--- /dev/null
+/* -*-c-*-
+ *
+ * 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 "/t/mpmont");
+ return (0);
+}
+
+#endif
+
+/*----- That's all, folks -------------------------------------------------*/
~mdw / catacomb / blobdiff