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1/* crypto/ec/ectest.c */
2/* ====================================================================
3 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 *
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 *
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in
14 * the documentation and/or other materials provided with the
15 * distribution.
16 *
17 * 3. All advertising materials mentioning features or use of this
18 * software must display the following acknowledgment:
19 * "This product includes software developed by the OpenSSL Project
20 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
21 *
22 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
23 * endorse or promote products derived from this software without
24 * prior written permission. For written permission, please contact
25 * openssl-core@openssl.org.
26 *
27 * 5. Products derived from this software may not be called "OpenSSL"
28 * nor may "OpenSSL" appear in their names without prior written
29 * permission of the OpenSSL Project.
30 *
31 * 6. Redistributions of any form whatsoever must retain the following
32 * acknowledgment:
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
35 *
36 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
37 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
38 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
39 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
40 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
41 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
42 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
43 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
44 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
45 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
46 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
47 * OF THE POSSIBILITY OF SUCH DAMAGE.
48 * ====================================================================
49 *
50 * This product includes cryptographic software written by Eric Young
51 * (eay@cryptsoft.com). This product includes software written by Tim
52 * Hudson (tjh@cryptsoft.com).
53 *
54 */
55
56#include <stdio.h>
57#include <stdlib.h>
58#ifdef FLAT_INC
59#include "e_os.h"
60#else
61#include "../e_os.h"
62#endif
63#include <string.h>
64#include <time.h>
65
66
67#ifdef OPENSSL_NO_EC
68int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; }
69#else
70
71
72#include <openssl/ec.h>
73#ifndef OPENSSL_NO_ENGINE
74#include <openssl/engine.h>
75#endif
76#include <openssl/err.h>
77
78#define ABORT do { \
79 fflush(stdout); \
80 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
81 ERR_print_errors_fp(stderr); \
82 EXIT(1); \
83} while (0)
84
85#if 0
86static void timings(EC_GROUP *group, int multi, BN_CTX *ctx)
87 {
88 clock_t clck;
89 int i, j;
90 BIGNUM *s, *s0;
91 EC_POINT *P;
92
93 s = BN_new();
94 s0 = BN_new();
95 if (s == NULL || s0 == NULL) ABORT;
96
97 if (!EC_GROUP_get_curve_GFp(group, s, NULL, NULL, ctx)) ABORT;
98 fprintf(stdout, "Timings for %d bit prime, ", (int)BN_num_bits(s));
99 if (!EC_GROUP_get_order(group, s, ctx)) ABORT;
100 fprintf(stdout, "%d bit scalars ", (int)BN_num_bits(s));
101 fflush(stdout);
102
103 P = EC_POINT_new(group);
104 if (P == NULL) ABORT;
105 EC_POINT_copy(P, EC_GROUP_get0_generator(group));
106
107 clck = clock();
108 for (i = 0; i < 10; i++)
109 {
110 if (!BN_pseudo_rand(s, BN_num_bits(s), 0, 0)) ABORT;
111 if (multi)
112 {
113 if (!BN_pseudo_rand(s0, BN_num_bits(s), 0, 0)) ABORT;
114 }
115 for (j = 0; j < 10; j++)
116 {
117 if (!EC_POINT_mul(group, P, s, multi ? P : NULL, multi ? s0 : NULL, ctx)) ABORT;
118 }
119 fprintf(stdout, ".");
120 fflush(stdout);
121 }
122 fprintf(stdout, "\n");
123
124 clck = clock() - clck;
125
126#ifdef CLOCKS_PER_SEC
127 /* "To determine the time in seconds, the value returned
128 * by the clock function should be divided by the value
129 * of the macro CLOCKS_PER_SEC."
