1 /* crypto/ec/ectest.c */
2 /*
3 * Originally written by Bodo Moeller for the OpenSSL project.
4 */
5 /* ====================================================================
6 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
7 *
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
10 * are met:
11 *
12 * 1. Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
14 *
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in
17 * the documentation and/or other materials provided with the
18 * distribution.
19 *
20 * 3. All advertising materials mentioning features or use of this
21 * software must display the following acknowledgment:
22 * "This product includes software developed by the OpenSSL Project
23 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
24 *
25 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
26 * endorse or promote products derived from this software without
27 * prior written permission. For written permission, please contact
28 * openssl-core@openssl.org.
29 *
30 * 5. Products derived from this software may not be called "OpenSSL"
31 * nor may "OpenSSL" appear in their names without prior written
32 * permission of the OpenSSL Project.
33 *
34 * 6. Redistributions of any form whatsoever must retain the following
35 * acknowledgment:
36 * "This product includes software developed by the OpenSSL Project
37 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
38 *
39 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
40 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
41 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
42 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
43 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
44 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
45 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
46 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
48 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
49 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
50 * OF THE POSSIBILITY OF SUCH DAMAGE.
51 * ====================================================================
52 *
53 * This product includes cryptographic software written by Eric Young
54 * (eay@cryptsoft.com). This product includes software written by Tim
55 * Hudson (tjh@cryptsoft.com).
56 *
57 */
58 /* ====================================================================
59 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
60 *
61 * Portions of the attached software ("Contribution") are developed by
62 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
63 *
64 * The Contribution is licensed pursuant to the OpenSSL open source
65 * license provided above.
66 *
67 * The elliptic curve binary polynomial software is originally written by
68 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
69 *
70 */
71
72 #include <stdio.h>
73 #include <stdlib.h>
74 #ifdef FLAT_INC
75 #include "e_os.h"
76 #else
77 #include "../e_os.h"
78 #endif
79 #include <string.h>
80 #include <time.h>
81
82
83 #ifdef OPENSSL_NO_EC
main(int argc,char * argv[])84 int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; }
85 #else
86
87
88 #include <openssl/ec.h>
89 #ifndef OPENSSL_NO_ENGINE
90 #include <openssl/engine.h>
91 #endif
92 #include <openssl/err.h>
93 #include <openssl/obj_mac.h>
94 #include <openssl/objects.h>
95 #include <openssl/rand.h>
96 #include <openssl/bn.h>
97
98 #if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12)
99 /* suppress "too big too optimize" warning */
100 #pragma warning(disable:4959)
101 #endif
102
103 #define ABORT do { \
104 fflush(stdout); \
105 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
106 ERR_print_errors_fp(stderr); \
107 EXIT(1); \
108 } while (0)
109
110 void prime_field_tests(void);
111 void char2_field_tests(void);
112 void internal_curve_test(void);
113
114 #define TIMING_BASE_PT 0
115 #define TIMING_RAND_PT 1
116 #define TIMING_SIMUL 2
117
118 #if 0
119 static void timings(EC_GROUP *group, int type, BN_CTX *ctx)
120 {
121 clock_t clck;
122 int i, j;
123 BIGNUM *s;
124 BIGNUM *r[10], *r0[10];
125 EC_POINT *P;
126
127 s = BN_new();
128 if (s == NULL) ABORT;
129
130 fprintf(stdout, "Timings for %d-bit field, ", EC_GROUP_get_degree(group));
131 if (!EC_GROUP_get_order(group, s, ctx)) ABORT;
132 fprintf(stdout, "%d-bit scalars ", (int)BN_num_bits(s));
133 fflush(stdout);
134
135 P = EC_POINT_new(group);
136 if (P == NULL) ABORT;
137 EC_POINT_copy(P, EC_GROUP_get0_generator(group));
138
139 for (i = 0; i < 10; i++)
140 {
141 if ((r[i] = BN_new()) == NULL) ABORT;
142 if (!BN_pseudo_rand(r[i], BN_num_bits(s), 0, 0)) ABORT;
143 if (type != TIMING_BASE_PT)
144 {
145 if ((r0[i] = BN_new()) == NULL) ABORT;
146 if (!BN_pseudo_rand(r0[i], BN_num_bits(s), 0, 0)) ABORT;
147 }
148 }
149
150 clck = clock();
151 for (i = 0; i < 10; i++)
152 {
153 for (j = 0; j < 10; j++)
154 {
155 if (!EC_POINT_mul(group, P, (type != TIMING_RAND_PT) ? r[i] : NULL,
156 (type != TIMING_BASE_PT) ? P : NULL, (type != TIMING_BASE_PT) ? r0[i] : NULL, ctx)) ABORT;
157 }
158 }
159 clck = clock() - clck;
160
161 fprintf(stdout, "\n");
162
163 #ifdef CLOCKS_PER_SEC
164 /* "To determine the time in seconds, the value returned
165 * by the clock function should be divided by the value
166 * of the macro CLOCKS_PER_SEC."
167 * -- ISO/IEC 9899 */
168 # define UNIT "s"
169 #else
170 /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
171 * -- cc on NeXTstep/OpenStep */
172 # define UNIT "units"
173 # define CLOCKS_PER_SEC 1
174 #endif
175
176 if (type == TIMING_BASE_PT) {
177 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
178 "base point multiplications", (double)clck/CLOCKS_PER_SEC);
179 } else if (type == TIMING_RAND_PT) {
180 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
181 "random point multiplications", (double)clck/CLOCKS_PER_SEC);
182 } else if (type == TIMING_SIMUL) {
183 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
184 "s*P+t*Q operations", (double)clck/CLOCKS_PER_SEC);
185 }
186 fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
187
188 EC_POINT_free(P);
189 BN_free(s);
190 for (i = 0; i < 10; i++)
191 {
192 BN_free(r[i]);
193 if (type != TIMING_BASE_PT) BN_free(r0[i]);
194 }
195 }
196 #endif
197
prime_field_tests()198 void prime_field_tests()
199 {
200 BN_CTX *ctx = NULL;
201 BIGNUM *p, *a, *b;
202 EC_GROUP *group;
203 EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
204 EC_POINT *P, *Q, *R;
205 BIGNUM *x, *y, *z;
206 unsigned char buf[100];
207 size_t i, len;
208 int k;
209
210 #if 1 /* optional */
211 ctx = BN_CTX_new();
212 if (!ctx) ABORT;
213 #endif
214
215 p = BN_new();
216 a = BN_new();
217 b = BN_new();
218 if (!p || !a || !b) ABORT;
219
220 if (!BN_hex2bn(&p, "17")) ABORT;
221 if (!BN_hex2bn(&a, "1")) ABORT;
222 if (!BN_hex2bn(&b, "1")) ABORT;
223
224 group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
225 * so that the library gets to choose the EC_METHOD */
226 if (!group) ABORT;
227
228 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
229
230 {
231 EC_GROUP *tmp;
232 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
233 if (!tmp) ABORT;
234 if (!EC_GROUP_copy(tmp, group)) ABORT;
235 EC_GROUP_free(group);
236 group = tmp;
237 }
238
239 if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;
240
241 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
242 BN_print_fp(stdout, p);
243 fprintf(stdout, ")\n a = 0x");
244 BN_print_fp(stdout, a);
245 fprintf(stdout, "\n b = 0x");
246 BN_print_fp(stdout, b);
247 fprintf(stdout, "\n");
248
249 P = EC_POINT_new(group);
250 Q = EC_POINT_new(group);
251 R = EC_POINT_new(group);
252 if (!P || !Q || !R) ABORT;
253
254 if (!EC_POINT_set_to_infinity(group, P)) ABORT;
255 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
256
257 buf[0] = 0;
258 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
259
260 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
261 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
262
263 x = BN_new();
264 y = BN_new();
265 z = BN_new();
266 if (!x || !y || !z) ABORT;
267
268 if (!BN_hex2bn(&x, "D")) ABORT;
269 if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
270 if (!EC_POINT_is_on_curve(group, Q, ctx))
271 {
272 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
273 fprintf(stderr, "Point is not on curve: x = 0x");
274 BN_print_fp(stderr, x);
275 fprintf(stderr, ", y = 0x");
276 BN_print_fp(stderr, y);
277 fprintf(stderr, "\n");
278 ABORT;
279 }
280
281 fprintf(stdout, "A cyclic subgroup:\n");
282 k = 100;
283 do
284 {
285 if (k-- == 0) ABORT;
286
287 if (EC_POINT_is_at_infinity(group, P))
288 fprintf(stdout, " point at infinity\n");
289 else
290 {
291 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
292
293 fprintf(stdout, " x = 0x");
294 BN_print_fp(stdout, x);
295 fprintf(stdout, ", y = 0x");
296 BN_print_fp(stdout, y);
297 fprintf(stdout, "\n");
298 }
299
300 if (!EC_POINT_copy(R, P)) ABORT;
301 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
302
303 #if 0 /* optional */
304 {
305 EC_POINT *points[3];
306
307 points[0] = R;
308 points[1] = Q;
309 points[2] = P;
310 if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
311 }
312 #endif
313
314 }
315 while (!EC_POINT_is_at_infinity(group, P));
316
317 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
318 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
319
320 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
321 if (len == 0) ABORT;
322 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
323 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
324 fprintf(stdout, "Generator as octect string, compressed form:\n ");
325 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
326
327 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
328 if (len == 0) ABORT;
329 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
330 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
331 fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n ");
332 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
333
334 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
335 if (len == 0) ABORT;
336 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
337 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
338 fprintf(stdout, "\nGenerator as octect string, hybrid form:\n ");
339 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
340
341 if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
342 fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
343 BN_print_fp(stdout, x);
344 fprintf(stdout, ", Y = 0x");
345 BN_print_fp(stdout, y);
346 fprintf(stdout, ", Z = 0x");
347 BN_print_fp(stdout, z);
348 fprintf(stdout, "\n");
349
350 if (!EC_POINT_invert(group, P, ctx)) ABORT;
351 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
352
353
354 /* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000)
355 * -- not a NIST curve, but commonly used */
356
357 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) ABORT;
358 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
359 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) ABORT;
360 if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) ABORT;
361 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
362
363 if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82")) ABORT;
364 if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
365 if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
366 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
367 if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257")) ABORT;
368 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
369
370 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
371 fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x");
372 BN_print_fp(stdout, x);
373 fprintf(stdout, "\n y = 0x");
374 BN_print_fp(stdout, y);
375 fprintf(stdout, "\n");
376 /* G_y value taken from the standard: */
377 if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
378 if (0 != BN_cmp(y, z)) ABORT;
379
380 fprintf(stdout, "verify degree ...");
381 if (EC_GROUP_get_degree(group) != 160) ABORT;
382 fprintf(stdout, " ok\n");
383
384 fprintf(stdout, "verify group order ...");
385 fflush(stdout);
386 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
387 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
388 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
389 fprintf(stdout, ".");
390 fflush(stdout);
391 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
392 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
393 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
394 fprintf(stdout, " ok\n");
395
396 if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
397 if (!EC_GROUP_copy(P_160, group)) ABORT;
398
399
400 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
401
402 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
403 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
404 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT;
405 if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT;
406 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
407
408 if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT;
409 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
410 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
411 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT;
412 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
413
414 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
415 fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x");
416 BN_print_fp(stdout, x);
417 fprintf(stdout, "\n y = 0x");
418 BN_print_fp(stdout, y);
419 fprintf(stdout, "\n");
420 /* G_y value taken from the standard: */
421 if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT;
422 if (0 != BN_cmp(y, z)) ABORT;
423
424 fprintf(stdout, "verify degree ...");
425 if (EC_GROUP_get_degree(group) != 192) ABORT;
426 fprintf(stdout, " ok\n");
427
428 fprintf(stdout, "verify group order ...");
429 fflush(stdout);
430 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
431 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
432 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
433 fprintf(stdout, ".");
434 fflush(stdout);
435 #if 0
436 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
437 #endif
438 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
439 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
440 fprintf(stdout, " ok\n");
441
442 if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
443 if (!EC_GROUP_copy(P_192, group)) ABORT;
444
445
446 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
447
448 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
449 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
450 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
451 if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
452 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
453
454 if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
455 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
456 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
457 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
458 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
459
460 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
461 fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x");
462 BN_print_fp(stdout, x);
463 fprintf(stdout, "\n y = 0x");
464 BN_print_fp(stdout, y);
465 fprintf(stdout, "\n");
466 /* G_y value taken from the standard: */
467 if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
468 if (0 != BN_cmp(y, z)) ABORT;
469
470 fprintf(stdout, "verify degree ...");
471 if (EC_GROUP_get_degree(group) != 224) ABORT;
472 fprintf(stdout, " ok\n");
473
474 fprintf(stdout, "verify group order ...");
475 fflush(stdout);
476 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
477 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
478 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
479 fprintf(stdout, ".");
480 fflush(stdout);
481 #if 0
482 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
483 #endif
484 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
485 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
486 fprintf(stdout, " ok\n");
487
488 if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
489 if (!EC_GROUP_copy(P_224, group)) ABORT;
490
491
492 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
493
494 if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
495 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
496 if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
497 if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT;
498 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
499
500 if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT;
501 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
502 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
503 if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
504 "84F3B9CAC2FC632551")) ABORT;
505 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
506
507 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
508 fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x");
509 BN_print_fp(stdout, x);
510 fprintf(stdout, "\n y = 0x");
511 BN_print_fp(stdout, y);
512 fprintf(stdout, "\n");
513 /* G_y value taken from the standard: */
514 if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT;
515 if (0 != BN_cmp(y, z)) ABORT;
516
517 fprintf(stdout, "verify degree ...");
518 if (EC_GROUP_get_degree(group) != 256) ABORT;
519 fprintf(stdout, " ok\n");
520
521 fprintf(stdout, "verify group order ...");
522 fflush(stdout);
523 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
524 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
525 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
526 fprintf(stdout, ".");
527 fflush(stdout);
528 #if 0
529 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
530 #endif
531 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
532 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
533 fprintf(stdout, " ok\n");
534
535 if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
536 if (!EC_GROUP_copy(P_256, group)) ABORT;
537
538
539 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
540
541 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
542 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT;
543 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
544 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
545 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT;
546 if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
547 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT;
548 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
549
550 if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
551 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
552 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
553 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
554 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
555 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT;
556 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
557
558 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
559 fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x");
560 BN_print_fp(stdout, x);
561 fprintf(stdout, "\n y = 0x");
562 BN_print_fp(stdout, y);
563 fprintf(stdout, "\n");
564 /* G_y value taken from the standard: */
565 if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
566 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT;
567 if (0 != BN_cmp(y, z)) ABORT;
568
569 fprintf(stdout, "verify degree ...");
570 if (EC_GROUP_get_degree(group) != 384) ABORT;
571 fprintf(stdout, " ok\n");
572
573 fprintf(stdout, "verify group order ...");
574 fflush(stdout);
575 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
576 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
577 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
578 fprintf(stdout, ".");
579 fflush(stdout);
580 #if 0
581 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
582 #endif
583 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
584 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
585 fprintf(stdout, " ok\n");
586
587 if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
588 if (!EC_GROUP_copy(P_384, group)) ABORT;
589
590
591 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
592
593 if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
594 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
595 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
596 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
597 if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
598 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
599 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
600 if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
601 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
602 "DF883D2C34F1EF451FD46B503F00")) ABORT;
603 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
604
605 if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
606 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
607 "3C1856A429BF97E7E31C2E5BD66")) ABORT;
608 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
609 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
610 if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
611 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
612 "C9B8899C47AEBB6FB71E91386409")) ABORT;
613 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
614
615 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
616 fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x");
617 BN_print_fp(stdout, x);
618 fprintf(stdout, "\n y = 0x");
619 BN_print_fp(stdout, y);
620 fprintf(stdout, "\n");
621 /* G_y value taken from the standard: */
622 if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
623 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
624 "7086A272C24088BE94769FD16650")) ABORT;
625 if (0 != BN_cmp(y, z)) ABORT;
626
627 fprintf(stdout, "verify degree ...");
628 if (EC_GROUP_get_degree(group) != 521) ABORT;
629 fprintf(stdout, " ok\n");
630
631 fprintf(stdout, "verify group order ...");
632 fflush(stdout);
633 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
634 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
635 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
636 fprintf(stdout, ".");
637 fflush(stdout);
638 #if 0
639 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
640 #endif
641 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
642 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
643 fprintf(stdout, " ok\n");
644
645 if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
646 if (!EC_GROUP_copy(P_521, group)) ABORT;
647
648
649 /* more tests using the last curve */
650
651 if (!EC_POINT_copy(Q, P)) ABORT;
652 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
653 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
654 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
655 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
656
657 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
658 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
659 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
660
661 {
662 const EC_POINT *points[3];
663 const BIGNUM *scalars[3];
664
665 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
666 points[0] = Q;
667 points[1] = Q;
668 points[2] = Q;
669
670 if (!BN_add(y, z, BN_value_one())) ABORT;
671 if (BN_is_odd(y)) ABORT;
672 if (!BN_rshift1(y, y)) ABORT;
673 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
674 scalars[1] = y;
675
676 fprintf(stdout, "combined multiplication ...");
677 fflush(stdout);
678
679 /* z is still the group order */
680 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
681 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
682 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
683 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
684
685 fprintf(stdout, ".");
686 fflush(stdout);
687
688 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
689 if (!BN_add(z, z, y)) ABORT;
690 BN_set_negative(z, 1);
691 scalars[0] = y;
692 scalars[1] = z; /* z = -(order + y) */
693
694 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
695 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
696
697 fprintf(stdout, ".");
698 fflush(stdout);
699
700 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
701 if (!BN_add(z, x, y)) ABORT;
702 BN_set_negative(z, 1);
703 scalars[0] = x;
704 scalars[1] = y;
705 scalars[2] = z; /* z = -(x+y) */
706
707 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
708 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
709
710 fprintf(stdout, " ok\n\n");
711 }
712
713
714 #if 0
715 timings(P_160, TIMING_BASE_PT, ctx);
716 timings(P_160, TIMING_RAND_PT, ctx);
717 timings(P_160, TIMING_SIMUL, ctx);
718 timings(P_192, TIMING_BASE_PT, ctx);
719 timings(P_192, TIMING_RAND_PT, ctx);
720 timings(P_192, TIMING_SIMUL, ctx);
721 timings(P_224, TIMING_BASE_PT, ctx);
722 timings(P_224, TIMING_RAND_PT, ctx);
723 timings(P_224, TIMING_SIMUL, ctx);
724 timings(P_256, TIMING_BASE_PT, ctx);
725 timings(P_256, TIMING_RAND_PT, ctx);
726 timings(P_256, TIMING_SIMUL, ctx);
727 timings(P_384, TIMING_BASE_PT, ctx);
728 timings(P_384, TIMING_RAND_PT, ctx);
729 timings(P_384, TIMING_SIMUL, ctx);
730 timings(P_521, TIMING_BASE_PT, ctx);
731 timings(P_521, TIMING_RAND_PT, ctx);
732 timings(P_521, TIMING_SIMUL, ctx);
733 #endif
734
735
736 if (ctx)
737 BN_CTX_free(ctx);
738 BN_free(p); BN_free(a); BN_free(b);
739 EC_GROUP_free(group);
740 EC_POINT_free(P);
741 EC_POINT_free(Q);
742 EC_POINT_free(R);
743 BN_free(x); BN_free(y); BN_free(z);
744
745 if (P_160) EC_GROUP_free(P_160);
746 if (P_192) EC_GROUP_free(P_192);
747 if (P_224) EC_GROUP_free(P_224);
748 if (P_256) EC_GROUP_free(P_256);
749 if (P_384) EC_GROUP_free(P_384);
750 if (P_521) EC_GROUP_free(P_521);
751
752 }
753
754 /* Change test based on whether binary point compression is enabled or not. */
755 #ifdef OPENSSL_EC_BIN_PT_COMP
756 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
757 if (!BN_hex2bn(&x, _x)) ABORT; \
758 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
759 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
760 if (!BN_hex2bn(&z, _order)) ABORT; \
761 if (!BN_hex2bn(&cof, _cof)) ABORT; \
762 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
763 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
764 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
765 BN_print_fp(stdout, x); \
766 fprintf(stdout, "\n y = 0x"); \
767 BN_print_fp(stdout, y); \
768 fprintf(stdout, "\n"); \
769 /* G_y value taken from the standard: */ \
770 if (!BN_hex2bn(&z, _y)) ABORT; \
771 if (0 != BN_cmp(y, z)) ABORT;
772 #else
773 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
774 if (!BN_hex2bn(&x, _x)) ABORT; \
775 if (!BN_hex2bn(&y, _y)) ABORT; \
776 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
777 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
778 if (!BN_hex2bn(&z, _order)) ABORT; \
779 if (!BN_hex2bn(&cof, _cof)) ABORT; \
780 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
781 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
782 BN_print_fp(stdout, x); \
783 fprintf(stdout, "\n y = 0x"); \
784 BN_print_fp(stdout, y); \
785 fprintf(stdout, "\n");
786 #endif
787
788 #define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
789 if (!BN_hex2bn(&p, _p)) ABORT; \
790 if (!BN_hex2bn(&a, _a)) ABORT; \
791 if (!BN_hex2bn(&b, _b)) ABORT; \
792 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
793 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
794 fprintf(stdout, "verify degree ..."); \
795 if (EC_GROUP_get_degree(group) != _degree) ABORT; \
796 fprintf(stdout, " ok\n"); \
797 fprintf(stdout, "verify group order ..."); \
798 fflush(stdout); \
799 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; \
800 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \
801 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \
802 fprintf(stdout, "."); \
803 fflush(stdout); \
804 /* if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; */ \
805 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \
806 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \
807 fprintf(stdout, " ok\n"); \
808 if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \
809 if (!EC_GROUP_copy(_variable, group)) ABORT;
810
char2_field_tests()811 void char2_field_tests()
812 {
813 BN_CTX *ctx = NULL;
814 BIGNUM *p, *a, *b;
815 EC_GROUP *group;
816 EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = NULL, *C2_K571 = NULL;
817 EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = NULL, *C2_B571 = NULL;
818 EC_POINT *P, *Q, *R;
819 BIGNUM *x, *y, *z, *cof;
820 unsigned char buf[100];
821 size_t i, len;
822 int k;
823
824 #if 1 /* optional */
825 ctx = BN_CTX_new();
826 if (!ctx) ABORT;
827 #endif
828
829 p = BN_new();
830 a = BN_new();
831 b = BN_new();
832 if (!p || !a || !b) ABORT;
833
834 if (!BN_hex2bn(&p, "13")) ABORT;
835 if (!BN_hex2bn(&a, "3")) ABORT;
836 if (!BN_hex2bn(&b, "1")) ABORT;
837
838 group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m
839 * so that the library gets to choose the EC_METHOD */
840 if (!group) ABORT;
841 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT;
842
843 {
844 EC_GROUP *tmp;
845 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
846 if (!tmp) ABORT;
847 if (!EC_GROUP_copy(tmp, group)) ABORT;
848 EC_GROUP_free(group);
849 group = tmp;
850 }
851
852 if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT;
853
854 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x");
855 BN_print_fp(stdout, p);
856 fprintf(stdout, ")\n a = 0x");
857 BN_print_fp(stdout, a);
858 fprintf(stdout, "\n b = 0x");
859 BN_print_fp(stdout, b);
860 fprintf(stdout, "\n(0x... means binary polynomial)\n");
861
862 P = EC_POINT_new(group);
863 Q = EC_POINT_new(group);
864 R = EC_POINT_new(group);
865 if (!P || !Q || !R) ABORT;
866
867 if (!EC_POINT_set_to_infinity(group, P)) ABORT;
868 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
869
870 buf[0] = 0;
871 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
872
873 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
874 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
875
876 x = BN_new();
877 y = BN_new();
878 z = BN_new();
879 cof = BN_new();
880 if (!x || !y || !z || !cof) ABORT;
881
882 if (!BN_hex2bn(&x, "6")) ABORT;
883 /* Change test based on whether binary point compression is enabled or not. */
884 #ifdef OPENSSL_EC_BIN_PT_COMP
885 if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT;
886 #else
887 if (!BN_hex2bn(&y, "8")) ABORT;
888 if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
889 #endif
890 if (!EC_POINT_is_on_curve(group, Q, ctx))
891 {
892 /* Change test based on whether binary point compression is enabled or not. */
893 #ifdef OPENSSL_EC_BIN_PT_COMP
894 if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
895 #endif
896 fprintf(stderr, "Point is not on curve: x = 0x");
897 BN_print_fp(stderr, x);
898 fprintf(stderr, ", y = 0x");
899 BN_print_fp(stderr, y);
900 fprintf(stderr, "\n");
901 ABORT;
902 }
903
904 fprintf(stdout, "A cyclic subgroup:\n");
905 k = 100;
906 do
907 {
908 if (k-- == 0) ABORT;
909
910 if (EC_POINT_is_at_infinity(group, P))
911 fprintf(stdout, " point at infinity\n");
912 else
913 {
914 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT;
915
916 fprintf(stdout, " x = 0x");
917 BN_print_fp(stdout, x);
918 fprintf(stdout, ", y = 0x");
919 BN_print_fp(stdout, y);
920 fprintf(stdout, "\n");
921 }
922
923 if (!EC_POINT_copy(R, P)) ABORT;
924 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
925 }
926 while (!EC_POINT_is_at_infinity(group, P));
927
928 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
929 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
930
931 /* Change test based on whether binary point compression is enabled or not. */
932 #ifdef OPENSSL_EC_BIN_PT_COMP
933 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
934 if (len == 0) ABORT;
935 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
936 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
937 fprintf(stdout, "Generator as octet string, compressed form:\n ");
938 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
939 #endif
940
941 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
942 if (len == 0) ABORT;
943 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
944 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
945 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n ");
946 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
947
948 /* Change test based on whether binary point compression is enabled or not. */
949 #ifdef OPENSSL_EC_BIN_PT_COMP
950 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
951 if (len == 0) ABORT;
952 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
953 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
954 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n ");
955 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
956 #endif
957
958 fprintf(stdout, "\n");
