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Ooops, how did that slip by? Fix return type of @ghcopy@.
[u/mdw/catacomb] / ec-bin.c
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ceb3f0c0 1/* -*-c-*-
2 *
c3caa2fa 3 * $Id: ec-bin.c,v 1.2 2004/03/21 22:52:06 mdw Exp $
ceb3f0c0 4 *
5 * Arithmetic for elliptic curves over binary fields
6 *
7 * (c) 2004 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-bin.c,v $
c3caa2fa 33 * Revision 1.2 2004/03/21 22:52:06 mdw
34 * Merge and close elliptic curve branch.
35 *
ceb3f0c0 36 * Revision 1.1.2.1 2004/03/21 22:39:46 mdw
37 * Elliptic curves on binary fields work.
38 *
39 */
40
41/*----- Header files ------------------------------------------------------*/
42
43#include <mLib/sub.h>
44
45#include "ec.h"
46
47/*----- Data structures ---------------------------------------------------*/
48
49typedef struct ecctx {
50 ec_curve c;
51 mp *a, *b;
52 mp *bb;
53} ecctx;
54
55/*----- Main code ---------------------------------------------------------*/
56
57static const ec_ops ec_binops, ec_binprojops;
58
59static ec *ecneg(ec_curve *c, ec *d, const ec *p)
60{
61 EC_COPY(d, p);
62 if (d->x)
63 d->y = F_ADD(c->f, d->y, d->y, d->x);
64 return (d);
65}
66
67static ec *ecprojneg(ec_curve *c, ec *d, const ec *p)
68{
69 EC_COPY(d, p);
70 if (d->x) {
71 mp *t = F_MUL(c->f, MP_NEW, d->x, d->z);
72 d->y = F_ADD(c->f, d->y, d->y, t);
73 MP_DROP(t);
74 }
75 return (d);
76}
77
78static ec *ecfind(ec_curve *c, ec *d, mp *x)
79{
80 /* write me */
81 return (0);
82}
83
84static ec *ecdbl(ec_curve *c, ec *d, const ec *a)
85{
86 if (EC_ATINF(a) || F_ZEROP(c->f, a->x))
87 EC_SETINF(d);
88 else {
89 field *f = c->f;
90 ecctx *cc = (ecctx *)c;
91 mp *lambda;
92 mp *dx, *dy;
93
94 dx = F_INV(f, MP_NEW, a->x); /* %$x^{-1}$% */
95 dy = F_MUL(f, MP_NEW, dx, a->y); /* %$y/x$% */
96 lambda = F_ADD(f, dy, dy, a->x); /* %$\lambda = x + y/x$% */
97
98 dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */
99 dx = F_ADD(f, dx, dx, lambda); /* %$\lambda^2 + \lambda$% */
100 dx = F_ADD(f, dx, dx, cc->a); /* %$x' = a + \lambda^2 + \lambda$% */
101
102 dy = F_ADD(f, MP_NEW, a->x, dx); /* %$ x + x' $% */
103 dy = F_MUL(f, dy, dy, lambda); /* %$ (x + x') \lambda$% */
104 dy = F_ADD(f, dy, dy, a->y); /* %$ (x + x') \lambda + y$% */
105 dy = F_ADD(f, dy, dy, dx); /* %$ y' = (x + x') \lambda + y + x'$% */
106
107 EC_DESTROY(d);
108 d->x = dx;
109 d->y = dy;
110 d->z = 0;
111 MP_DROP(lambda);
112 }
113 return (d);
114}
115
116static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a)
117{
118 if (EC_ATINF(a) || F_ZEROP(c->f, a->x))
119 EC_SETINF(d);
120 else {
121 field *f = c->f;
122 ecctx *cc = (ecctx *)c;
123 mp *dx, *dy, *dz, *u, *v;
124
125 dy = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */
126 dx = F_MUL(f, MP_NEW, dy, cc->bb); /* %$c z^2$% */
127 dx = F_ADD(f, dx, dx, a->x); /* %$x + c z^2$% */
128 dz = F_SQR(f, MP_NEW, dx); /* %$(x + c z^2)^2$% */
