b0ab12e6 |
1 | /* -*-c-*- |
2 | * |
41cb1beb |
3 | * $Id: ec-prime.c,v 1.3 2003/05/15 23:25:59 mdw Exp $ |
b0ab12e6 |
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 $ |
41cb1beb |
33 | * Revision 1.3 2003/05/15 23:25:59 mdw |
34 | * Make elliptic curve stuff build. |
35 | * |
b085fd91 |
36 | * Revision 1.2 2002/01/13 13:48:44 mdw |
37 | * Further progress. |
38 | * |
b0ab12e6 |
39 | * Revision 1.1 2001/04/29 18:12:33 mdw |
40 | * Prototype version. |
41 | * |
42 | */ |
43 | |
44 | /*----- Header files ------------------------------------------------------*/ |
45 | |
41cb1beb |
46 | #include <mLib/sub.h> |
47 | |
b0ab12e6 |
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 | |
41cb1beb |
59 | static const ec_ops ec_primeops; |
60 | |
61 | static ec *ecneg(ec_curve *c, ec *d, const ec *p) |
b085fd91 |
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) |
b0ab12e6 |
69 | { |
b085fd91 |
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); |
41cb1beb |
85 | lambda = F_MUL(f, MP_NEW, dx, dy); |
b085fd91 |
86 | |
87 | dx = F_SQR(f, dx, lambda); |
41cb1beb |
88 | dy = F_DBL(f, dy, a->x); |
b085fd91 |
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); |
b0ab12e6 |
93 | |
b085fd91 |
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 | { |
b0ab12e6 |
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); |
b085fd91 |
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)) { |
b0ab12e6 |
122 | EC_SETINF(d); |
b085fd91 |
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); |
41cb1beb |
131 | lambda = F_MUL(f, MP_NEW, dx, dy); |
b085fd91 |
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); |
b0ab12e6 |
140 | |
b085fd91 |
141 | EC_DESTROY(d); |
142 | d->x = dx; |
143 | d->y = dy; |
144 | d->z = 0; |
145 | MP_DROP(lambda); |
b0ab12e6 |
146 | } |
b085fd91 |
147 | return (d); |
b0ab12e6 |
148 | } |
149 | |
41cb1beb |
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 | |
b0ab12e6 |
222 | /*----- That's all, folks -------------------------------------------------*/ |