m);
- MP_DROP(mm->r);
- MP_DROP(mm->r2);
- MP_DROP(mm->mi);
-}
-
-/* --- @mpmont_reduce@ --- *
- *
- * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
- * @mp *d@ = destination
- * @mp *a@ = source, assumed positive
- *
- * Returns: Result, %$a R^{-1} \bmod m$%.
- */
-
-#ifdef MPMONT_DISABLE
-
-mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
-{
- mp_div(0, &d, a, mm->m);
- return (d);
-}
-
-#else
-
-mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
-{
- size_t n = mm->n;
-
- /* --- Check for serious Karatsuba reduction --- */
-
- if (n > MPK_THRESH * 3) {
- mp al;
- mpw *vl;
- mp *u;
-
- if (MP_LEN(a) >= n)
- vl = a->v + n;
- else
- vl = a->vl;
- mp_build(&al, a->v, vl);
- u = mp_mul(MP_NEW, &al, mm->mi);
- if (MP_LEN(u) > n)
- u->vl = u->v + n;
- u = mp_mul(u, u, mm->m);
- d = mp_add(d, a, u);
- mp_drop(u);
- }
-
- /* --- Otherwise do it the hard way --- */
-
- else {
- mpw *dv, *dvl;
- mpw *mv, *mvl;
- mpw mi;
- size_t k = n;
-
- /* --- Initial conditioning of the arguments --- */
-
- a = MP_COPY(a);
- if (d)
- MP_DROP(d);
- d = a;
- MP_DEST(d, 2 * n + 1, a->f);
-
- dv = d->v; dvl = d->vl;
- mv = mm->m->v; mvl = mm->m->vl;
-
- /* --- Let's go to work --- */
-
- mi = mm->mi->v[0];
- while (k--) {
- mpw u = MPW(*dv * mi);
- MPX_UMLAN(dv, dvl, mv, mvl, u);
- dv++;
- }
- }
-
- /* --- Wrap everything up --- */
-
- memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n));
- d->vl -= n;
- if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
- mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
- if (d->f & MP_NEG) {
- mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
- d->f &= ~MP_NEG;
- }
- MP_SHRINK(d);
- return (d);
-}
-
-#endif
-
-/* --- @mpmont_mul@ --- *
- *
- * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
- * @mp *d@ = destination
- * @mp *a, *b@ = sources, assumed positive
- *
- * Returns: Result, %$a b R^{-1} \bmod m$%.
- */
-
-#ifdef MPMONT_DISABLE
-
-mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
-{
- d = mp_mul(d, a, b);
- mp_div(0, &d, d, mm->m);
- return (d);
-}
-
-#else
-
-mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
-{
- if (mm->n > MPK_THRESH * 3) {
- d = mp_mul(d, a, b);
- d = mpmont_reduce(mm, d, d);
- } else {
- mpw *dv, *dvl;
- mpw *av, *avl;
- mpw *bv, *bvl;
- mpw *mv, *mvl;
- mpw y;
- size_t n, i;
- mpw mi;
-
- /* --- Initial conditioning of the arguments --- */
-
- if (MP_LEN(a) > MP_LEN(b)) {
- mp *t = a; a = b; b = t;
- }
- n = MP_LEN(mm->m);
-
- a = MP_COPY(a);
- b = MP_COPY(b);
- MP_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF);
- dv = d->v; dvl = d->vl;
- MPX_ZERO(dv, dvl);
- av = a->v; avl = a->vl;
- bv = b->v; bvl = b->vl;
- mv = mm->m->v; mvl = mm->m->vl;
- y = *bv;
-
- /* --- Montgomery multiplication phase --- */
-
- i = 0;
- mi = mm->mi->v[0];
- while (i < n && av < avl) {
- mpw x = *av++;
- mpw u = MPW((*dv + x * y) * mi);
- MPX_UMLAN(dv, dvl, bv, bvl, x);
- MPX_UMLAN(dv, dvl, mv, mvl, u);
- dv++;
- i++;
- }
-
- /* --- Simpler Montgomery reduction phase --- */
-
- while (i < n) {
- mpw u = MPW(*dv * mi);
- MPX_UMLAN(dv, dvl, mv, mvl, u);
- dv++;
- i++;
- }
-
- /* --- Done --- */
-
- memmove(d->v, dv, MPWS(dvl - dv));
- d->vl -= dv - d->v;
- if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
- mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
