--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: gf-gcd.c,v 1.1.2.1 2004/03/21 22:39:46 mdw Exp $
+ *
+ * Euclidian algorithm on binary polynomials
+ *
+ * (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.
+ */
+
+/*----- Revision history --------------------------------------------------*
+ *
+ * $Log: gf-gcd.c,v $
+ * Revision 1.1.2.1 2004/03/21 22:39:46 mdw
+ * Elliptic curves on binary fields work.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "gf.h"
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @gf_gcd@ --- *
+ *
+ * Arguments: @mp **gcd, **xx, **yy@ = where to write the results
+ * @mp *a, *b@ = sources (must be nonzero)
+ *
+ *
+ * Returns: ---
+ *
+ * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
+ * @ax + by = gcd(a, b)@. This is useful for computing modular
+ * inverses.
+ */
+
+void gf_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
+{
+ mp *x = MP_ONE, *X = MP_ZERO;
+ mp *y = MP_ZERO, *Y = MP_ONE;
+ mp *u, *v;
+ mp *q = MP_NEW;
+ unsigned f = 0;
+
+#define f_swap 1u
+#define f_ext 2u
+
+ /* --- Sort out some initial flags --- */
+
+ if (xx || yy)
+ f |= f_ext;
+
+ /* --- Ensure that @a@ is larger than @b@ --- *
+ *
+ * If they're the same length we don't care which order they're in, so this
+ * unsigned comparison is fine.
+ */
+
+ if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
+ { mp *t = a; a = b; b = t; }
+ f |= f_swap;
+ }
+
+ /* --- Check for zeroness --- */
+
+ if (MP_EQ(b, MP_ZERO)) {
+
+ /* --- Store %$|a|$% as the GCD --- */
+
+ if (gcd) {
+ if (*gcd) MP_DROP(*gcd);
+ a = MP_COPY(a);
+ *gcd = a;
+ }
+
+ /* --- Store %$1$% and %$0$% in the appropriate bins --- */
+
+ if (f & f_ext) {
+ if (f & f_swap) {
+ mp **t = xx; xx = yy; yy = t;
+ }
+ if (xx) {
+ if (*xx) MP_DROP(*xx);
+ if (MP_EQ(a, MP_ZERO))
+ *xx = MP_ZERO;
+ else
+ *xx = MP_ONE;
+ }
+ if (yy) {
+ if (*yy) MP_DROP(*yy);
+ *yy = MP_ZERO;
+ }
+ }
+ return;
+ }
+
+ /* --- Take a reference to the arguments --- */
+
+ a = MP_COPY(a);
+ b = MP_COPY(b);
+
+ /* --- Make sure @a@ and @b@ are not both even --- */
+
+ MP_SPLIT(a); a->f &= ~MP_NEG;
+ MP_SPLIT(b); b->f &= ~MP_NEG;
+
+ u = MP_COPY(a);
+ v = MP_COPY(b);
+
+ while (MP_LEN(v)) {
+ mp *t;
+ gf_div(&q, &u, u, v);
+ if (f & f_ext) {
+ t = gf_mul(MP_NEW, X, q);
+ t = gf_add(t, x, t);
+ MP_DROP(x); x = X; X = t;
+ t = gf_mul(MP_NEW, Y, q);
+ t = gf_add(t, y, t);
+ MP_DROP(y); y = Y; Y = t;
+ }
+ t = u; u = v; v = t;
+ }
+
+ MP_DROP(q);
+ if (!gcd)
+ MP_DROP(u);
+ else {
+ if (*gcd) MP_DROP(*gcd);
+ u->f &= ~MP_NEG;
+ *gcd = u;
+ }
+
+ /* --- Perform a little normalization --- */
+
+ if (f & f_ext) {
+
+ /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */
+
+ if (f & f_swap) {
+ mp *t = x; x = y; y = t;
+ t = a; a = b; b = t;
+ }
+
+ /* --- Store the results --- */
+
+ if (!xx)
+ MP_DROP(x);
+ else {
+ if (*xx) MP_DROP(*xx);
+ *xx = x;
+ }
+
+ if (!yy)
+ MP_DROP(y);
+ else {
+ if (*yy) MP_DROP(*yy);
+ *yy = y;
+ }
+ }
+
+ MP_DROP(v);
+ MP_DROP(X); MP_DROP(Y);
+ MP_DROP(a); MP_DROP(b);
+}
+
+/*----- Test rig ----------------------------------------------------------*/
+
+#ifdef TEST_RIG
+
+static int gcd(dstr *v)
+{
+ int ok = 1;
+ mp *a = *(mp **)v[0].buf;
+ mp *b = *(mp **)v[1].buf;
+ mp *g = *(mp **)v[2].buf;
+ mp *x = *(mp **)v[3].buf;
+ mp *y = *(mp **)v[4].buf;
+
+ mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW;
+ gf_gcd(&gg, &xx, &yy, a, b);
+ if (!MP_EQ(x, xx)) {
+ fputs("\n*** mp_gcd(x) failed", stderr);
+ fputs("\na = ", stderr); mp_writefile(a, stderr, 16);
+ fputs("\nb = ", stderr); mp_writefile(b, stderr, 16);
+ fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 16);
+ fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 16);
+ fputc('\n', stderr);
+ ok = 0;
+ }
+ if (!MP_EQ(y, yy)) {
+ fputs("\n*** mp_gcd(y) failed", stderr);
+ fputs("\na = ", stderr); mp_writefile(a, stderr, 16);
+ fputs("\nb = ", stderr); mp_writefile(b, stderr, 16);
+ fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 16);
+ fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 16);
+ fputc('\n', stderr);
+ ok = 0;
+ }
+
+ if (!ok) {
+ mp *ax = gf_mul(MP_NEW, a, xx);
+ mp *by = gf_mul(MP_NEW, b, yy);
+ ax = gf_add(ax, ax, by);
+ if (MP_EQ(ax, gg))
+ fputs("\n*** (Alternative result found.)\n", stderr);
+ MP_DROP(ax);
+ MP_DROP(by);
+ }
+
+ if (!MP_EQ(g, gg)) {
+ fputs("\n*** mp_gcd(gcd) failed", stderr);
+ fputs("\na = ", stderr); mp_writefile(a, stderr, 16);
+ fputs("\nb = ", stderr); mp_writefile(b, stderr, 16);
+ fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 16);
+ fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 16);
+ fputc('\n', stderr);
+ ok = 0;
+ }
+ MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y);
+ MP_DROP(gg); MP_DROP(xx); MP_DROP(yy);
+ assert(mparena_count(MPARENA_GLOBAL) == 0);
+ return (ok);
+}
+
+static test_chunk tests[] = {
+ { "gcd", gcd, { &type_mp, &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/gf");
+ return (0);
+}
+
+#endif
+
+/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff