--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: mpbarrett.c,v 1.1 1999/12/10 23:21:59 mdw Exp $
+ *
+ * Barrett modular 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.
+ */
+
+/*----- Revision history --------------------------------------------------*
+ *
+ * $Log: mpbarrett.c,v $
+ * Revision 1.1 1999/12/10 23:21:59 mdw
+ * Barrett reduction support: works with even moduli.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "mp.h"
+#include "mpbarrett.h"
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @mpbarrett_create@ --- *
+ *
+ * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
+ * @mp *m@ = modulus to work to
+ *
+ *
+ * Returns: ---
+ *
+ * Use: Initializes a Barrett reduction context ready for use.
+ */
+
+void mpbarrett_create(mpbarrett *mb, mp *m)
+{
+ mp *b;
+
+ /* --- Validate the arguments --- */
+
+ assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0));
+
+ /* --- Compute %$\mu$% --- */
+
+ mp_shrink(m);
+ mb->k = MP_LEN(m);
+ mb->m = MP_COPY(m);
+ b = mp_lsl(MP_NEW, MP_ONE, 2 * MPW_BITS * mb->k);
+ mp_div(&b, 0, b, m);
+ mb->mu = b;
+}
+
+/* --- @mpbarrett_destroy@ --- *
+ *
+ * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
+ *
+ * Returns: ---
+ *
+ * Use: Destroys a Barrett reduction context releasing any resources
+ * claimed.
+ */
+
+void mpbarrett_destroy(mpbarrett *mb)
+{
+ mp_drop(mb->m);
+ mp_drop(mb->mu);
+}
+
+/* --- @mpbarrett_reduce@ --- *
+ *
+ * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
+ * @mp *d@ = destination for result
+ * @mp *m@ = number to reduce
+ *
+ * Returns: The residue of @m@ modulo the number in the reduction
+ * context.
+ *
+ * Use: Performs an efficient modular reduction. The argument is
+ * assumed to be positive.
+ */
+
+mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m)
+{
+ mp *q;
+ size_t k = mb->k;
+
+ /* --- Special case if @m@ is too small --- */
+
+ if (MP_LEN(m) < k) {
+ m = MP_COPY(m);
+ MP_DROP(d);
+ return (m);
+ }
+
+ /* --- First stage --- */
+
+ {
+ mp qq;
+ mp_build(&qq, m->v + (k - 1), m->vl);
+ q = mp_mul(MP_NEW, &qq, mb->mu);
+ q = mp_lsr(q, q, MPW_BITS * (k + 1));
+ }
+
+ /* --- Second stage --- */
+
+ {
+ mp *r;
+ mpw *mvl;
+
+ MP_COPY(m);
+ if (MP_LEN(m) <= k + 1)
+ mvl = m->vl;
+ else
+ mvl = m->v + k + 1;
+ r = mp_create(k + 1);
+ mpx_umul(r->v, r->vl, q->v, q->vl, mb->m->v, mb->m->vl);
+ r->f = (q->f | mb->m->f) & MP_BURN;
+ MP_MODIFY(d, k + 1);
+ mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl);
+ d->f = (m->f | r->f) & MP_BURN;
+ MP_DROP(r);
+ MP_DROP(q);
+ MP_DROP(m);
+ }
+
+ /* --- Final stage --- */
+
+ MP_SHRINK(d);
+ while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl))
+ mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl);
+
+ MP_SHRINK(d);
+ return (d);
+}
+
+/* --- @mpbarrett_exp@ --- *
+ *
+ * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
+ * @mp *d@ = fake destination
+ * @mp *a@ = base
+ * @mp *e@ = exponent
+ *
+ * Returns: Result, %$a^e \bmod m$%.
+ */
+
+mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e)
+{
+ mpscan sc;
+ mp *x = MP_ONE;
+ mp *spare = MP_NEW;
+
+ a = MP_COPY(a);
+ mp_scan(&sc, e);
+ if (MP_STEP(&sc)) {
+ size_t sq = 0;
+ for (;;) {
+ mp *dd;
+ if (MP_BIT(&sc)) {
+ while (sq) {
+ dd = mp_sqr(spare, a);
+ dd = mpbarrett_reduce(mb, dd, dd);
+ spare = a; a = dd;
+ sq--;
+ }
+ dd = mp_mul(spare, x, a);
+ dd = mpbarrett_reduce(mb, dd, dd);
+ spare = x; x = dd;
+ }
+ sq++;
+ if (!MP_STEP(&sc))
+ break;
+ }
+ }
+
+ MP_DROP(a);
+ if (spare != MP_NEW)
+ MP_DROP(spare);
+ if (d != MP_NEW)
+ MP_DROP(d);
+ return (x);
+}
+
+/*----- Test rig ----------------------------------------------------------*/
+
+#ifdef TEST_RIG
+
+static int vmod(dstr *v)
+{
+ mp *x = *(mp **)v[0].buf;
+ mp *n = *(mp **)v[1].buf;
+ mp *r = *(mp **)v[2].buf;
+ mp *s;
+ mpbarrett mb;
+ int ok = 1;
+
+ mpbarrett_create(&mb, n);
+ s = mpbarrett_reduce(&mb, MP_NEW, x);
+
+ if (MP_CMP(s, !=, r)) {
+ fputs("\n*** barrett reduction failure\n", stderr);
+ fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr);
+ fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr);
+ fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr);
+ fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr);
+ ok = 0;
+ }
+
+ mpbarrett_destroy(&mb);
+ mp_drop(x);
+ mp_drop(n);
+ mp_drop(r);
+ mp_drop(s);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
+ return (ok);
+}
+
+static int vexp(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;
+ mp *mr;
+ int ok = 1;
+
+ mpbarrett mb;
+ mpbarrett_create(&mb, m);
+
+ mr = mpbarrett_exp(&mb, MP_NEW, a, b);
+
+ if (MP_CMP(mr, !=, r)) {
+ fputs("\n*** barrett modexp failed", stderr);
+ fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
+ fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
+ fputs("\n e = ", 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(m);
+ mp_drop(a);
+ mp_drop(b);
+ mp_drop(r);
+ mp_drop(mr);
+ mpbarrett_destroy(&mb);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
+ return ok;
+}
+
+static test_chunk tests[] = {
+ { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } },
+ { "mpbarrett-exp", vexp, { &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/mpbarrett");
+ return (0);
+}
+
+#endif
+
+/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff