3 * Testbed for elliptic curve arithmetic over binary fields
5 * (c) 2004 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
12 * Catacomb is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU Library General Public License as
14 * published by the Free Software Foundation; either version 2 of the
15 * License, or (at your option) any later version.
17 * Catacomb is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU Library General Public License for more details.
22 * You should have received a copy of the GNU Library General Public
23 * License along with Catacomb; if not, write to the Free
24 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
28 /*----- Object types ------------------------------------------------------*/
30 obj ec2_curve { a, b, p };
31 obj ec2_pt { x, y, e };
32 obj ecpp_pt { x, y, z, e };
34 /*----- Main code ---------------------------------------------------------*/
36 define ec2_curve(a, b, p)
38 local obj ec2_curve e;
45 define ec2_pt(x, y, e)
54 define ec2_pt_print(a)
56 print "(" : a.x : ", " : a.y : ")" :;
59 define ec2_pt_add(a, b)
68 else if (!istype(a, b))
69 quit "bad type arguments to ec2_pt_add";
71 quit "points from different curves in ec2_pt_add";
75 alpha = ((a.y + b.y) * gf_inv(a.x + b.x, e.p)) % e.p;
76 d.x = (e.a + alpha^2 + alpha + a.x + b.x) % e.p;
77 } else if (a.y != b.y || a.x == gf(0))
80 alpha = a.x + a.y * gf_inv(a.x, e.p) % e.p;
81 d.x = (e.a + alpha^2 + alpha) % e.p;
83 d.y = ((a.x + d.x) * alpha + d.x + a.y) % e.p;
97 alpha = a.x + a.y * gf_inv(a.x, e.p) % e.p;
98 d.x = (e.a + alpha^2 + alpha) % e.p;
99 d.y = ((a.x + d.x) * alpha + d.x + a.y) % e.p;
104 define ec2_pt_sub(a, b) { return ec2_pt_add(a, ec2_pt_neg(b)); }
115 define ec2_pt_check(a)
120 if ((a.y^2 + a.x * a.y) % e.p != (a.x^3 + e.a * a.x^2 + e.b) % e.p)
121 quit "bad curve point";
124 define ec2_pt_mul(a, b)
132 } else if (istype(b, 1)) {
136 return (newerror("bad arguments to ec2_pt_mul"));
148 /*----- FIPS186-2 standard curves -----------------------------------------*/
150 b163 = ec2_curve(gf(1),gf(0x20a601907b8c953ca1481eb10512f78744a3205fd),
151 gf(0x800000000000000000000000000000000000000c9));
152 b163_r = 5846006549323611672814742442876390689256843201587;
153 b163_g = ec2_pt(0x3f0eba16286a2d57ea0991168d4994637e8343e36,
154 0x0d51fbc6c71a0094fa2cdd545b11c5c0c797324f1, b163);
156 /*----- That's all, folks -------------------------------------------------*/