| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: ec-prime.c,v 1.3 2003/05/15 23:25:59 mdw Exp $ |
| 4 | * |
| 5 | * Elliptic curves over prime fields |
| 6 | * |
| 7 | * (c) 2001 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: ec-prime.c,v $ |
| 33 | * Revision 1.3 2003/05/15 23:25:59 mdw |
| 34 | * Make elliptic curve stuff build. |
| 35 | * |
| 36 | * Revision 1.2 2002/01/13 13:48:44 mdw |
| 37 | * Further progress. |
| 38 | * |
| 39 | * Revision 1.1 2001/04/29 18:12:33 mdw |
| 40 | * Prototype version. |
| 41 | * |
| 42 | */ |
| 43 | |
| 44 | /*----- Header files ------------------------------------------------------*/ |
| 45 | |
| 46 | #include <mLib/sub.h> |
| 47 | |
| 48 | #include "ec.h" |
| 49 | |
| 50 | /*----- Data structures ---------------------------------------------------*/ |
| 51 | |
| 52 | typedef struct ecctx { |
| 53 | ec_curve c; |
| 54 | mp *a, *b; |
| 55 | } ecctx; |
| 56 | |
| 57 | /*----- Main code ---------------------------------------------------------*/ |
| 58 | |
| 59 | static const ec_ops ec_primeops; |
| 60 | |
| 61 | static ec *ecneg(ec_curve *c, ec *d, const ec *p) |
| 62 | { |
| 63 | EC_COPY(d, p); |
| 64 | d->y = F_NEG(c->f, d->y, d->y); |
| 65 | return (d); |
| 66 | } |
| 67 | |
| 68 | static ec *ecdbl(ec_curve *c, ec *d, const ec *a) |
| 69 | { |
| 70 | if (EC_ATINF(a)) |
| 71 | EC_SETINF(d); |
| 72 | else if (!MP_LEN(a->y)) |
| 73 | EC_COPY(d, a); |
| 74 | else { |
| 75 | field *f = c->f; |
| 76 | ecctx *cc = (ecctx *)c; |
| 77 | mp *lambda; |
| 78 | mp *dy, *dx; |
| 79 | |
| 80 | dx = F_SQR(f, MP_NEW, a->x); |
| 81 | dy = F_DBL(f, MP_NEW, a->y); |
| 82 | dx = F_TPL(f, dx, dx); |
| 83 | dx = F_ADD(f, dx, dx, cc->a); |
| 84 | dy = F_INV(f, dy, dy); |
| 85 | lambda = F_MUL(f, MP_NEW, dx, dy); |
| 86 | |
| 87 | dx = F_SQR(f, dx, lambda); |
| 88 | dy = F_DBL(f, dy, a->x); |
| 89 | dx = F_SUB(f, dx, dx, dy); |
| 90 | dy = F_SUB(f, dy, a->x, dx); |
| 91 | dy = F_MUL(f, dy, lambda, dy); |
| 92 | dy = F_SUB(f, dy, dy, a->y); |
| 93 | |
| 94 | EC_DESTROY(d); |
| 95 | d->x = dx; |
| 96 | d->y = dy; |
| 97 | d->z = 0; |
| 98 | MP_DROP(lambda); |
| 99 | } |
| 100 | return (d); |
| 101 | } |
| 102 | |
| 103 | static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b) |
| 104 | { |
| 105 | if (a == b) |
| 106 | ecdbl(c, d, a); |
| 107 | else if (EC_ATINF(a)) |
| 108 | EC_COPY(d, b); |
| 109 | else if (EC_ATINF(b)) |
| 110 | EC_COPY(d, a); |
| 111 | else { |
| 112 | field *f = c->f; |
| 113 | mp *lambda; |
| 114 | mp *dy, *dx; |
| 115 | |
| 116 | if (!MP_EQ(a->x, b->x)) { |
| 117 | dy = F_SUB(f, MP_NEW, a->y, b->y); |
| 118 | dx = F_SUB(f, MP_NEW, a->x, b->x); |
| 119 | dx = F_INV(f, dx, dx); |
| 120 | lambda = F_MUL(f, MP_NEW, dy, dx); |
| 121 | } else if (!MP_LEN(a->y) || !MP_EQ(a->y, b->y)) { |
| 122 | EC_SETINF(d); |
| 123 | return (d); |
| 124 | } else { |
| 125 | ecctx *cc = (ecctx *)c; |
| 126 | dx = F_SQR(f, MP_NEW, a->x); |