- if ((a->f ^ b->f) & MP_NEG)
- mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
- MP_SHRINK(d);
- d->f = (a->f | b->f) & MP_BURN;
- MP_DROP(a);
- MP_DROP(b);
- }
-
- return (d);
-}
-
-#endif
-
-/*----- Test rig ----------------------------------------------------------*/
-
-#ifdef TEST_RIG
-
-static int tcreate(dstr *v)
-{
- mp *m = *(mp **)v[0].buf;
- mp *mi = *(mp **)v[1].buf;
- mp *r = *(mp **)v[2].buf;
- mp *r2 = *(mp **)v[3].buf;
-
- mpmont mm;
- int ok = 1;
-
- mpmont_create(&mm, m);
-
- if (mm.mi->v[0] != mi->v[0]) {
- fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
- (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
- fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
- fputc('\n', stderr);
- ok = 0;
- }
-
- if (!MP_EQ(mm.r, r)) {
- fputs("\n*** bad r", stderr);
- fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
- fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
- fputs("\n found ", stderr); mp_writefile(mm.r, stderr, 10);
- fputc('\n', stderr);
- ok = 0;
- }
-
- if (!MP_EQ(mm.r2, r2)) {
- fputs("\n*** bad r2", stderr);
- fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
- fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
- fputs("\n found ", stderr); mp_writefile(mm.r2, stderr, 10);
- fputc('\n', stderr);
- ok = 0;
- }
-
- MP_DROP(m);
- MP_DROP(mi);
- MP_DROP(r);
- MP_DROP(r2);
- mpmont_destroy(&mm);
- assert(mparena_count(MPARENA_GLOBAL) == 0);
- return (ok);
-}
-
-static int tmul(dstr *v)
-{
- mp *m = *(mp **)v[0].buf;
- mp *a = *(mp **)v[1].buf;
- mp *b = *(mp **)v[2].buf;
- mp *r = *(mp **)v[3].buf;
- int ok = 1;
-
- mpmont mm;
- mpmont_create(&mm, m);
-
- {
- mp *qr = mp_mul(MP_NEW, a, b);
- mp_div(0, &qr, qr, m);
-
- if (!MP_EQ(qr, r)) {
- fputs("\n*** classical modmul failed", stderr);
- fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
- fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
- fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
- fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
- fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
- fputc('\n', stderr);
- ok = 0;
- }
-
- mp_drop(qr);
- }
-
- {
- mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
- mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
- mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
- mr = mpmont_reduce(&mm, mr, mr);
- if (!MP_EQ(mr, r)) {
- fputs("\n*** montgomery modmul failed", stderr);
- fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
- fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
- fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
- fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
- fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
- fputc('\n', stderr);
- ok = 0;
- }
- MP_DROP(ar); MP_DROP(br);
- mp_drop(mr);
- }
-
-
- MP_DROP(m);
- MP_DROP(a);
- MP_DROP(b);
- MP_DROP(r);
- mpmont_destroy(&mm);
- assert(mparena_count(MPARENA_GLOBAL) == 0);
- return ok;
-}
-
-static test_chunk tests[] = {
- { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
- { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
- { 0, 0, { 0 } },
-};
-
-int main(int argc, char *argv[])
-{
- sub_init();
- test_run(argc, argv, tests, SRCDIR "/tests/mpmont");
- return (0);
-}
-
-#endif
-
-/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff