1 /* crypto/ec/ectest.c */
3 * Originally written by Bodo Moeller for the OpenSSL project.
5 /* ====================================================================
6 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
12 * 1. Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
34 * 6. Redistributions of any form whatsoever must retain the following
36 * "This product includes software developed by the OpenSSL Project
37 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
58 /* ====================================================================
59 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
61 * Portions of the attached software ("Contribution") are developed by
62 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
64 * The Contribution is licensed pursuant to the OpenSSL open source
65 * license provided above.
67 * The elliptic curve binary polynomial software is originally written by
68 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
84 int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; }
88 #include <openssl/ec.h>
89 #ifndef OPENSSL_NO_ENGINE
90 #include <openssl/engine.h>
92 #include <openssl/err.h>
93 #include <openssl/obj_mac.h>
94 #include <openssl/objects.h>
95 #include <openssl/rand.h>
99 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
100 ERR_print_errors_fp(stderr); \
104 void prime_field_tests(void);
105 void char2_field_tests(void);
106 void internal_curve_test(void);
108 #define TIMING_BASE_PT 0
109 #define TIMING_RAND_PT 1
110 #define TIMING_SIMUL 2
113 static void timings(EC_GROUP *group, int type, BN_CTX *ctx)
118 BIGNUM *r[10], *r0[10];
122 if (s == NULL) ABORT;
124 fprintf(stdout, "Timings for %d-bit field, ", EC_GROUP_get_degree(group));
125 if (!EC_GROUP_get_order(group, s, ctx)) ABORT;
126 fprintf(stdout, "%d-bit scalars ", (int)BN_num_bits(s));
129 P = EC_POINT_new(group);
130 if (P == NULL) ABORT;
131 EC_POINT_copy(P, EC_GROUP_get0_generator(group));
133 for (i = 0; i < 10; i++)
135 if ((r[i] = BN_new()) == NULL) ABORT;
136 if (!BN_pseudo_rand(r[i], BN_num_bits(s), 0, 0)) ABORT;
137 if (type != TIMING_BASE_PT)
139 if ((r0[i] = BN_new()) == NULL) ABORT;
140 if (!BN_pseudo_rand(r0[i], BN_num_bits(s), 0, 0)) ABORT;
145 for (i = 0; i < 10; i++)
147 for (j = 0; j < 10; j++)
149 if (!EC_POINT_mul(group, P, (type != TIMING_RAND_PT) ? r[i] : NULL,
150 (type != TIMING_BASE_PT) ? P : NULL, (type != TIMING_BASE_PT) ? r0[i] : NULL, ctx)) ABORT;
153 clck = clock() - clck;
155 fprintf(stdout, "\n");
157 #ifdef CLOCKS_PER_SEC
158 /* "To determine the time in seconds, the value returned
159 * by the clock function should be divided by the value
160 * of the macro CLOCKS_PER_SEC."
164 /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
165 * -- cc on NeXTstep/OpenStep */
166 # define UNIT "units"
167 # define CLOCKS_PER_SEC 1
170 if (type == TIMING_BASE_PT) {
171 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
172 "base point multiplications", (double)clck/CLOCKS_PER_SEC);
173 } else if (type == TIMING_RAND_PT) {
174 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
175 "random point multiplications", (double)clck/CLOCKS_PER_SEC);
176 } else if (type == TIMING_SIMUL) {
177 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
178 "s*P+t*Q operations", (double)clck/CLOCKS_PER_SEC);
180 fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
184 for (i = 0; i < 10; i++)
187 if (type != TIMING_BASE_PT) BN_free(r0[i]);
192 void prime_field_tests()
197 EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
200 unsigned char buf[100];
212 if (!p || !a || !b) ABORT;
214 if (!BN_hex2bn(&p, "17")) ABORT;
215 if (!BN_hex2bn(&a, "1")) ABORT;
216 if (!BN_hex2bn(&b, "1")) ABORT;
218 group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
219 * so that the library gets to choose the EC_METHOD */
222 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
226 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
228 if (!EC_GROUP_copy(tmp, group));
229 EC_GROUP_free(group);
233 if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;
235 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
236 BN_print_fp(stdout, p);
237 fprintf(stdout, ")\n a = 0x");
238 BN_print_fp(stdout, a);
239 fprintf(stdout, "\n b = 0x");
240 BN_print_fp(stdout, b);
241 fprintf(stdout, "\n");
243 P = EC_POINT_new(group);
244 Q = EC_POINT_new(group);
245 R = EC_POINT_new(group);
246 if (!P || !Q || !R) ABORT;
248 if (!EC_POINT_set_to_infinity(group, P)) ABORT;
249 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
252 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
254 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
255 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
260 if (!x || !y || !z) ABORT;
262 if (!BN_hex2bn(&x, "D")) ABORT;
263 if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
264 if (!EC_POINT_is_on_curve(group, Q, ctx))
266 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
267 fprintf(stderr, "Point is not on curve: x = 0x");
268 BN_print_fp(stderr, x);
269 fprintf(stderr, ", y = 0x");
270 BN_print_fp(stderr, y);
271 fprintf(stderr, "\n");
275 fprintf(stdout, "A cyclic subgroup:\n");
281 if (EC_POINT_is_at_infinity(group, P))
282 fprintf(stdout, " point at infinity\n");
285 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
287 fprintf(stdout, " x = 0x");
288 BN_print_fp(stdout, x);
289 fprintf(stdout, ", y = 0x");
290 BN_print_fp(stdout, y);
291 fprintf(stdout, "\n");
294 if (!EC_POINT_copy(R, P)) ABORT;
295 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
304 if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
309 while (!EC_POINT_is_at_infinity(group, P));
311 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
312 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
314 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
316 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
317 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
318 fprintf(stdout, "Generator as octect string, compressed form:\n ");
319 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
321 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
323 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
324 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
325 fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n ");
326 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
328 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
330 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
331 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
332 fprintf(stdout, "\nGenerator as octect string, hybrid form:\n ");
333 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
335 if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
336 fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
337 BN_print_fp(stdout, x);
338 fprintf(stdout, ", Y = 0x");
339 BN_print_fp(stdout, y);
340 fprintf(stdout, ", Z = 0x");
341 BN_print_fp(stdout, z);
342 fprintf(stdout, "\n");
344 if (!EC_POINT_invert(group, P, ctx)) ABORT;
345 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
348 /* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000)
349 * -- not a NIST curve, but commonly used */
351 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) ABORT;
352 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
353 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) ABORT;
354 if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) ABORT;
355 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
357 if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82")) ABORT;
358 if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
359 if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
360 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
361 if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257")) ABORT;
362 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
364 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
365 fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x");
366 BN_print_fp(stdout, x);
367 fprintf(stdout, "\n y = 0x");
368 BN_print_fp(stdout, y);
369 fprintf(stdout, "\n");
370 /* G_y value taken from the standard: */
371 if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
372 if (0 != BN_cmp(y, z)) ABORT;
374 fprintf(stdout, "verify degree ...");
375 if (EC_GROUP_get_degree(group) != 160) ABORT;
376 fprintf(stdout, " ok\n");
378 fprintf(stdout, "verify group order ...");
380 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
381 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
382 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
383 fprintf(stdout, ".");
385 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
386 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
387 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
388 fprintf(stdout, " ok\n");
390 if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
391 if (!EC_GROUP_copy(P_160, group)) ABORT;
394 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
396 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
397 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
398 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT;
399 if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT;
400 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
402 if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT;
403 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
404 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
405 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT;
406 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
408 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
409 fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x");
410 BN_print_fp(stdout, x);
411 fprintf(stdout, "\n y = 0x");
412 BN_print_fp(stdout, y);
413 fprintf(stdout, "\n");
414 /* G_y value taken from the standard: */
415 if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT;
416 if (0 != BN_cmp(y, z)) ABORT;
418 fprintf(stdout, "verify degree ...");
419 if (EC_GROUP_get_degree(group) != 192) ABORT;
420 fprintf(stdout, " ok\n");
422 fprintf(stdout, "verify group order ...");
424 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
425 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
426 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
427 fprintf(stdout, ".");
429 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
430 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
431 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
432 fprintf(stdout, " ok\n");
434 if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
435 if (!EC_GROUP_copy(P_192, group)) ABORT;
438 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
440 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
441 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
442 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
443 if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
444 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
446 if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
447 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
448 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
449 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
450 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
452 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
453 fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x");
454 BN_print_fp(stdout, x);
455 fprintf(stdout, "\n y = 0x");
456 BN_print_fp(stdout, y);
457 fprintf(stdout, "\n");
458 /* G_y value taken from the standard: */
459 if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
460 if (0 != BN_cmp(y, z)) ABORT;
462 fprintf(stdout, "verify degree ...");
463 if (EC_GROUP_get_degree(group) != 224) ABORT;
464 fprintf(stdout, " ok\n");
466 fprintf(stdout, "verify group order ...");
468 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
469 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
470 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
471 fprintf(stdout, ".");
473 if (!EC_GROUP_precompute_mult(group, 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, " ok\n");
478 if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
479 if (!EC_GROUP_copy(P_224, group)) ABORT;
482 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
484 if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
485 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
486 if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
487 if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT;
488 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
490 if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT;
491 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
492 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
493 if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
494 "84F3B9CAC2FC632551")) ABORT;
495 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
497 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
498 fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x");
499 BN_print_fp(stdout, x);
500 fprintf(stdout, "\n y = 0x");
501 BN_print_fp(stdout, y);
502 fprintf(stdout, "\n");
503 /* G_y value taken from the standard: */
504 if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT;
505 if (0 != BN_cmp(y, z)) ABORT;
507 fprintf(stdout, "verify degree ...");
508 if (EC_GROUP_get_degree(group) != 256) ABORT;
509 fprintf(stdout, " ok\n");
511 fprintf(stdout, "verify group order ...");
513 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
514 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
515 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
516 fprintf(stdout, ".");
518 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
519 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
520 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
521 fprintf(stdout, " ok\n");
523 if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
524 if (!EC_GROUP_copy(P_256, group)) ABORT;
527 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
529 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
530 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT;
531 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
532 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
533 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT;
534 if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
535 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT;
536 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
538 if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
539 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
540 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
541 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
542 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
543 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT;
544 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
546 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
547 fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x");
548 BN_print_fp(stdout, x);
549 fprintf(stdout, "\n y = 0x");
550 BN_print_fp(stdout, y);
551 fprintf(stdout, "\n");
552 /* G_y value taken from the standard: */
553 if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
554 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT;
555 if (0 != BN_cmp(y, z)) ABORT;
557 fprintf(stdout, "verify degree ...");
558 if (EC_GROUP_get_degree(group) != 384) ABORT;
559 fprintf(stdout, " ok\n");
561 fprintf(stdout, "verify group order ...");
563 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
564 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
565 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
566 fprintf(stdout, ".");
568 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
569 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
570 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
571 fprintf(stdout, " ok\n");
573 if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
574 if (!EC_GROUP_copy(P_384, group)) ABORT;
577 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
579 if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
580 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
581 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
582 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
583 if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
584 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
585 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
586 if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
587 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
588 "DF883D2C34F1EF451FD46B503F00")) ABORT;
589 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
591 if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
592 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
593 "3C1856A429BF97E7E31C2E5BD66")) ABORT;
594 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
595 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
596 if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
597 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
598 "C9B8899C47AEBB6FB71E91386409")) ABORT;
599 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
601 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
602 fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x");
603 BN_print_fp(stdout, x);
604 fprintf(stdout, "\n y = 0x");
605 BN_print_fp(stdout, y);
606 fprintf(stdout, "\n");
607 /* G_y value taken from the standard: */
608 if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
609 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
610 "7086A272C24088BE94769FD16650")) ABORT;
611 if (0 != BN_cmp(y, z)) ABORT;
613 fprintf(stdout, "verify degree ...");
614 if (EC_GROUP_get_degree(group) != 521) ABORT;
615 fprintf(stdout, " ok\n");
617 fprintf(stdout, "verify group order ...");
619 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
620 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
621 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
622 fprintf(stdout, ".");
624 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
625 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
626 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
627 fprintf(stdout, " ok\n");
629 if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
630 if (!EC_GROUP_copy(P_521, group)) ABORT;
633 /* more tests using the last curve */
635 if (!EC_POINT_copy(Q, P)) ABORT;
636 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
637 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
638 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
639 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
641 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
642 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
643 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
646 const EC_POINT *points[3];
647 const BIGNUM *scalars[3];
649 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
654 if (!BN_add(y, z, BN_value_one())) ABORT;
655 if (BN_is_odd(y)) ABORT;
656 if (!BN_rshift1(y, y)) ABORT;
657 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
660 fprintf(stdout, "combined multiplication ...");
663 /* z is still the group order */
664 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
665 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
666 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
667 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
669 fprintf(stdout, ".");
672 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
673 if (!BN_add(z, z, y)) ABORT;
676 scalars[1] = z; /* z = -(order + y) */
678 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
679 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
681 fprintf(stdout, ".");
684 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
685 if (!BN_add(z, x, y)) ABORT;
689 scalars[2] = z; /* z = -(x+y) */
691 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
692 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
694 fprintf(stdout, " ok\n\n");
699 timings(P_160, TIMING_BASE_PT, ctx);
700 timings(P_160, TIMING_RAND_PT, ctx);
701 timings(P_160, TIMING_SIMUL, ctx);
702 timings(P_192, TIMING_BASE_PT, ctx);
703 timings(P_192, TIMING_RAND_PT, ctx);
704 timings(P_192, TIMING_SIMUL, ctx);
705 timings(P_224, TIMING_BASE_PT, ctx);
706 timings(P_224, TIMING_RAND_PT, ctx);
707 timings(P_224, TIMING_SIMUL, ctx);
708 timings(P_256, TIMING_BASE_PT, ctx);
709 timings(P_256, TIMING_RAND_PT, ctx);
710 timings(P_256, TIMING_SIMUL, ctx);
711 timings(P_384, TIMING_BASE_PT, ctx);
712 timings(P_384, TIMING_RAND_PT, ctx);
713 timings(P_384, TIMING_SIMUL, ctx);
714 timings(P_521, TIMING_BASE_PT, ctx);
715 timings(P_521, TIMING_RAND_PT, ctx);
716 timings(P_521, TIMING_SIMUL, ctx);
722 BN_free(p); BN_free(a); BN_free(b);
723 EC_GROUP_free(group);
727 BN_free(x); BN_free(y); BN_free(z);
729 if (P_160) EC_GROUP_free(P_160);
730 if (P_192) EC_GROUP_free(P_192);
731 if (P_224) EC_GROUP_free(P_224);
732 if (P_256) EC_GROUP_free(P_256);
733 if (P_384) EC_GROUP_free(P_384);
734 if (P_521) EC_GROUP_free(P_521);
738 /* Change test based on whether binary point compression is enabled or not. */
739 #ifdef OPENSSL_EC_BIN_PT_COMP
740 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
741 if (!BN_hex2bn(&x, _x)) ABORT; \
742 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
743 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
744 if (!BN_hex2bn(&z, _order)) ABORT; \
745 if (!BN_hex2bn(&cof, _cof)) ABORT; \
746 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
747 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
748 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
749 BN_print_fp(stdout, x); \
750 fprintf(stdout, "\n y = 0x"); \
751 BN_print_fp(stdout, y); \
752 fprintf(stdout, "\n"); \
753 /* G_y value taken from the standard: */ \
754 if (!BN_hex2bn(&z, _y)) ABORT; \
755 if (0 != BN_cmp(y, z)) ABORT;
757 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
758 if (!BN_hex2bn(&x, _x)) ABORT; \
759 if (!BN_hex2bn(&y, _y)) ABORT; \
760 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
761 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
762 if (!BN_hex2bn(&z, _order)) ABORT; \
763 if (!BN_hex2bn(&cof, _cof)) ABORT; \
764 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
765 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
766 BN_print_fp(stdout, x); \
767 fprintf(stdout, "\n y = 0x"); \
768 BN_print_fp(stdout, y); \
769 fprintf(stdout, "\n");
772 #define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
773 if (!BN_hex2bn(&p, _p)) ABORT; \
774 if (!BN_hex2bn(&a, _a)) ABORT; \
775 if (!BN_hex2bn(&b, _b)) ABORT; \
776 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
777 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
778 fprintf(stdout, "verify degree ..."); \
779 if (EC_GROUP_get_degree(group) != _degree) ABORT; \
780 fprintf(stdout, " ok\n"); \
781 fprintf(stdout, "verify group order ..."); \
783 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; \
784 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \
785 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \
786 fprintf(stdout, "."); \
788 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; \
789 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \
790 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \
791 fprintf(stdout, " ok\n"); \
792 if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \
793 if (!EC_GROUP_copy(_variable, group)) ABORT;
795 void char2_field_tests()
800 EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = NULL, *C2_K571 = NULL;
801 EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = NULL, *C2_B571 = NULL;
803 BIGNUM *x, *y, *z, *cof;
804 unsigned char buf[100];
816 if (!p || !a || !b) ABORT;
818 if (!BN_hex2bn(&p, "13")) ABORT;
819 if (!BN_hex2bn(&a, "3")) ABORT;
820 if (!BN_hex2bn(&b, "1")) ABORT;
822 group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m
823 * so that the library gets to choose the EC_METHOD */
825 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT;
829 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
831 if (!EC_GROUP_copy(tmp, group));
832 EC_GROUP_free(group);
836 if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT;
838 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x");
839 BN_print_fp(stdout, p);
840 fprintf(stdout, ")\n a = 0x");
841 BN_print_fp(stdout, a);
842 fprintf(stdout, "\n b = 0x");
843 BN_print_fp(stdout, b);
844 fprintf(stdout, "\n(0x... means binary polynomial)\n");
846 P = EC_POINT_new(group);
847 Q = EC_POINT_new(group);
848 R = EC_POINT_new(group);
849 if (!P || !Q || !R) ABORT;
851 if (!EC_POINT_set_to_infinity(group, P)) ABORT;
852 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
855 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
857 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
858 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
864 if (!x || !y || !z || !cof) ABORT;
866 if (!BN_hex2bn(&x, "6")) ABORT;
867 /* Change test based on whether binary point compression is enabled or not. */
