--- /dev/null
+/* -*-c-*-
+ *
+ * Efficient reduction modulo nice primes
+ *
+ * (c) 2004 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 <mLib/darray.h>
+#include <mLib/macros.h>
+
+#include "mp.h"
+#include "mpreduce.h"
+#include "mpreduce-exp.h"
+
+/*----- Data structures ---------------------------------------------------*/
+
+DA_DECL(instr_v, mpreduce_instr);
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @mpreduce_create@ --- *
+ *
+ * Arguments: @gfreduce *r@ = structure to fill in
+ * @mp *x@ = an integer
+ *
+ * Returns: Zero if successful; nonzero on failure.
+ *
+ * Use: Initializes a context structure for reduction.
+ */
+
+int mpreduce_create(mpreduce *r, mp *p)
+{
+ mpscan sc;
+ enum { Z = 0, Z1 = 2, X = 4, X0 = 6 };
+ unsigned st = Z;
+ instr_v iv = DA_INIT;
+ unsigned long d, i;
+ unsigned op;
+ size_t w, b, bb;
+
+ /* --- Fill in the easy stuff --- */
+
+ if (!MP_POSP(p))
+ return (-1);
+ d = mp_bits(p);
+ r->lim = d/MPW_BITS;
+ r->s = d%MPW_BITS;
+ if (r->s)
+ r->lim++;
+ r->p = mp_copy(p);
+
+ /* --- Stash a new instruction --- */
+
+#define INSTR(op_, argx_, argy_) do { \
+ DA_ENSURE(&iv, 1); \
+ DA(&iv)[DA_LEN(&iv)].op = (op_); \
+ DA(&iv)[DA_LEN(&iv)].argx = (argx_); \
+ DA(&iv)[DA_LEN(&iv)].argy = (argy_); \
+ DA_EXTEND(&iv, 1); \
+} while (0)
+
+ /* --- Main loop --- *
+ *
+ * A simple state machine decomposes @p@ conveniently into positive and
+ * negative powers of 2. The pure form of the state machine is left below
+ * for reference (and in case I need inspiration for a NAF exponentiator).
+ */
+
+#ifdef DEBUG
+ for (i = 0, mp_scan(&sc, p); mp_step(&sc); i++) {
+ switch (st | mp_bit(&sc)) {
+ case Z | 1: st = Z1; break;
+ case Z1 | 0: st = Z; printf("+ %lu\n", i - 1); break;
+ case Z1 | 1: st = X; printf("- %lu\n", i - 1); break;
+ case X | 0: st = X0; break;
+ case X0 | 1: st = X; printf("- %lu\n", i - 1); break;
+ case X0 | 0: st = Z; printf("+ %lu\n", i - 1); break;
+ }
+ }
+ if (st >= X) printf("+ %lu\n", i - 1);
+ st = Z;
+#endif
+
+ bb = MPW_BITS - (d + 1)%MPW_BITS;
+ for (i = 0, mp_scan(&sc, p); i < d && mp_step(&sc); i++) {
+ switch (st | mp_bit(&sc)) {
+ case Z | 1: st = Z1; break;
+ case Z1 | 0: st = Z; op = MPRI_SUB; goto instr;
+ case Z1 | 1: st = X; op = MPRI_ADD; goto instr;
+ case X | 0: st = X0; break;
+ case X0 | 1: st = X; op = MPRI_ADD; goto instr;
+ case X0 | 0: st = Z; op = MPRI_SUB; goto instr;
+ instr:
+ w = (d - i)/MPW_BITS + 1;
+ b = (bb + i)%MPW_BITS;
+ INSTR(op | !!b, w, b);
+ }
+ }
+ if (DA_LEN(&iv) && (DA(&iv)[DA_LEN(&iv) - 1].op & ~1u) == MPRI_SUB) {
+ mp_drop(r->p);
+ DA_DESTROY(&iv);
+ return (-1);
+ }
+
+#undef INSTR
+
+ /* --- Wrap up --- */
+
+ r->in = DA_LEN(&iv);
+ if (!r->in)
+ r->iv = 0;
+ else if (!r->s) {
+ r->iv = xmalloc(r->in * sizeof(mpreduce_instr));
+ memcpy(r->iv, DA(&iv), r->in * sizeof(mpreduce_instr));
+ } else {
+ r->iv = xmalloc(r->in * 2 * sizeof(mpreduce_instr));
+ for (i = 0; i < r->in; i++) {
+ r->iv[i] = DA(&iv)[i];
+ op = r->iv[i].op & ~1u;
+ w = r->iv[i].argx;
+ b = r->iv[i].argy;
+ b += r->s;
+ if (b >= MPW_BITS) {
+ b -= MPW_BITS;
+ w--;
+ }
+ if (b) op |= 1;
+ r->iv[i + r->in].op = op;
+ r->iv[i + r->in].argx = w;
+ r->iv[i + r->in].argy = b;
+ }
+ }
+ DA_DESTROY(&iv);
+
+#ifdef DEBUG
+ mpreduce_dump(r, stdout);
+#endif
+ return (0);
+}
+
+/* --- @mpreduce_destroy@ --- *
+ *
+ * Arguments: @mpreduce *r@ = structure to free
+ *
+ * Returns: ---
+ *
+ * Use: Reclaims the resources from a reduction context.
+ */
+
+void mpreduce_destroy(mpreduce *r)
+{
+ mp_drop(r->p);
+ if (r->iv) xfree(r->iv);
+}
+
+/* --- @mpreduce_dump@ --- *
+ *
+ * Arguments: @mpreduce *r@ = structure to dump
+ * @FILE *fp@ = file to dump on
+ *
+ * Returns: ---
+ *
+ * Use: Dumps a reduction context.
+ */
+
+void mpreduce_dump(mpreduce *r, FILE *fp)
+{
+ size_t i;
+ static const char *opname[] = { "add", "addshift", "sub", "subshift" };
+
+ fprintf(fp, "mod = "); mp_writefile(r->p, fp, 16);
+ fprintf(fp, "\n lim = %lu; s = %d\n", (unsigned long)r->lim, r->s);
+ for (i = 0; i < r->in; i++) {
+ assert(r->iv[i].op < N(opname));
+ fprintf(fp, " %s %lu %lu\n",
+ opname[r->iv[i].op],
+ (unsigned long)r->iv[i].argx,
+ (unsigned long)r->iv[i].argy);
+ }
+ if (r->s) {
+ fprintf(fp, "tail end charlie\n");
+ for (i = r->in; i < 2 * r->in; i++) {
+ assert(r->iv[i].op < N(opname));
+ fprintf(fp, " %s %lu %lu\n",
+ opname[r->iv[i].op],
+ (unsigned long)r->iv[i].argx,
+ (unsigned long)r->iv[i].argy);
+ }
+ }
+}
+
+/* --- @mpreduce_do@ --- *
+ *
+ * Arguments: @mpreduce *r@ = reduction context
+ * @mp *d@ = destination
+ * @mp *x@ = source
+ *
+ * Returns: Destination, @x@ reduced modulo the reduction poly.
+ */
+
+static void run(const mpreduce_instr *i, const mpreduce_instr *il,
+ mpw *v, mpw z)
+{
+ for (; i < il; i++) {
+#ifdef DEBUG
+ mp vv;
+ mp_build(&vv, v - i->argx, v + 1);
+ printf(" 0x"); mp_writefile(&vv, stdout, 16);
+ printf(" %c (0x%lx << %u) == 0x",
+ (i->op & ~1u) == MPRI_ADD ? '+' : '-',
+ (unsigned long)z,
+ i->argy);
+#endif
+ switch (i->op) {
+ case MPRI_ADD: MPX_UADDN(v - i->argx, v + 1, z); break;
+ case MPRI_ADDLSL: mpx_uaddnlsl(v - i->argx, v + 1, z, i->argy); break;
+ case MPRI_SUB: MPX_USUBN(v - i->argx, v + 1, z); break;
+ case MPRI_SUBLSL: mpx_usubnlsl(v - i->argx, v + 1, z, i->argy); break;
+ default:
+ abort();
+ }
+#ifdef DEBUG
+ mp_build(&vv, v - i->argx, v + 1);
+ mp_writefile(&vv, stdout, 16);
+ printf("\n");
+#endif
+ }
+}
+
+mp *mpreduce_do(mpreduce *r, mp *d, mp *x)
+{
+ mpw *v, *vl;
+ const mpreduce_instr *il;
+ mpw z;
+
+#ifdef DEBUG
+ mp *_r = 0, *_rr = 0;
+#endif
+
+ /* --- If source is negative, divide --- */
+
+ if (MP_NEGP(x)) {
+ mp_div(0, &d, x, r->p);
+ return (d);
+ }
+
+ /* --- Try to reuse the source's space --- */
+
+ MP_COPY(x);
+ if (d) MP_DROP(d);
+ MP_DEST(x, MP_LEN(x), x->f);
+
+ /* --- Do the reduction --- */
+
+#ifdef DEBUG
+ _r = MP_NEW;
+ mp_div(0, &_r, x, r->p);
+ MP_PRINTX("x", x);
+ _rr = 0;
+#endif
+
+ il = r->iv + r->in;
+ if (MP_LEN(x) >= r->lim) {
+ v = x->v + r->lim;
+ vl = x->vl;
+ while (vl-- > v) {
+ while (*vl) {
+ z = *vl;
+ *vl = 0;
+ run(r->iv, il, vl, z);
+#ifdef DEBUG
+ MP_PRINTX("x", x);
+ mp_div(0, &_rr, x, r->p);
+ assert(MP_EQ(_r, _rr));
+#endif
+ }
+ }
+ if (r->s) {
+ while (*vl >> r->s) {
+ z = *vl >> r->s;
+ *vl &= ((1 << r->s) - 1);
+ run(r->iv + r->in, il + r->in, vl, z);
+#ifdef DEBUG
+ MP_PRINTX("x", x);
+ mp_div(0, &_rr, x, r->p);
+ assert(MP_EQ(_r, _rr));
+#endif
+ }
+ }
+ }
+
+ /* --- Finishing touches --- */
+
+ MP_SHRINK(x);
+ if (MP_CMP(x, >=, r->p))
+ x = mp_sub(x, x, r->p);
+
+ /* --- Done --- */
+
+#ifdef DEBUG
+ assert(MP_EQ(_r, x));
+ mp_drop(_r);
+ mp_drop(_rr);
+#endif
+ return (x);
+}
+
+/* --- @mpreduce_exp@ --- *
+ *
+ * Arguments: @mpreduce *mr@ = pointer to reduction context
+ * @mp *d@ = fake destination
+ * @mp *a@ = base
+ * @mp *e@ = exponent
+ *
+ * Returns: Result, %$a^e \bmod m$%.