130 * -- ISO/IEC 9899 */
131# define UNIT "s"
132#else
133 /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
134 * -- cc on NeXTstep/OpenStep */
135# define UNIT "units"
136# define CLOCKS_PER_SEC 1
137#endif
138
139 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
140 multi ? "s*P+t*Q operations" : "point multiplications",
141 (double)clck/CLOCKS_PER_SEC);
142 fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
143
144 EC_POINT_free(P);
145 BN_free(s);
146 BN_free(s0);
147 }
148#endif
149
150int main(int argc, char *argv[])
151 {
152 BN_CTX *ctx = NULL;
153 BIGNUM *p, *a, *b;
154 EC_GROUP *group;
155 EC_GROUP *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
156 EC_POINT *P, *Q, *R;
157 BIGNUM *x, *y, *z;
158 unsigned char buf[100];
159 size_t i, len;
160 int k;
161
162 /* enable memory leak checking unless explicitly disabled */
163 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
164 {
165 CRYPTO_malloc_debug_init();
166 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL);
167 }
168 else
169 {
170 /* OPENSSL_DEBUG_MEMORY=off */
171 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
172 }
173 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
174 ERR_load_crypto_strings();
175
176#if 1 /* optional */
177 ctx = BN_CTX_new();
178 if (!ctx) ABORT;
179#endif
180
181 p = BN_new();
182 a = BN_new();
183 b = BN_new();
184 if (!p || !a || !b) ABORT;
185
186 if (!BN_hex2bn(&p, "17")) ABORT;
187 if (!BN_hex2bn(&a, "1")) ABORT;
188 if (!BN_hex2bn(&b, "1")) ABORT;
189
190 group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
191 * so that the library gets to choose the EC_METHOD */
192 if (!group) ABORT;
193
194 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
195
196 {
197 EC_GROUP *tmp;
198 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
199 if (!tmp) ABORT;
200 if (!EC_GROUP_copy(tmp, group)) ABORT;
201 EC_GROUP_free(group);
202 group = tmp;
203 }
204
205 if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;
206
207 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
208 BN_print_fp(stdout, p);
209 fprintf(stdout, ")\n a = 0x");
210 BN_print_fp(stdout, a);
211 fprintf(stdout, "\n b = 0x");
212 BN_print_fp(stdout, b);
213 fprintf(stdout, "\n");
214
215 P = EC_POINT_new(group);
216 Q = EC_POINT_new(group);
217 R = EC_POINT_new(group);
218 if (!P || !Q || !R) ABORT;
219
220 if (!EC_POINT_set_to_infinity(group, P)) ABORT;
221 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
222
223 buf[0] = 0;
224 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
225
226 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
227 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
228
229 x = BN_new();
230 y = BN_new();
231 z = BN_new();
232 if (!x || !y || !z) ABORT;
233
234 if (!BN_hex2bn(&x, "D")) ABORT;
235 if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
236 if (!EC_POINT_is_on_curve(group, Q, ctx))
237 {
238 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
239 fprintf(stderr, "Point is not on curve: x = 0x");
240 BN_print_fp(stderr, x);
241 fprintf(stderr, ", y = 0x");
242 BN_print_fp(stderr, y);
243 fprintf(stderr, "\n");
244 ABORT;
245 }
246
247 fprintf(stdout, "A cyclic subgroup:\n");
248 k = 100;
249 do
250 {
251 if (k-- == 0) ABORT;
252
253 if (EC_POINT_is_at_infinity(group, P))
254 fprintf(stdout, " point at infinity\n");
255 else
256 {
257 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
258
259 fprintf(stdout, " x = 0x");
260 BN_print_fp(stdout, x);
261 fprintf(stdout, ", y = 0x");
262 BN_print_fp(stdout, y);
263 fprintf(stdout, "\n");
264 }
265
266 if (!EC_POINT_copy(R, P)) ABORT;
267 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
268
269#if 0 /* optional */
270 {
271 EC_POINT *points[3];
272
273 points[0] = R;
274 points[1] = Q;
275 points[2] = P;
276 if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
277 }
278#endif
279
280 }
281 while (!EC_POINT_is_at_infinity(group, P));
282
283 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
284 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
285
286 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
287 if (len == 0) ABORT;
288 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
289 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
290 fprintf(stdout, "Generator as octect string, compressed form:\n ");
291 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
292
293 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
294 if (len == 0) ABORT;
295 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
296 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
297 fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n ");
298 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
299
300 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
301 if (len == 0) ABORT;
302 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
303 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
304 fprintf(stdout, "\nGenerator as octect string, hybrid form:\n ");
305 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
306
307 if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
308 fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
309 BN_print_fp(stdout, x);
310 fprintf(stdout, ", Y = 0x");
311 BN_print_fp(stdout, y);
312 fprintf(stdout, ", Z = 0x");
313 BN_print_fp(stdout, z);
314 fprintf(stdout, "\n");
315
316 if (!EC_POINT_invert(group, P, ctx)) ABORT;
317 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
318
319
320 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
321
322 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
323 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
324 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT;
325 if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT;
326 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
327
328 if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT;
329 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
330 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
331 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT;
332 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
333
334 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
335 fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x");
336 BN_print_fp(stdout, x);
337 fprintf(stdout, "\n y = 0x");
338 BN_print_fp(stdout, y);
339 fprintf(stdout, "\n");
340 /* G_y value taken from the standard: */
341 if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT;
342 if (0 != BN_cmp(y, z)) ABORT;
343
344 fprintf(stdout, "verify group order ...");
345 fflush(stdout);
346 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
347 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
348 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
349 fprintf(stdout, ".");
350 fflush(stdout);
351 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
352 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
353 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
354 fprintf(stdout, " ok\n");
355
356 if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
357 if (!EC_GROUP_copy(P_192, group)) ABORT;
358
359
360 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
361
362 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
363 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
364 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
365 if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
366 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
367
368 if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
369 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
370 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
371 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
372 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
373
374 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
375 fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x");
376 BN_print_fp(stdout, x);
377 fprintf(stdout, "\n y = 0x");
378 BN_print_fp(stdout, y);
379 fprintf(stdout, "\n");
380 /* G_y value taken from the standard: */
381 if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
382 if (0 != BN_cmp(y, z)) ABORT;
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_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
397 if (!EC_GROUP_copy(P_224, group)) ABORT;
398
399
400 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
401
402 if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
403 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
404 if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
405 if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT;
406 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
407
408 if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) 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, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
412 "84F3B9CAC2FC632551")) ABORT;
413 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
414
415 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
416 fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x");
417 BN_print_fp(stdout, x);
418 fprintf(stdout, "\n y = 0x");
419 BN_print_fp(stdout, y);
420 fprintf(stdout, "\n");
421 /* G_y value taken from the standard: */
422 if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT;
423 if (0 != BN_cmp(y, z)) ABORT;
424
425 fprintf(stdout, "verify group order ...");
426 fflush(stdout);
427 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
428 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
429 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
430 fprintf(stdout, ".");
431 fflush(stdout);
432 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
433 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
434 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
435 fprintf(stdout, " ok\n");
436
437 if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
438 if (!EC_GROUP_copy(P_256, group)) ABORT;
439
440
441 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
442
443 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
444 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT;
445 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
446 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
447 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT;
448 if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
449 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT;
450 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
451
452 if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
453 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
454 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
455 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
456 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
457 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) 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-384 -- 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, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
468 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT;
469 if (0 != BN_cmp(y, z)) ABORT;
470
471 fprintf(stdout, "verify group order ...");
472 fflush(stdout);
473 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
