| 1 | /* -*-apcalc-*- |
| 2 | * |
| 3 | * $Id: ecp.cal,v 1.1.4.2 2004/03/20 00:13:31 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 1.1.4.2 2004/03/20 00:13:31 mdw |
| 34 | * Projective coordinates for prime curves |
| 35 | * |
| 36 | * Revision 1.1.4.1 2003/06/10 13:43:53 mdw |
| 37 | * Simple (non-projective) curves over prime fields now seem to work. |
| 38 | * |
| 39 | * Revision 1.1 2000/10/08 16:01:37 mdw |
| 40 | * Prototypes of various bits of code. |
| 41 | * |
| 42 | */ |
| 43 | |
| 44 | /*----- Object types ------------------------------------------------------*/ |
| 45 | |
| 46 | obj ecp_curve { a, b, p }; |
| 47 | obj ecp_pt { x, y, e }; |
| 48 | obj ecpp_pt { x, y, z, e }; |
| 49 | |
| 50 | /*----- Main code ---------------------------------------------------------*/ |
| 51 | |
| 52 | define ecp_curve(a, b, p) |
| 53 | { |
| 54 | local obj ecp_curve e; |
| 55 | e.a = a; |
| 56 | e.b = b; |
| 57 | e.p = p; |
| 58 | return (e); |
| 59 | } |
| 60 | |
| 61 | define ecp_pt(x, y, e) |
| 62 | { |
| 63 | local obj ecp_pt p; |
| 64 | p.x = x % e.p; |
| 65 | p.y = y % e.p; |
| 66 | p.e = e; |
| 67 | return (p); |
| 68 | } |
| 69 | |
| 70 | define ecpp_pt(p) |
| 71 | { |
| 72 | local obj ecpp_pt pp; |
| 73 | if (istype(p, 1)) |
| 74 | return (0); |
| 75 | pp.x = p.x; |
| 76 | pp.y = p.y; |
| 77 | pp.z = 1; |
| 78 | pp.e = p.e; |
| 79 | return (pp); |
| 80 | } |
| 81 | |
| 82 | define ecpp_fix(pp) |
| 83 | { |
| 84 | local obj ecp_pt p; |
| 85 | local e, zi, z2, z3; |
| 86 | if (istype(pp, 1) || pp.z == 0) |
| 87 | return (0); |
| 88 | e = pp.e; |
| 89 | zi = minv(pp.z, e.p); |
| 90 | z2 = zi * zi; |
| 91 | z3 = zi * z2; |
| 92 | p.x = pp.x * z2 % e.p; |
| 93 | p.y = pp.y * z3 % e.p; |
| 94 | p.e = e; |
| 95 | return (p); |
| 96 | } |
| 97 | |
| 98 | define ecpp_dbl(a) |
| 99 | { |
| 100 | local m, s, t, y2; |
| 101 | local e; |
| 102 | local obj ecpp_pt d; |
| 103 | if (istype(a, 1) || a.y == 0) |
| 104 | return (0); |
| 105 | e = a.e; |
| 106 | if (e.a % e.p == e.p - 3) { |
| 107 | m = a.z^3 % e.p; |
| 108 | m = 3 * (a.x + t4) * (a.x - t4) % e.p; |
| 109 | } else { |
| 110 | m = (3 * a.x^2 - e.a * a.z^4) % e.p; |
| 111 | } |
| 112 | d.z = 2 * a.y * a.z % e.p; |
| 113 | y2 = a.y^2 % e.p; |
| 114 | s = 4 * a.x * a.y % e.p; |
| 115 | d.x = (m^2 - 2 * s) % e.p; |
| 116 | d.y = (m * (s - d.x) - y * y2^2) % e.p; |
| 117 | d.e = e; |
| 118 | return (d); |
| 119 | } |
| 120 | |
| 121 | define ecpp_add(a, b) |
| 122 | { |
| 123 | if (a == 0) |
| 124 | d = b; |
| 125 | else if (b == 0) |
| 126 | d = a; |
| 127 | else if (!istype(a, b)) |
| 128 | quit "bad type arguments to ecp_pt_add"; |
| 129 | else if (a.e != b.e) |
| 130 | quit "points from different curves in ecp_pt_add"; |
| 131 | else { |
| 132 | e = a.e; |
| 133 | |
| 134 | } |
| 135 | |
| 136 | define ecp_pt_print(a) |
| 137 | { |
| 138 | print "(" : a.x : ", " : a.y : ")" :; |
| 139 | } |
| 140 | |
| 141 | define ecp_pt_add(a, b) |
| 142 | { |
| 143 | local e, alpha; |
| 144 | local obj ecp_pt d; |
| 145 | |
| 146 | if (a == 0) |
| 147 | d = b; |
| 148 | else if (b == 0) |
| 149 | d = a; |
| 150 | else if (!istype(a, b)) |
| 151 | quit "bad type arguments to ecp_pt_add"; |
| 152 | else if (a.e != b.e) |
| 153 | quit "points from different curves in ecp_pt_add"; |
| 154 | else { |
| 155 | e = a.e; |
| 156 | if (a.x == b.x) { |
| 157 | if (a.y != b.y) { |
| 158 | return (0); |
| 159 | } |
| 160 | alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p; |
| 161 | } else |
| 162 | alpha = (b.y - a.y) * minv(b.x - a.x, e.p) % e.p; |
| 163 | |
| 164 | d.x = (alpha^2 - a.x - b.x) % e.p; |
| 165 | d.y = (-a.y + alpha * (a.x - d.x)) % e.p; |
| 166 | d.e = e; |
| 167 | } |
| 168 | |
| 169 | return (d); |
| 170 | } |
| 171 | |
| 172 | define ecp_pt_dbl(a) |
| 173 | { |
| 174 | local e, alpha; |
| 175 | local obj ecp_pt d; |
| 176 | if (istype(a, 1)) |
| 177 | return (0); |
| 178 | e = a.e; |
| 179 | alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p; |
| 180 | d.x = (alpha^2 - 2 * a.x) % e.p; |
| 181 | d.y = (-a.y + alpha * (a.x - d.x)) % e.p; |
| 182 | d.e = e; |
| 183 | return (d); |
| 184 | } |
| 185 | |
| 186 | define ecp_pt_neg(a) |
| 187 | { |
| 188 | local obj ecp_pt d; |
| 189 | d.x = a.x; |
| 190 | d.y = -a.y; |
| 191 | d.e = a.e; |
| 192 | return (d); |
| 193 | } |
| 194 | |
| 195 | define ecp_pt_check(a) |
| 196 | { |
| 197 | local e; |
| 198 | |
| 199 | e = a.e; |
| 200 | if (a.y^2 % e.p != (a.x^3 + e.a * a.x + e.b) % e.p) |
| 201 | quit "bad curve point"; |
| 202 | } |
| 203 | |
| 204 | define ecp_pt_mul(a, b) |
| 205 | { |
| 206 | local p, n; |
| 207 | local d; |
| 208 | |
| 209 | if (istype(a, 1)) { |
| 210 | n = a; |
| 211 | p = b; |
| 212 | } else if (istype(b, 1)) { |
| 213 | n = b; |
| 214 | p = a; |
| 215 | } else |
| 216 | return (newerror("bad arguments to ecp_pt_mul")); |
| 217 | |
| 218 | d = 0; |
| 219 | while (n) { |
| 220 | if (n & 1) |
| 221 | d += p; |
| 222 | n >>= 1; |
| 223 | p = ecp_pt_dbl(p); |
| 224 | } |
| 225 | return (d); |
| 226 | } |
| 227 | |
| 228 | /*----- FIPS186-2 standard curves -----------------------------------------*/ |
| 229 | |
| 230 | p192 = ecp_curve(-3, 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1, |
| 231 | 6277101735386680763835789423207666416083908700390324961279); |
| 232 | p192_r = 6277101735386680763835789423176059013767194773182842284081; |
| 233 | p192_g = ecp_pt(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, |
| 234 | 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811, p192); |
| 235 | |
| 236 | /*----- That's all, folks -------------------------------------------------*/ |
| 237 | |