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>
96 #include <openssl/bn.h>
98 #if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12)
99 /* suppress "too big too optimize" warning */
100 #pragma warning(disable:4959)
105 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
106 ERR_print_errors_fp(stderr); \
110 #define TIMING_BASE_PT 0
111 #define TIMING_RAND_PT 1
112 #define TIMING_SIMUL 2
115 static void timings(EC_GROUP *group, int type, BN_CTX *ctx)
120 BIGNUM *r[10], *r0[10];
124 if (s == NULL) ABORT;
126 fprintf(stdout, "Timings for %d-bit field, ", EC_GROUP_get_degree(group));
127 if (!EC_GROUP_get_order(group, s, ctx)) ABORT;
128 fprintf(stdout, "%d-bit scalars ", (int)BN_num_bits(s));
131 P = EC_POINT_new(group);
132 if (P == NULL) ABORT;
133 EC_POINT_copy(P, EC_GROUP_get0_generator(group));
135 for (i = 0; i < 10; i++)
137 if ((r[i] = BN_new()) == NULL) ABORT;
138 if (!BN_pseudo_rand(r[i], BN_num_bits(s), 0, 0)) ABORT;
139 if (type != TIMING_BASE_PT)
141 if ((r0[i] = BN_new()) == NULL) ABORT;
142 if (!BN_pseudo_rand(r0[i], BN_num_bits(s), 0, 0)) ABORT;
147 for (i = 0; i < 10; i++)
149 for (j = 0; j < 10; j++)
151 if (!EC_POINT_mul(group, P, (type != TIMING_RAND_PT) ? r[i] : NULL,
152 (type != TIMING_BASE_PT) ? P : NULL, (type != TIMING_BASE_PT) ? r0[i] : NULL, ctx)) ABORT;
155 clck = clock() - clck;
157 fprintf(stdout, "\n");
159 #ifdef CLOCKS_PER_SEC
160 /* "To determine the time in seconds, the value returned
161 * by the clock function should be divided by the value
162 * of the macro CLOCKS_PER_SEC."
166 /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
167 * -- cc on NeXTstep/OpenStep */
168 # define UNIT "units"
169 # define CLOCKS_PER_SEC 1
172 if (type == TIMING_BASE_PT) {
173 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
174 "base point multiplications", (double)clck/CLOCKS_PER_SEC);
175 } else if (type == TIMING_RAND_PT) {
176 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
177 "random point multiplications", (double)clck/CLOCKS_PER_SEC);
178 } else if (type == TIMING_SIMUL) {
179 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
180 "s*P+t*Q operations", (double)clck/CLOCKS_PER_SEC);
182 fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
186 for (i = 0; i < 10; i++)
189 if (type != TIMING_BASE_PT) BN_free(r0[i]);
194 /* test multiplication with group order, long and negative scalars */
195 static void group_order_tests(EC_GROUP *group)
197 BIGNUM *n1, *n2, *order;
198 EC_POINT *P = EC_POINT_new(group);
199 EC_POINT *Q = EC_POINT_new(group);
200 BN_CTX *ctx = BN_CTX_new();
202 n1 = BN_new(); n2 = BN_new(); order = BN_new();
203 fprintf(stdout, "verify group order ...");
205 if (!EC_GROUP_get_order(group, order, ctx)) ABORT;
206 if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT;
207 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
208 fprintf(stdout, ".");
210 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
211 if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT;
212 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
213 fprintf(stdout, " ok\n");
214 fprintf(stdout, "long/negative scalar tests ... ");
215 if (!BN_one(n1)) ABORT;
217 if (!BN_sub(n1, n1, order)) ABORT;
218 if(!EC_POINT_mul(group, Q, NULL, P, n1, ctx)) ABORT;
219 if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
221 if (!BN_add(n2, order, BN_value_one())) ABORT;
222 if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT;
223 if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
224 /* n2 = (1 - order) * (1 + order) */
225 if (!BN_mul(n2, n1, n2, ctx)) ABORT;
226 if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT;
227 if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
228 fprintf(stdout, "ok\n");
237 static void prime_field_tests()
242 EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
245 unsigned char buf[100];
257 if (!p || !a || !b) ABORT;
259 if (!BN_hex2bn(&p, "17")) ABORT;
260 if (!BN_hex2bn(&a, "1")) ABORT;
261 if (!BN_hex2bn(&b, "1")) ABORT;
263 group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
264 * so that the library gets to choose the EC_METHOD */
267 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
271 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
273 if (!EC_GROUP_copy(tmp, group)) ABORT;
274 EC_GROUP_free(group);
278 if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;
280 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
281 BN_print_fp(stdout, p);
282 fprintf(stdout, ")\n a = 0x");
283 BN_print_fp(stdout, a);
284 fprintf(stdout, "\n b = 0x");
285 BN_print_fp(stdout, b);
286 fprintf(stdout, "\n");
288 P = EC_POINT_new(group);
289 Q = EC_POINT_new(group);
290 R = EC_POINT_new(group);
291 if (!P || !Q || !R) ABORT;
293 if (!EC_POINT_set_to_infinity(group, P)) ABORT;
294 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
297 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
299 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
300 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
305 if (!x || !y || !z) ABORT;
307 if (!BN_hex2bn(&x, "D")) ABORT;
308 if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
309 if (!EC_POINT_is_on_curve(group, Q, ctx))
311 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
312 fprintf(stderr, "Point is not on curve: x = 0x");
313 BN_print_fp(stderr, x);
314 fprintf(stderr, ", y = 0x");
315 BN_print_fp(stderr, y);
316 fprintf(stderr, "\n");
320 fprintf(stdout, "A cyclic subgroup:\n");
326 if (EC_POINT_is_at_infinity(group, P))
327 fprintf(stdout, " point at infinity\n");
330 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
332 fprintf(stdout, " x = 0x");
333 BN_print_fp(stdout, x);
334 fprintf(stdout, ", y = 0x");
335 BN_print_fp(stdout, y);
336 fprintf(stdout, "\n");
339 if (!EC_POINT_copy(R, P)) ABORT;
340 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
349 if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
354 while (!EC_POINT_is_at_infinity(group, P));
356 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
357 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
359 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
361 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
362 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
363 fprintf(stdout, "Generator as octet string, compressed form:\n ");
364 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
366 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
368 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
369 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
370 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n ");
371 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
373 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
375 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
376 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
377 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n ");
378 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
380 if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
381 fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
382 BN_print_fp(stdout, x);
383 fprintf(stdout, ", Y = 0x");
384 BN_print_fp(stdout, y);
385 fprintf(stdout, ", Z = 0x");
386 BN_print_fp(stdout, z);
387 fprintf(stdout, "\n");
389 if (!EC_POINT_invert(group, P, ctx)) ABORT;
390 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
393 /* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000)
394 * -- not a NIST curve, but commonly used */
396 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) ABORT;
397 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
398 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) ABORT;
399 if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) ABORT;
400 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
402 if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82")) ABORT;
403 if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
404 if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
405 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
406 if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257")) ABORT;
407 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
409 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
410 fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x");
411 BN_print_fp(stdout, x);
412 fprintf(stdout, "\n y = 0x");
413 BN_print_fp(stdout, y);
414 fprintf(stdout, "\n");
415 /* G_y value taken from the standard: */
416 if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
417 if (0 != BN_cmp(y, z)) ABORT;
419 fprintf(stdout, "verify degree ...");
420 if (EC_GROUP_get_degree(group) != 160) ABORT;
421 fprintf(stdout, " ok\n");
423 group_order_tests(group);
425 if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
426 if (!EC_GROUP_copy(P_160, group)) ABORT;
429 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
431 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
432 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
433 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT;
434 if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT;
435 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
437 if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT;
438 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
439 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
440 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT;
441 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
443 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
444 fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x");
445 BN_print_fp(stdout, x);
446 fprintf(stdout, "\n y = 0x");
447 BN_print_fp(stdout, y);
448 fprintf(stdout, "\n");
449 /* G_y value taken from the standard: */
450 if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT;
451 if (0 != BN_cmp(y, z)) ABORT;
453 fprintf(stdout, "verify degree ...");
454 if (EC_GROUP_get_degree(group) != 192) ABORT;
455 fprintf(stdout, " ok\n");
457 group_order_tests(group);
459 if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
460 if (!EC_GROUP_copy(P_192, group)) ABORT;
463 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
465 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
466 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
467 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
468 if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
469 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
471 if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
472 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
473 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
474 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
475 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
477 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
478 fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x");
479 BN_print_fp(stdout, x);
480 fprintf(stdout, "\n y = 0x");
481 BN_print_fp(stdout, y);
482 fprintf(stdout, "\n");
483 /* G_y value taken from the standard: */
484 if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
485 if (0 != BN_cmp(y, z)) ABORT;
487 fprintf(stdout, "verify degree ...");
488 if (EC_GROUP_get_degree(group) != 224) ABORT;
489 fprintf(stdout, " ok\n");
491 group_order_tests(group);
493 if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
494 if (!EC_GROUP_copy(P_224, group)) ABORT;
497 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
499 if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
500 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
501 if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
502 if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT;
503 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
505 if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT;
506 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
507 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
508 if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
509 "84F3B9CAC2FC632551")) ABORT;
510 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
512 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
513 fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x");
514 BN_print_fp(stdout, x);
515 fprintf(stdout, "\n y = 0x");
516 BN_print_fp(stdout, y);
517 fprintf(stdout, "\n");
518 /* G_y value taken from the standard: */
519 if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT;
520 if (0 != BN_cmp(y, z)) ABORT;
522 fprintf(stdout, "verify degree ...");
523 if (EC_GROUP_get_degree(group) != 256) ABORT;
524 fprintf(stdout, " ok\n");
526 group_order_tests(group);
528 if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
529 if (!EC_GROUP_copy(P_256, group)) ABORT;
532 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
534 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
535 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT;
536 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
537 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
538 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT;
539 if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
540 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT;
541 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
543 if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
544 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
545 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
546 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
547 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
548 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT;
549 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
551 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
552 fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x");
553 BN_print_fp(stdout, x);
554 fprintf(stdout, "\n y = 0x");
555 BN_print_fp(stdout, y);
556 fprintf(stdout, "\n");
557 /* G_y value taken from the standard: */
558 if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
559 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT;
560 if (0 != BN_cmp(y, z)) ABORT;
562 fprintf(stdout, "verify degree ...");
563 if (EC_GROUP_get_degree(group) != 384) ABORT;
564 fprintf(stdout, " ok\n");
566 group_order_tests(group);
568 if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
569 if (!EC_GROUP_copy(P_384, group)) ABORT;
572 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
574 if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
575 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
576 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
577 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
578 if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
579 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
580 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
581 if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
582 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
583 "DF883D2C34F1EF451FD46B503F00")) ABORT;
584 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
586 if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
587 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
588 "3C1856A429BF97E7E31C2E5BD66")) ABORT;