474 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
475 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
476 fprintf(stdout, ".");
477 fflush(stdout);
478 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
479 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
480 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
481 fprintf(stdout, " ok\n");
482
483 if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
484 if (!EC_GROUP_copy(P_384, group)) ABORT;
485
486
487 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
488
489 if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
490 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
491 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
492 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
493 if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
494 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
495 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
496 if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
497 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
498 "DF883D2C34F1EF451FD46B503F00")) ABORT;
499 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
500
501 if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
502 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
503 "3C1856A429BF97E7E31C2E5BD66")) ABORT;
504 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
505 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
506 if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
507 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
508 "C9B8899C47AEBB6FB71E91386409")) ABORT;
509 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
510
511 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
512 fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x");
513 BN_print_fp(stdout, x);
514 fprintf(stdout, "\n y = 0x");
515 BN_print_fp(stdout, y);
516 fprintf(stdout, "\n");
517 /* G_y value taken from the standard: */
518 if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
519 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
520 "7086A272C24088BE94769FD16650")) ABORT;
521 if (0 != BN_cmp(y, z)) ABORT;
522
523 fprintf(stdout, "verify group order ...");
524 fflush(stdout);
525 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
526 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
527 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
528 fprintf(stdout, ".");
529 fflush(stdout);
530 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
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_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
536 if (!EC_GROUP_copy(P_521, group)) ABORT;
537
538
539 /* more tests using the last curve */
540
541 if (!EC_POINT_copy(Q, P)) ABORT;
542 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
543 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
544 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
545 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
546
547 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
548 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
549 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
550
551 {
552 const EC_POINT *points[3];
553 const BIGNUM *scalars[3];
554
555 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
556 points[0] = Q;
557 points[1] = Q;
558 points[2] = Q;
559
560 if (!BN_add(y, z, BN_value_one())) ABORT;
561 if (BN_is_odd(y)) ABORT;
562 if (!BN_rshift1(y, y)) ABORT;
563 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
564 scalars[1] = y;
565
566 fprintf(stdout, "combined multiplication ...");
567 fflush(stdout);
568
569 /* z is still the group order */
570 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
571 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
572 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
573 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
574
575 fprintf(stdout, ".");
576 fflush(stdout);
577
578 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
579 if (!BN_add(z, z, y)) ABORT;
580 z->neg = 1;
581 scalars[0] = y;
582 scalars[1] = z; /* z = -(order + y) */
583
584 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
585 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
586
587 fprintf(stdout, ".");
588 fflush(stdout);
589
590 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
591 if (!BN_add(z, x, y)) ABORT;
592 z->neg = 1;
593 scalars[0] = x;
594 scalars[1] = y;
595 scalars[2] = z; /* z = -(x+y) */
596
597 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
598 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
599
600 fprintf(stdout, " ok\n\n");
601 }
602
603
604#if 0
605 timings(P_192, 0, ctx);
606 timings(P_192, 1, ctx);
607 timings(P_224, 0, ctx);
608 timings(P_224, 1, ctx);
609 timings(P_256, 0, ctx);
610 timings(P_256, 1, ctx);
611 timings(P_384, 0, ctx);
612 timings(P_384, 1, ctx);
613 timings(P_521, 0, ctx);
614 timings(P_521, 1, ctx);
615#endif
616
617
618 if (ctx)
619 BN_CTX_free(ctx);
620 BN_free(p); BN_free(a); BN_free(b);
621 EC_GROUP_free(group);
622 EC_POINT_free(P);
623 EC_POINT_free(Q);
624 EC_POINT_free(R);
625 BN_free(x); BN_free(y); BN_free(z);
626
627 if (P_192) EC_GROUP_free(P_192);
628 if (P_224) EC_GROUP_free(P_224);
629 if (P_256) EC_GROUP_free(P_256);
630 if (P_384) EC_GROUP_free(P_384);
631 if (P_521) EC_GROUP_free(P_521);
632
633#ifndef OPENSSL_NO_ENGINE
634 ENGINE_cleanup();
635#endif
636 CRYPTO_cleanup_all_ex_data();
637 ERR_free_strings();
638 ERR_remove_state(0);
639 CRYPTO_mem_leaks_fp(stderr);
640
641 return 0;
642 }
643#endif
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-04-26 21:08:06 +0000