| 127 | dx = F_TPL(f, dx, dx); |
| 128 | dx = F_ADD(f, dx, dx, cc->a); |
| 129 | dy = F_DBL(f, MP_NEW, a->y); |
| 130 | dy = F_INV(f, dy, dy); |
| 131 | lambda = F_MUL(f, MP_NEW, dx, dy); |
| 132 | } |
| 133 | |
| 134 | dx = F_SQR(f, dx, lambda); |
| 135 | dx = F_SUB(f, dx, dx, a->x); |
| 136 | dx = F_SUB(f, dx, dx, b->x); |
| 137 | dy = F_SUB(f, dy, b->x, dx); |
| 138 | dy = F_MUL(f, dy, lambda, dy); |
| 139 | dy = F_SUB(f, dy, dy, b->y); |
| 140 | |
| 141 | EC_DESTROY(d); |
| 142 | d->x = dx; |
| 143 | d->y = dy; |
| 144 | d->z = 0; |
| 145 | MP_DROP(lambda); |
| 146 | } |
| 147 | return (d); |
| 148 | } |
| 149 | |
| 150 | static void ecdestroy(ec_curve *c) |
| 151 | { |
| 152 | ecctx *cc = (ecctx *)c; |
| 153 | MP_DROP(cc->a); |
| 154 | MP_DROP(cc->b); |
| 155 | DESTROY(cc); |
| 156 | } |
| 157 | |
| 158 | /* --- @ec_prime@, @ec_primeproj@ --- * |
| 159 | * |
| 160 | * Arguments: @field *f@ = the underyling field for this elliptic curve |
| 161 | * @mp *a, *b@ = the coefficients for this curve |
| 162 | * |
| 163 | * Returns: A pointer to the curve. |
| 164 | * |
| 165 | * Use: Creates a curve structure for an elliptic curve defined over |
| 166 | * a prime field. The @primeproj@ variant uses projective |
| 167 | * coordinates, which can be a win. |
| 168 | */ |
| 169 | |
| 170 | extern ec_curve *ec_prime(field *f, mp *a, mp *b) |
| 171 | { |
| 172 | ecctx *cc = CREATE(ecctx); |
| 173 | cc->c.ops = &ec_primeops; |
| 174 | cc->c.f = f; |
| 175 | cc->a = MP_COPY(a); |
| 176 | cc->b = MP_COPY(b); |
| 177 | return (&cc->c); |
| 178 | } |
| 179 | |
| 180 | static const ec_ops ec_primeops = { |
| 181 | ecdestroy, ec_idin, ec_idout, 0, ecneg, ecadd, ec_stdsub, ecdbl |
| 182 | }; |
| 183 | |
| 184 | /*----- Test rig ----------------------------------------------------------*/ |
| 185 | |
| 186 | #ifdef TEST_RIG |
| 187 | |
| 188 | #define MP(x) mp_readstring(MP_NEW, #x, 0, 0) |
| 189 | |
| 190 | int main(void) |
| 191 | { |
| 192 | field *f; |
| 193 | ec_curve *c; |
| 194 | ec g = EC_INIT, d = EC_INIT; |
| 195 | mp *p, *a, *b, *r; |
| 196 | |
| 197 | a = MP(-3); |
| 198 | b = MP(0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1); |
| 199 | p = MP(6277101735386680763835789423207666416083908700390324961279); |
| 200 | r = MP(6277101735386680763835789423176059013767194773182842284081); |
| 201 | |
| 202 | f = field_prime(p); |
| 203 | c = ec_prime(f, a, b); |
| 204 | |
| 205 | g.x = MP(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012); |
| 206 | g.y = MP(0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811); |
| 207 | |
| 208 | ec_mul(c, &d, &g, r); |
| 209 | MP_PRINT("d.x", d.x); |
| 210 | MP_PRINT("d.y", d.y); |
| 211 | |
| 212 | ec_destroy(&d); |
| 213 | ec_destroy(&g); |
| 214 | ec_destroycurve(c); |
| 215 | F_DESTROY(f); |
| 216 | |
| 217 | return (0); |
| 218 | } |
| 219 | |
| 220 | #endif |
| 221 | |
| 222 | /*----- That's all, folks -------------------------------------------------*/ |