+ */
+
+mp *mpreduce_exp(mpreduce *mr, mp *d, mp *a, mp *e)
+{
+ mp *x = MP_ONE;
+ mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
+
+ MP_SHRINK(e);
+ MP_COPY(a);
+ if (MP_ZEROP(e))
+ ;
+ else {
+ if (MP_NEGP(e))
+ a = mp_modinv(a, a, mr->p);
+ if (MP_LEN(e) < EXP_THRESH)
+ EXP_SIMPLE(x, a, e);
+ else
+ EXP_WINDOW(x, a, e);
+ }
+ mp_drop(a);
+ mp_drop(d);
+ mp_drop(spare);
+ return (x);
+}
+
+/*----- Test rig ----------------------------------------------------------*/
+
+
+#ifdef TEST_RIG
+
+#define MP(x) mp_readstring(MP_NEW, #x, 0, 0)
+
+static int vreduce(dstr *v)
+{
+ mp *d = *(mp **)v[0].buf;
+ mp *n = *(mp **)v[1].buf;
+ mp *r = *(mp **)v[2].buf;
+ mp *c;
+ int ok = 1;
+ mpreduce rr;
+
+ mpreduce_create(&rr, d);
+ c = mpreduce_do(&rr, MP_NEW, n);
+ if (!MP_EQ(c, r)) {
+ fprintf(stderr, "\n*** reduction failed\n*** ");
+ mpreduce_dump(&rr, stderr);
+ fprintf(stderr, "\n*** n = "); mp_writefile(n, stderr, 10);
+ fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 10);
+ fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 10);
+ fprintf(stderr, "\n");
+ ok = 0;
+ }
+ mpreduce_destroy(&rr);
+ mp_drop(n); mp_drop(d); mp_drop(r); mp_drop(c);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
+ return (ok);
+}
+
+static int vmodexp(dstr *v)
+{
+ mp *p = *(mp **)v[0].buf;
+ mp *g = *(mp **)v[1].buf;
+ mp *x = *(mp **)v[2].buf;
+ mp *r = *(mp **)v[3].buf;
+ mp *c;
+ int ok = 1;
+ mpreduce rr;
+
+ mpreduce_create(&rr, p);
+ c = mpreduce_exp(&rr, MP_NEW, g, x);
+ if (!MP_EQ(c, r)) {
+ fprintf(stderr, "\n*** modexp failed\n*** ");
+ fprintf(stderr, "\n*** p = "); mp_writefile(p, stderr, 10);
+ fprintf(stderr, "\n*** g = "); mp_writefile(g, stderr, 10);
+ fprintf(stderr, "\n*** x = "); mp_writefile(x, stderr, 10);
+ fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 10);
+ fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 10);
+ fprintf(stderr, "\n");
+ ok = 0;
+ }
+ mpreduce_destroy(&rr);
+ mp_drop(p); mp_drop(g); mp_drop(r); mp_drop(x); mp_drop(c);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
+ return (ok);
+}
+
+static test_chunk defs[] = {
+ { "reduce", vreduce, { &type_mp, &type_mp, &type_mp, 0 } },
+ { "modexp", vmodexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
+ { 0, 0, { 0 } }
+};
+
+int main(int argc, char *argv[])
+{
+ test_run(argc, argv, defs, SRCDIR"/t/mpreduce");
+ return (0);
+}
+
+#endif
+
+/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff