| 1 | /* -*-apcalc-*- |
| 2 | * |
| 3 | * $Id: ecp.cal,v 1.1 2000/10/08 16:01:37 mdw Exp $ |
| 4 | * |
| 5 | * Testbed for elliptic curve arithmetic over prime fields |
| 6 | * |
| 7 | * (c) 2000 Straylight/Edgeware |
| 8 | */ |
| 9 | |
| 10 | /*----- Licensing notice --------------------------------------------------* |
| 11 | * |
| 12 | * This file is part of Catacomb. |
| 13 | * |
| 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. |
| 18 | * |
| 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. |
| 23 | * |
| 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, |
| 27 | * MA 02111-1307, USA. |
| 28 | */ |
| 29 | |
| 30 | /*----- Revision history --------------------------------------------------* |
| 31 | * |
| 32 | * $Log: ecp.cal,v $ |
| 33 | * Revision 1.1 2000/10/08 16:01:37 mdw |
| 34 | * Prototypes of various bits of code. |
| 35 | * |
| 36 | */ |
| 37 | |
| 38 | /*----- Object types ------------------------------------------------------*/ |
| 39 | |
| 40 | obj ecp_curve { a, b, p }; |
| 41 | obj ecp_pt { x, y, e }; |
| 42 | |
| 43 | /*----- Main code ---------------------------------------------------------*/ |
| 44 | |
| 45 | define ecp_curve(a, b, p) |
| 46 | { |
| 47 | local obj ecp_curve e; |
| 48 | e.a = a; |
| 49 | e.b = b; |
| 50 | e.p = p; |
| 51 | return (e); |
| 52 | } |
| 53 | |
| 54 | define ecp_pt(x, y, e) |
| 55 | { |
| 56 | local obj ecp_pt p; |
| 57 | p.x = x % e.p; |
| 58 | p.y = y % e.p; |
| 59 | p.e = e; |
| 60 | return (p); |
| 61 | } |
| 62 | |
| 63 | define ecp_pt_print(a) |
| 64 | { |
| 65 | print "(" : a.x : ", " : a.y : ")" :; |
| 66 | } |
| 67 | |
| 68 | define ecp_pt_add(a, b) |
| 69 | { |
| 70 | local e, alpha; |
| 71 | local obj ecp_pt d; |
| 72 | |
| 73 | if (a == 0) |
| 74 | d = b; |
| 75 | else if (b == 0) |
| 76 | d = a; |
| 77 | else if (!istype(a, b)) |
| 78 | quit "bad type arguments to ecp_pt_add"; |
| 79 | else if (a.e != b.e) |
| 80 | quit "points from different curves in ecp_pt_add"; |
| 81 | else { |
| 82 | e = a.e; |
| 83 | if (a.x == b.x) { |
| 84 | if (a.y != b.y) { |
| 85 | return (0); |
| 86 | } |
| 87 | alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p; |
| 88 | } else |
| 89 | alpha = (b.y - a.y) * minv(b.x - a.x, e.p) % e.p; |
| 90 | |
| 91 | d.x = (alpha^2 - a.x - b.x) % e.p; |
| 92 | d.y = (-a.y + alpha * (a.x - d.x)) % e.p; |
| 93 | d.e = e; |
| 94 | } |
| 95 | |
| 96 | return (d); |
| 97 | } |
| 98 | |
| 99 | define ecp_pt_neg(a) |
| 100 | { |
| 101 | local obj ecp_pt d; |
| 102 | d.x = a.x; |
| 103 | d.y = -a.y; |
| 104 | d.e = a.e; |
| 105 | return (d); |
| 106 | } |
| 107 | |
| 108 | define ecp_pt_mul(a, b) |
| 109 | { |
| 110 | local p, n; |
| 111 | local d; |
| 112 | |
| 113 | if (istype(a, 1)) { |
| 114 | n = a; |
| 115 | p = b; |
| 116 | } else if (istype(b, 1)) { |
| 117 | n = b; |
| 118 | p = a; |
| 119 | } else |
| 120 | return (newerror("bad arguments to ecp_pt_mul")); |
| 121 | |
| 122 | d = 0; |
| 123 | while (n) { |
| 124 | if (n & 1) |
| 125 | d += p; |
| 126 | n >>= 1; |
| 127 | p += p; |
| 128 | } |
| 129 | return (d); |
| 130 | } |
| 131 | |
| 132 | /*----- That's all, folks -------------------------------------------------*/ |
| 133 | |