3 * $Id: ec2.cal,v 1.1.2.1 2004/03/21 22:39:46 mdw Exp $
5 * Testbed for elliptic curve arithmetic over binary fields
7 * (c) 2004 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
14 * Catacomb is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU Library General Public License as
16 * published by the Free Software Foundation; either version 2 of the
17 * License, or (at your option) any later version.
19 * Catacomb is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU Library General Public License for more details.
24 * You should have received a copy of the GNU Library General Public
25 * License along with Catacomb; if not, write to the Free
26 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
30 /*----- Revision history --------------------------------------------------*
33 * Revision 1.1.2.1 2004/03/21 22:39:46 mdw
34 * Elliptic curves on binary fields work.
36 * Revision 1.1.4.2 2004/03/20 00:13:31 mdw
37 * Projective coordinates for prime curves
39 * Revision 1.1.4.1 2003/06/10 13:43:53 mdw
40 * Simple (non-projective) curves over prime fields now seem to work.
42 * Revision 1.1 2000/10/08 16:01:37 mdw
43 * Prototypes of various bits of code.
47 /*----- Object types ------------------------------------------------------*/
49 obj ec2_curve { a, b, p };
50 obj ec2_pt { x, y, e };
51 obj ecpp_pt { x, y, z, e };
53 /*----- Main code ---------------------------------------------------------*/
55 define ec2_curve(a, b, p)
57 local obj ec2_curve e;
64 define ec2_pt(x, y, e)
73 define ec2_pt_print(a)
75 print "(" : a.x : ", " : a.y : ")" :;
78 define ec2_pt_add(a, b)
83 print "> ecadd: ", a, b;
88 else if (!istype(a, b))
89 quit "bad type arguments to ec2_pt_add";
91 quit "points from different curves in ec2_pt_add";
95 alpha = ((a.y + b.y) * gf_inv(a.x + b.x, e.p)) % e.p;
96 d.x = (e.a + alpha^2 + alpha + a.x + b.x) % e.p;
97 } else if (a.y != b.y || a.x == gf(0))
100 alpha = a.x + a.y * gf_inv(a.x, e.p) % e.p;
101 d.x = (e.a + alpha^2 + alpha) % e.p;
103 d.y = ((a.x + d.x) * alpha + d.x + a.y) % e.p;
107 print "< ecadd: ", d;
115 print "> ecdbl: ", a;
119 alpha = a.x + a.y * gf_inv(a.x, e.p) % e.p;
120 d.x = (e.a + alpha^2 + alpha) % e.p;
121 d.y = ((a.x + d.x) * alpha + d.x + a.y) % e.p;
123 print "< ecdbl: ", d;
127 define ec2_pt_sub(a, b) { return ec2_pt_add(a, ec2_pt_neg(b)); }
138 define ec2_pt_check(a)
143 if ((a.y^2 + a.x * a.y) % e.p != (a.x^3 + e.a * a.x^2 + e.b) % e.p)
144 quit "bad curve point";
147 define ec2_pt_mul(a, b)
155 } else if (istype(b, 1)) {
159 return (newerror("bad arguments to ec2_pt_mul"));
171 /*----- FIPS186-2 standard curves -----------------------------------------*/
173 b163 = ec2_curve(gf(1),gf(0x20a601907b8c953ca1481eb10512f78744a3205fd),
174 gf(0x800000000000000000000000000000000000000c9));
175 b163_r = 5846006549323611672814742442876390689256843201587;
176 b163_g = ec2_pt(0x3f0eba16286a2d57ea0991168d4994637e8343e36,
177 0x0d51fbc6c71a0094fa2cdd545b11c5c0c797324f1, b163);
179 /*----- That's all, folks -------------------------------------------------*/