959
960 if (!EC_POINT_invert(group, P, ctx)) ABORT;
961 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
962
963
964 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
965 CHAR2_CURVE_TEST
966 (
967 "NIST curve K-163",
968 "0800000000000000000000000000000000000000C9",
969 "1",
970 "1",
971 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
972 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
973 1,
974 "04000000000000000000020108A2E0CC0D99F8A5EF",
975 "2",
976 163,
977 C2_K163
978 );
979
980 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
981 CHAR2_CURVE_TEST
982 (
983 "NIST curve B-163",
984 "0800000000000000000000000000000000000000C9",
985 "1",
986 "020A601907B8C953CA1481EB10512F78744A3205FD",
987 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
988 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
989 1,
990 "040000000000000000000292FE77E70C12A4234C33",
991 "2",
992 163,
993 C2_B163
994 );
995
996 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
997 CHAR2_CURVE_TEST
998 (
999 "NIST curve K-233",
1000 "020000000000000000000000000000000000000004000000000000000001",
1001 "0",
1002 "1",
1003 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
1004 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
1005 0,
1006 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
1007 "4",
1008 233,
1009 C2_K233
1010 );
1011
1012 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
1013 CHAR2_CURVE_TEST
1014 (
1015 "NIST curve B-233",
1016 "020000000000000000000000000000000000000004000000000000000001",
1017 "000000000000000000000000000000000000000000000000000000000001",
1018 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
1019 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
1020 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
1021 1,
1022 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
1023 "2",
1024 233,
1025 C2_B233
1026 );
1027
1028 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
1029 CHAR2_CURVE_TEST
1030 (
1031 "NIST curve K-283",
1032 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1033 "0",
1034 "1",
1035 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
1036 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
1037 0,
1038 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
1039 "4",
1040 283,
1041 C2_K283
1042 );
1043
1044 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
1045 CHAR2_CURVE_TEST
1046 (
1047 "NIST curve B-283",
1048 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1049 "000000000000000000000000000000000000000000000000000000000000000000000001",
1050 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
1051 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
1052 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1053 1,
1054 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
1055 "2",
1056 283,
1057 C2_B283
1058 );
1059
1060 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
1061 CHAR2_CURVE_TEST
1062 (
1063 "NIST curve K-409",
1064 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1065 "0",
1066 "1",
1067 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
1068 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1069 1,
1070 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
1071 "4",
1072 409,
1073 C2_K409
1074 );
1075
1076 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
1077 CHAR2_CURVE_TEST
1078 (
1079 "NIST curve B-409",
1080 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1081 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1082 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
1083 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
1084 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1085 1,
1086 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
1087 "2",
1088 409,
1089 C2_B409
1090 );
1091
1092 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
1093 CHAR2_CURVE_TEST
1094 (
1095 "NIST curve K-571",
1096 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1097 "0",
1098 "1",
1099 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1100 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1101 0,
1102 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1103 "4",
1104 571,
1105 C2_K571
1106 );
1107
1108 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
1109 CHAR2_CURVE_TEST
1110 (
1111 "NIST curve B-571",
1112 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1113 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1114 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1115 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1116 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1117 1,
1118 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1119 "2",
1120 571,
1121 C2_B571
1122 );
1123
1124 /* more tests using the last curve */
1125
1126 if (!EC_POINT_copy(Q, P)) ABORT;
1127 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
1128 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
1129 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
1130 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
1131
1132 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
1133 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
1134 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
1135
1136 {
1137 const EC_POINT *points[3];
1138 const BIGNUM *scalars[3];
1139
1140 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
1141 points[0] = Q;
1142 points[1] = Q;
1143 points[2] = Q;
1144
1145 if (!BN_add(y, z, BN_value_one())) ABORT;
1146 if (BN_is_odd(y)) ABORT;
1147 if (!BN_rshift1(y, y)) ABORT;