868 #ifdef OPENSSL_EC_BIN_PT_COMP
869 if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT;
871 if (!BN_hex2bn(&y, "8")) ABORT;
872 if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
874 if (!EC_POINT_is_on_curve(group, Q, ctx))
876 /* Change test based on whether binary point compression is enabled or not. */
877 #ifdef OPENSSL_EC_BIN_PT_COMP
878 if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
880 fprintf(stderr, "Point is not on curve: x = 0x");
881 BN_print_fp(stderr, x);
882 fprintf(stderr, ", y = 0x");
883 BN_print_fp(stderr, y);
884 fprintf(stderr, "\n");
888 fprintf(stdout, "A cyclic subgroup:\n");
894 if (EC_POINT_is_at_infinity(group, P))
895 fprintf(stdout, " point at infinity\n");
898 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT;
900 fprintf(stdout, " x = 0x");
901 BN_print_fp(stdout, x);
902 fprintf(stdout, ", y = 0x");
903 BN_print_fp(stdout, y);
904 fprintf(stdout, "\n");
907 if (!EC_POINT_copy(R, P)) ABORT;
908 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
910 while (!EC_POINT_is_at_infinity(group, P));
912 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
913 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
915 /* Change test based on whether binary point compression is enabled or not. */
916 #ifdef OPENSSL_EC_BIN_PT_COMP
917 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
919 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
920 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
921 fprintf(stdout, "Generator as octet string, compressed form:\n ");
922 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
925 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
927 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
928 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
929 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n ");
930 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
932 /* Change test based on whether binary point compression is enabled or not. */
933 #ifdef OPENSSL_EC_BIN_PT_COMP
934 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
936 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
937 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
938 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n ");
939 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
942 fprintf(stdout, "\n");
944 if (!EC_POINT_invert(group, P, ctx)) ABORT;
945 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
948 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
952 "0800000000000000000000000000000000000000C9",
955 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
956 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
958 "04000000000000000000020108A2E0CC0D99F8A5EF",
964 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
968 "0800000000000000000000000000000000000000C9",
970 "020A601907B8C953CA1481EB10512F78744A3205FD",
971 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
972 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
974 "040000000000000000000292FE77E70C12A4234C33",
980 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
984 "020000000000000000000000000000000000000004000000000000000001",
987 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
988 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
990 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
996 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
1000 "020000000000000000000000000000000000000004000000000000000001",
1001 "000000000000000000000000000000000000000000000000000000000001",
1002 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
1003 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
1004 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
1006 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
1012 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
1016 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1019 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
1020 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
1022 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
1028 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
1032 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1033 "000000000000000000000000000000000000000000000000000000000000000000000001",
1034 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
1035 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
1036 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1038 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
1044 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
1048 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1051 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
1052 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1054 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
1060 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
1064 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1065 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1066 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
1067 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
1068 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1070 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
1076 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
1080 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1083 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1084 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1086 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1092 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
1096 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1097 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1098 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1099 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1100 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1102 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1108 /* more tests using the last curve */
1110 if (!EC_POINT_copy(Q, P)) ABORT;
1111 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
1112 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
1113 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
1114 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
1116 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
1117 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
1118 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
1121 const EC_POINT *points[3];
1122 const BIGNUM *scalars[3];
1124 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
1129 if (!BN_add(y, z, BN_value_one())) ABORT;
1130 if (BN_is_odd(y)) ABORT;
1131 if (!BN_rshift1(y, y)) ABORT;
1132 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
1135 fprintf(stdout, "combined multiplication ...");
1138 /* z is still the group order */
1139 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
1140 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
1141 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
1142 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
1144 fprintf(stdout, ".");
1147 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
1148 if (!BN_add(z, z, y)) ABORT;
1151 scalars[1] = z; /* z = -(order + y) */
1153 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
1154 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1156 fprintf(stdout, ".");
1159 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
1160 if (!BN_add(z, x, y)) ABORT;
1164 scalars[2] = z; /* z = -(x+y) */
1166 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
1167 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1169 fprintf(stdout, " ok\n\n");
1174 timings(C2_K163, TIMING_BASE_PT, ctx);
1175 timings(C2_K163, TIMING_RAND_PT, ctx);
1176 timings(C2_K163, TIMING_SIMUL, ctx);
1177 timings(C2_B163, TIMING_BASE_PT, ctx);
1178 timings(C2_B163, TIMING_RAND_PT, ctx);
1179 timings(C2_B163, TIMING_SIMUL, ctx);
1180 timings(C2_K233, TIMING_BASE_PT, ctx);
1181 timings(C2_K233, TIMING_RAND_PT, ctx);
1182 timings(C2_K233, TIMING_SIMUL, ctx);
1183 timings(C2_B233, TIMING_BASE_PT, ctx);
1184 timings(C2_B233, TIMING_RAND_PT, ctx);
1185 timings(C2_B233, TIMING_SIMUL, ctx);
1186 timings(C2_K283, TIMING_BASE_PT, ctx);
1187 timings(C2_K283, TIMING_RAND_PT, ctx);
1188 timings(C2_K283, TIMING_SIMUL, ctx);
1189 timings(C2_B283, TIMING_BASE_PT, ctx);
1190 timings(C2_B283, TIMING_RAND_PT, ctx);
1191 timings(C2_B283, TIMING_SIMUL, ctx);
1192 timings(C2_K409, TIMING_BASE_PT, ctx);
1193 timings(C2_K409, TIMING_RAND_PT, ctx);
1194 timings(C2_K409, TIMING_SIMUL, ctx);
1195 timings(C2_B409, TIMING_BASE_PT, ctx);
1196 timings(C2_B409, TIMING_RAND_PT, ctx);
1197 timings(C2_B409, TIMING_SIMUL, ctx);
1198 timings(C2_K571, TIMING_BASE_PT, ctx);
1199 timings(C2_K571, TIMING_RAND_PT, ctx);
1200 timings(C2_K571, TIMING_SIMUL, ctx);
1201 timings(C2_B571, TIMING_BASE_PT, ctx);
1202 timings(C2_B571, TIMING_RAND_PT, ctx);
1203 timings(C2_B571, TIMING_SIMUL, ctx);
1209 BN_free(p); BN_free(a); BN_free(b);
1210 EC_GROUP_free(group);
1214 BN_free(x); BN_free(y); BN_free(z); BN_free(cof);
1216 if (C2_K163) EC_GROUP_free(C2_K163);
1217 if (C2_B163) EC_GROUP_free(C2_B163);
1218 if (C2_K233) EC_GROUP_free(C2_K233);
1219 if (C2_B233) EC_GROUP_free(C2_B233);
1220 if (C2_K283) EC_GROUP_free(C2_K283);
1221 if (C2_B283) EC_GROUP_free(C2_B283);
1222 if (C2_K409) EC_GROUP_free(C2_K409);
1223 if (C2_B409) EC_GROUP_free(C2_B409);
1224 if (C2_K571) EC_GROUP_free(C2_K571);
1225 if (C2_B571) EC_GROUP_free(C2_B571);
1229 void internal_curve_test(void)
1231 EC_builtin_curve *curves = NULL;
1232 size_t crv_len = 0, n = 0;
1235 crv_len = EC_get_builtin_curves(NULL, 0);
1237 curves = OPENSSL_malloc(sizeof(EC_builtin_curve) * crv_len);
1242 if (!EC_get_builtin_curves(curves, crv_len))
1244 OPENSSL_free(curves);
1248 fprintf(stdout, "testing internal curves: ");
1250 for (n = 0; n < crv_len; n++)
1252 EC_GROUP *group = NULL;
1253 int nid = curves[n].nid;
1254 if ((group = EC_GROUP_new_by_nid(nid)) == NULL)
1257 fprintf(stdout, "\nEC_GROUP_new_by_nid() failed with"
1258 " curve %s\n", OBJ_nid2sn(nid));
1259 /* try next curve */
1262 if (!EC_GROUP_check(group, NULL))
1265 fprintf(stdout, "\nEC_GROUP_check() failed with"
1266 " curve %s\n", OBJ_nid2sn(nid));
1267 EC_GROUP_free(group);
1268 /* try the next curve */
1271 fprintf(stdout, ".");
1273 EC_GROUP_free(group);
1276 fprintf(stdout, " ok\n");
1278 fprintf(stdout, " failed\n");
1279 OPENSSL_free(curves);
1283 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
1285 int main(int argc, char *argv[])
1288 /* enable memory leak checking unless explicitly disabled */
1289 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
1291 CRYPTO_malloc_debug_init();
1292 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL);
1296 /* OPENSSL_DEBUG_MEMORY=off */
1297 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
1299 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
1300 ERR_load_crypto_strings();
1302 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
1304 prime_field_tests();
1306 char2_field_tests();
1307 /* test the internal curves */
1308 internal_curve_test();
1310 #ifndef OPENSSL_NO_ENGINE
1313 CRYPTO_cleanup_all_ex_data();
1315 ERR_remove_state(0);
1316 CRYPTO_mem_leaks_fp(stderr);