/* -*-c-*-
*
- * $Id: gf-gcd.c,v 1.1.2.1 2004/03/21 22:39:46 mdw Exp $
+ * $Id$
*
* Euclidian algorithm on binary polynomials
*
* (c) 2004 Straylight/Edgeware
*/
-/*----- Licensing notice --------------------------------------------------*
+/*----- Licensing notice --------------------------------------------------*
*
* This file is part of Catacomb.
*
* 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"
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;
+ /* --- Main extended Euclidean algorithm --- */
u = MP_COPY(a);
v = MP_COPY(b);
- while (MP_LEN(v)) {
+ while (!MP_ZEROP(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);
+ t = gf_add(t, t, x);
MP_DROP(x); x = X; X = t;
t = gf_mul(MP_NEW, Y, q);
- t = gf_add(t, y, t);
+ t = gf_add(t, t, y);
MP_DROP(y); y = Y; Y = t;
}
t = u; u = v; v = t;
MP_DROP(v);
MP_DROP(X); MP_DROP(Y);
- MP_DROP(a); MP_DROP(b);
+}
+
+/* -- @gf_modinv@ --- *
+ *
+ * Arguments: @mp *d@ = destination
+ * @mp *x@ = argument
+ * @mp *p@ = modulus
+ *
+ * Returns: The inverse %$x^{-1} \bmod p$%.
+ *
+ * Use: Computes a modular inverse, the catch being that the
+ * arguments and results are binary polynomials. An assertion
+ * fails if %$p$% has no inverse.
+ */
+
+mp *gf_modinv(mp *d, mp *x, mp *p)
+{
+ mp *g = MP_NEW;
+ gf_gcd(&g, 0, &d, p, x);
+ assert(MP_EQ(g, MP_ONE));
+ mp_drop(g);
+ return (d);
}
/*----- Test rig ----------------------------------------------------------*/
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("\n*** gf_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("\n*** gf_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);
}
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("\n*** gf_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);