1148 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
1149 scalars[1] = y;
1150
1151 fprintf(stdout, "combined multiplication ...");
1152 fflush(stdout);
1153
1154 /* z is still the group order */
1155 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
1156 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
1157 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
1158 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
1159
1160 fprintf(stdout, ".");
1161 fflush(stdout);
1162
1163 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
1164 if (!BN_add(z, z, y)) ABORT;
1165 BN_set_negative(z, 1);
1166 scalars[0] = y;
1167 scalars[1] = z; /* z = -(order + y) */
1168
1169 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
1170 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1171
1172 fprintf(stdout, ".");
1173 fflush(stdout);
1174
1175 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
1176 if (!BN_add(z, x, y)) ABORT;
1177 BN_set_negative(z, 1);
1178 scalars[0] = x;
1179 scalars[1] = y;
1180 scalars[2] = z; /* z = -(x+y) */
1181
1182 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
1183 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1184
1185 fprintf(stdout, " ok\n\n");
1186 }
1187
1188
1189 #if 0
1190 timings(C2_K163, TIMING_BASE_PT, ctx);
1191 timings(C2_K163, TIMING_RAND_PT, ctx);
1192 timings(C2_K163, TIMING_SIMUL, ctx);
1193 timings(C2_B163, TIMING_BASE_PT, ctx);
1194 timings(C2_B163, TIMING_RAND_PT, ctx);
1195 timings(C2_B163, TIMING_SIMUL, ctx);
1196 timings(C2_K233, TIMING_BASE_PT, ctx);
1197 timings(C2_K233, TIMING_RAND_PT, ctx);
1198 timings(C2_K233, TIMING_SIMUL, ctx);
1199 timings(C2_B233, TIMING_BASE_PT, ctx);
1200 timings(C2_B233, TIMING_RAND_PT, ctx);
1201 timings(C2_B233, TIMING_SIMUL, ctx);
1202 timings(C2_K283, TIMING_BASE_PT, ctx);
1203 timings(C2_K283, TIMING_RAND_PT, ctx);
1204 timings(C2_K283, TIMING_SIMUL, ctx);
1205 timings(C2_B283, TIMING_BASE_PT, ctx);
1206 timings(C2_B283, TIMING_RAND_PT, ctx);
1207 timings(C2_B283, TIMING_SIMUL, ctx);
1208 timings(C2_K409, TIMING_BASE_PT, ctx);
1209 timings(C2_K409, TIMING_RAND_PT, ctx);
1210 timings(C2_K409, TIMING_SIMUL, ctx);
1211 timings(C2_B409, TIMING_BASE_PT, ctx);
1212 timings(C2_B409, TIMING_RAND_PT, ctx);
1213 timings(C2_B409, TIMING_SIMUL, ctx);
1214 timings(C2_K571, TIMING_BASE_PT, ctx);
1215 timings(C2_K571, TIMING_RAND_PT, ctx);
1216 timings(C2_K571, TIMING_SIMUL, ctx);
1217 timings(C2_B571, TIMING_BASE_PT, ctx);
1218 timings(C2_B571, TIMING_RAND_PT, ctx);
1219 timings(C2_B571, TIMING_SIMUL, ctx);
1220 #endif
1221
1222
1223 if (ctx)
1224 BN_CTX_free(ctx);
1225 BN_free(p); BN_free(a); BN_free(b);
1226 EC_GROUP_free(group);
1227 EC_POINT_free(P);
1228 EC_POINT_free(Q);
1229 EC_POINT_free(R);
1230 BN_free(x); BN_free(y); BN_free(z); BN_free(cof);
1231
1232 if (C2_K163) EC_GROUP_free(C2_K163);
1233 if (C2_B163) EC_GROUP_free(C2_B163);
1234 if (C2_K233) EC_GROUP_free(C2_K233);
1235 if (C2_B233) EC_GROUP_free(C2_B233);
1236 if (C2_K283) EC_GROUP_free(C2_K283);
1237 if (C2_B283) EC_GROUP_free(C2_B283);
1238 if (C2_K409) EC_GROUP_free(C2_K409);
1239 if (C2_B409) EC_GROUP_free(C2_B409);
1240 if (C2_K571) EC_GROUP_free(C2_K571);
1241 if (C2_B571) EC_GROUP_free(C2_B571);
1242
1243 }
1244
internal_curve_test(void)1245 void internal_curve_test(void)
1246 {
1247 EC_builtin_curve *curves = NULL;
1248 size_t crv_len = 0, n = 0;
1249 int ok = 1;
1250
1251 crv_len = EC_get_builtin_curves(NULL, 0);
1252
1253 curves = OPENSSL_malloc(sizeof(EC_builtin_curve) * crv_len);
1254
1255 if (curves == NULL)
1256 return;
1257
1258 if (!EC_get_builtin_curves(curves, crv_len))
1259 {
1260 OPENSSL_free(curves);
1261 return;
1262 }
1263
1264 fprintf(stdout, "testing internal curves: ");
1265
1266 for (n = 0; n < crv_len; n++)
1267 {
1268 EC_GROUP *group = NULL;
1269 int nid = curves[n].nid;
1270 if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL)
1271 {
1272 ok = 0;
1273 fprintf(stdout, "\nEC_GROUP_new_curve_name() failed with"
1274 " curve %s\n", OBJ_nid2sn(nid));
1275 /* try next curve */
1276 continue;
1277 }
1278 if (!EC_GROUP_check(group, NULL))
1279 {
1280 ok = 0;
1281 fprintf(stdout, "\nEC_GROUP_check() failed with"
1282 " curve %s\n", OBJ_nid2sn(nid));
1283 EC_GROUP_free(group);
1284 /* try the next curve */
1285 continue;
1286 }
1287 fprintf(stdout, ".");
1288 fflush(stdout);
1289 EC_GROUP_free(group);
1290 }
1291 if (ok)
1292 fprintf(stdout, " ok\n");
1293 else
1294 fprintf(stdout, " failed\n");
1295 OPENSSL_free(curves);
1296 return;
1297 }
1298
1299 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
1300
main(int argc,char * argv[])1301 int main(int argc, char *argv[])
1302 {
1303
1304 /* enable memory leak checking unless explicitly disabled */
1305 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
1306 {
1307 CRYPTO_malloc_debug_init();
1308 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL);
1309 }
1310 else
1311 {
1312 /* OPENSSL_DEBUG_MEMORY=off */
1313 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
1314 }
1315 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
1316 ERR_load_crypto_strings();
1317
1318 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
1319
1320 prime_field_tests();
1321 puts("");
1322 char2_field_tests();
1323 /* test the internal curves */
1324 internal_curve_test();
1325
1326 #ifndef OPENSSL_NO_ENGINE
1327 ENGINE_cleanup();
1328 #endif
1329 CRYPTO_cleanup_all_ex_data();
1330 ERR_free_strings();
1331 ERR_remove_state(0);
1332 CRYPTO_mem_leaks_fp(stderr);
1333
1334 return 0;
1335 }
1336 #endif
1337