129 dx = F_SQR(f, dx, dz); /* %$x' = (x + c z^2)^4$% */
130
131 dz = F_MUL(f, dz, dy, a->x); /* %$z' = x z^2$% */
132
133 dy = F_SQR(f, dy, a->x); /* %$x^2$% */
134 u = F_MUL(f, MP_NEW, a->y, a->z); /* %$y z$% */
135 u = F_ADD(f, u, u, dz); /* %$z' + y z$% */
136 u = F_ADD(f, u, u, dy); /* %$u = z' + x^2 + y z$% */
137
138 v = F_SQR(f, MP_NEW, dy); /* %$x^4$% */
139 dy = F_MUL(f, dy, v, dz); /* %$x^4 z'$% */
140 v = F_MUL(f, v, u, dx); /* %$u x'$% */
141 dy = F_ADD(f, dy, dy, v); /* %$y' = x^4 z' + u x'$% */
142
143 EC_DESTROY(d);
144 d->x = dx;
145 d->y = dy;
146 d->z = dz;
147 MP_DROP(u);
148 MP_DROP(v);
149 assert(!(d->x->f & MP_DESTROYED));
150 assert(!(d->y->f & MP_DESTROYED));
151 assert(!(d->z->f & MP_DESTROYED));
152 }
153 return (d);
154}
155
156static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b)
157{
158 if (a == b)
159 ecdbl(c, d, a);
160 else if (EC_ATINF(a))
161 EC_COPY(d, b);
162 else if (EC_ATINF(b))
163 EC_COPY(d, a);
164 else {
165 field *f = c->f;
166 ecctx *cc = (ecctx *)c;
167 mp *lambda;
168 mp *dx, *dy;
169
170 if (!MP_EQ(a->x, b->x)) {
171 dx = F_ADD(f, MP_NEW, a->x, b->x); /* %$x_0 + x_1$% */
172 dy = F_INV(f, MP_NEW, dx); /* %$(x_0 + x_1)^{-1}$% */
173 dx = F_ADD(f, dx, a->y, b->y); /* %$y_0 + y_1$% */
174 lambda = F_MUL(f, MP_NEW, dy, dx);
175 /* %$\lambda = (y_0 + y_1)/(x_0 + x_1)$% */
176
177 dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */
178 dx = F_ADD(f, dx, dx, lambda); /* %$\lambda^2 + \lambda$% */
179 dx = F_ADD(f, dx, dx, cc->a); /* %$a + \lambda^2 + \lambda$% */
180 dx = F_ADD(f, dx, dx, a->x); /* %$a + \lambda^2 + \lambda + x_0$% */
181 dx = F_ADD(f, dx, dx, b->x);
182 /* %$x' = a + \lambda^2 + \lambda + x_0 + x_1$% */
183 } else if (!MP_EQ(a->y, b->y) || F_ZEROP(f, a->x)) {
184 EC_SETINF(d);
185 return (d);
186 } else {
187 dx = F_INV(f, MP_NEW, a->x); /* %$x^{-1}$% */
188 dy = F_MUL(f, MP_NEW, dx, a->y); /* %$y/x$% */
189 lambda = F_ADD(f, dy, dy, a->x); /* %$\lambda = x + y/x$% */
190
191 dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */
192 dx = F_ADD(f, dx, dx, lambda); /* %$\lambda^2 + \lambda$% */
193 dx = F_ADD(f, dx, dx, cc->a); /* %$x' = a + \lambda^2 + \lambda$% */
194 dy = MP_NEW;
195 }
196
197 dy = F_ADD(f, dy, a->x, dx); /* %$ x + x' $% */
198 dy = F_MUL(f, dy, dy, lambda); /* %$ (x + x') \lambda$% */
199 dy = F_ADD(f, dy, dy, a->y); /* %$ (x + x') \lambda + y$% */
200 dy = F_ADD(f, dy, dy, dx); /* %$ y' = (x + x') \lambda + y + x'$% */
201
202 EC_DESTROY(d);
203 d->x = dx;
204 d->y = dy;
205 d->z = 0;
206 MP_DROP(lambda);
207 }
208 return (d);
209}
210
211static ec *ecprojadd(ec_curve *c, ec *d, const ec *a, const ec *b)
212{
213 if (a == b)
214 c->ops->dbl(c, d, a);
215 else if (EC_ATINF(a))
216 EC_COPY(d, b);
217 else if (EC_ATINF(b))
218 EC_COPY(d, a);
219 else {
220 field *f = c->f;
221 ecctx *cc = (ecctx *)c;
222 mp *dx, *dy, *dz, *u, *uu, *v, *t, *s, *ss, *r, *w, *l;
223
224 dz = F_SQR(f, MP_NEW, b->z); /* %$z_1^2$% */
225 u = F_MUL(f, MP_NEW, dz, a->x); /* %$u_0 = x_0 z_1^2$% */
226 t = F_MUL(f, MP_NEW, dz, b->z); /* %$z_1^3$% */
227 s = F_MUL(f, MP_NEW, t, a->y); /* %$s_0 = y_0 z_1^3$% */
228
229 dz = F_SQR(f, dz, a->z); /* %$z_0^2$% */
230 uu = F_MUL(f, MP_NEW, dz, b->x); /* %$u_1 = x_1 z_0^2$% */
231 t = F_MUL(f, t, dz, a->z); /* %$z_0^3$% */
232 ss = F_MUL(f, MP_NEW, t, b->y); /* %$s_1 = y_1 z_0^3$% */
233
234 w = F_ADD(f, u, u, uu); /* %$r = u_0 + u_1$% */
235 r = F_ADD(f, s, s, ss); /* %$w = s_0 + s_1$% */
236 if (F_ZEROP(f, w)) {
237 MP_DROP(w);
238 MP_DROP(uu);
239 MP_DROP(ss);
240 MP_DROP(t);
241 MP_DROP(dz);
242 if (F_ZEROP(f, r)) {
243 MP_DROP(r);
244 return (c->ops->dbl(c, d, a));
245 } else {
246 MP_DROP(r);
247 EC_SETINF(d);
248 return (d);
249 }
250 }
251
252 l = F_MUL(f, t, a->z, w); /* %$l = z_0 w$% */
253
254 dz = F_MUL(f, dz, l, b->z); /* %$z' = l z_1$% */
255
256 ss = F_MUL(f, ss, r, b->x); /* %$r x_1$% */
257 t = F_MUL(f, uu, l, b->y); /* %$l y_1$% */
258 v = F_ADD(f, ss, ss, t); /* %$v = r x_1 + l y_1$% */
259
260 t = F_ADD(f, t, r, dz); /* %$t = r + z'$% */
261
262 uu = F_SQR(f, MP_NEW, dz); /* %$z'^2$% */
263 dx = F_MUL(f, MP_NEW, uu, cc->a); /* %$a z'^2$% */
264 uu = F_MUL(f, uu, t, r); /* %$t r$% */
265 dx = F_ADD(f, dx, dx, uu); /* %$a z'^2 + t r$% */
266 r = F_SQR(f, r, w); /* %$w^2$% */
267 uu = F_MUL(f, uu, r, w); /* %$w^3$% */
268 dx = F_ADD(f, dx, dx, uu); /* %$x' = a z'^2 + t r + w^3$% */
269
270 r = F_SQR(f, r, l); /* %$l^2$% */
271 dy = F_MUL(f, uu, v, r); /* %$v l^2$% */
272 l = F_MUL(f, l, t, dx); /* %$t x'$% */
273 dy = F_ADD(f, dy, dy, l); /* %$y' = t x' + v l^2$% */
274
275 EC_DESTROY(d);
276 d->x = dx;
277 d->y = dy;
278 d->z = dz;
279 MP_DROP(l);
280 MP_DROP(r);
281 MP_DROP(w);
282 MP_DROP(t);
283 MP_DROP(v);
284 }
285 return (d);
286}
287
288static int eccheck(ec_curve *c, const ec *p)
289{
290 ecctx *cc = (ecctx *)c;
291 field *f = c->f;
292 int rc;
293 mp *u, *v;
294
295 v = F_SQR(f, MP_NEW, p->x);
296 u = F_MUL(f, MP_NEW, v, p->x);
297 v = F_MUL(f, v, v, cc->a);
298 u = F_ADD(f, u, u, v);
299 u = F_ADD(f, u, u, cc->b);
300 v = F_MUL(f, v, p->x, p->y);
301 u = F_ADD(f, u, u, v);
302 v = F_SQR(f, v, p->y);
303 u = F_ADD(f, u, u, v);
304 rc = F_ZEROP(f, u);
305 mp_drop(u);
306 mp_drop(v);
307 return (rc);
308}
309
310static int ecprojcheck(ec_curve *c, const ec *p)
311{
312 ec t = EC_INIT;
313 int rc;
314
315 c->ops->fix(c, &t, p);
316 rc = eccheck(c, &t);
317 EC_DESTROY(&t);
318 return (rc);
319}
320
321static void ecdestroy(ec_curve *c)
322{
323 ecctx *cc = (ecctx *)c;
324 MP_DROP(cc->a);
325 MP_DROP(cc->b);
326 if (cc->bb) MP_DROP(cc->bb);
327 DESTROY(cc);
328}
329
330/* --- @ec_bin@, @ec_binproj@ --- *
331 *
332 * Arguments: @field *f@ = the underlying field for this elliptic curve
333 * @mp *a, *b@ = the coefficients for this curve
334 *
335 * Returns: A pointer to the curve.
336 *
337 * Use: Creates a curve structure for an elliptic curve defined over
338 * a binary field. The @binproj@ variant uses projective
339 * coordinates, which can be a win.
340 */
341
342ec_curve *ec_bin(field *f, mp *a, mp *b)
343{
344 ecctx *cc = CREATE(ecctx);
345 cc->c.ops = &ec_binops;
346 cc->c.f = f;
347 cc->a = F_IN(f, MP_NEW, a);
348 cc->b = F_IN(f, MP_NEW, b);
349 cc->bb = 0;
350 return (&cc->c);
351}
352
353ec_curve *ec_binproj(field *f, mp *a, mp *b)
354{
355 ecctx *cc = CREATE(ecctx);
356 cc->c.ops = &ec_binprojops;
357 cc->c.f = f;
358 cc->a = F_IN(f, MP_NEW, a);
359 cc->b = F_IN(f, MP_NEW, b);
360 cc->bb = F_SQRT(f, MP_NEW, b);
361 cc->bb = F_SQRT(f, cc->bb, cc->bb);
362 return (&cc->c);
363}
364
365static const ec_ops ec_binops = {
366 ecdestroy, ec_idin, ec_idout, ec_idfix,
367 0, ecneg, ecadd, ec_stdsub, ecdbl, eccheck
368};
369
370static const ec_ops ec_binprojops = {
371 ecdestroy, ec_projin, ec_projout, ec_projfix,
372 0, ecprojneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck
373};
374
375/*----- Test rig ----------------------------------------------------------*/
376
377#ifdef TEST_RIG
378
379#define MP(x) mp_readstring(MP_NEW, #x, 0, 0)
380
381int main(int argc, char *argv[])
382{
383 field *f;
384 ec_curve *c;
385 ec g = EC_INIT, d = EC_INIT;
386 mp *p, *a, *b, *r;
387 int i, n = argc == 1 ? 1 : atoi(argv[1]);
388
389 printf("ec-bin: ");
390 fflush(stdout);
391 a = MP(1);
392 b = MP(0x066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad);
393 p = MP(0x20000000000000000000000000000000000000004000000000000000001);
394 r =
395 MP(6901746346790563787434755862277025555839812737345013555379383634485462);
396
397 f = field_binpoly(p);
398 c = ec_binproj(f, a, b);
399
400 g.x = MP(0x0fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b);
401 g.y = MP(0x1006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052);
402
403 for (i = 0; i < n; i++) {
404 ec_mul(c, &d, &g, r);
405 if (EC_ATINF(&d)) {
406 fprintf(stderr, "zero too early\n");
407 return (1);
408 }
409 ec_add(c, &d, &d, &g);
410 if (!EC_ATINF(&d)) {
411 fprintf(stderr, "didn't reach zero\n");
412 MP_EPRINTX("d.x", d.x);
413 MP_EPRINTX("d.y", d.y);
414 MP_EPRINTX("d.z", d.y);
415 return (1);
416 }
417 ec_destroy(&d);
418 }
419
420 ec_destroy(&g);
421 ec_destroycurve(c);
422 F_DESTROY(f);
423 MP_DROP(p); MP_DROP(a); MP_DROP(b); MP_DROP(r);
424 assert(!mparena_count(&mparena_global));
425 printf("ok\n");
426 return (0);
427}
428
429#endif
430
431/*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)