589 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
590 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
591 if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
592 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
593 "C9B8899C47AEBB6FB71E91386409")) ABORT;
594 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
596 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
597 fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x");
598 BN_print_fp(stdout, x);
599 fprintf(stdout, "\n y = 0x");
600 BN_print_fp(stdout, y);
601 fprintf(stdout, "\n");
602 /* G_y value taken from the standard: */
603 if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
604 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
605 "7086A272C24088BE94769FD16650")) ABORT;
606 if (0 != BN_cmp(y, z)) ABORT;
608 fprintf(stdout, "verify degree ...");
609 if (EC_GROUP_get_degree(group) != 521) ABORT;
610 fprintf(stdout, " ok\n");
612 group_order_tests(group);
614 if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
615 if (!EC_GROUP_copy(P_521, group)) ABORT;
618 /* more tests using the last curve */
620 if (!EC_POINT_copy(Q, P)) ABORT;
621 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
622 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
623 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
624 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
626 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
627 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
628 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
631 const EC_POINT *points[4];
632 const BIGNUM *scalars[4];
635 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
641 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
642 if (!BN_add(y, z, BN_value_one())) ABORT;
643 if (BN_is_odd(y)) ABORT;
644 if (!BN_rshift1(y, y)) ABORT;
645 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
648 fprintf(stdout, "combined multiplication ...");
651 /* z is still the group order */
652 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
653 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
654 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
655 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
657 fprintf(stdout, ".");
660 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
661 if (!BN_add(z, z, y)) ABORT;
662 BN_set_negative(z, 1);
664 scalars[1] = z; /* z = -(order + y) */
666 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
667 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
669 fprintf(stdout, ".");
672 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
673 if (!BN_add(z, x, y)) ABORT;
674 BN_set_negative(z, 1);
677 scalars[2] = z; /* z = -(x+y) */
681 scalars[3] = &scalar3;
683 if (!EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx)) ABORT;
684 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
686 fprintf(stdout, " ok\n\n");
693 timings(P_160, TIMING_BASE_PT, ctx);
694 timings(P_160, TIMING_RAND_PT, ctx);
695 timings(P_160, TIMING_SIMUL, ctx);
696 timings(P_192, TIMING_BASE_PT, ctx);
697 timings(P_192, TIMING_RAND_PT, ctx);
698 timings(P_192, TIMING_SIMUL, ctx);
699 timings(P_224, TIMING_BASE_PT, ctx);
700 timings(P_224, TIMING_RAND_PT, ctx);
701 timings(P_224, TIMING_SIMUL, ctx);
702 timings(P_256, TIMING_BASE_PT, ctx);
703 timings(P_256, TIMING_RAND_PT, ctx);
704 timings(P_256, TIMING_SIMUL, ctx);
705 timings(P_384, TIMING_BASE_PT, ctx);
706 timings(P_384, TIMING_RAND_PT, ctx);
707 timings(P_384, TIMING_SIMUL, ctx);
708 timings(P_521, TIMING_BASE_PT, ctx);
709 timings(P_521, TIMING_RAND_PT, ctx);
710 timings(P_521, TIMING_SIMUL, ctx);
716 BN_free(p); BN_free(a); BN_free(b);
717 EC_GROUP_free(group);
721 BN_free(x); BN_free(y); BN_free(z);
723 if (P_160) EC_GROUP_free(P_160);
724 if (P_192) EC_GROUP_free(P_192);
725 if (P_224) EC_GROUP_free(P_224);
726 if (P_256) EC_GROUP_free(P_256);
727 if (P_384) EC_GROUP_free(P_384);
728 if (P_521) EC_GROUP_free(P_521);
732 /* Change test based on whether binary point compression is enabled or not. */
733 #ifdef OPENSSL_EC_BIN_PT_COMP
734 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
735 if (!BN_hex2bn(&x, _x)) ABORT; \
736 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
737 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
738 if (!BN_hex2bn(&z, _order)) ABORT; \
739 if (!BN_hex2bn(&cof, _cof)) ABORT; \
740 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
741 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
742 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
743 BN_print_fp(stdout, x); \
744 fprintf(stdout, "\n y = 0x"); \
745 BN_print_fp(stdout, y); \
746 fprintf(stdout, "\n"); \
747 /* G_y value taken from the standard: */ \
748 if (!BN_hex2bn(&z, _y)) ABORT; \
749 if (0 != BN_cmp(y, z)) ABORT;
751 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
752 if (!BN_hex2bn(&x, _x)) ABORT; \
753 if (!BN_hex2bn(&y, _y)) ABORT; \
754 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
755 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
756 if (!BN_hex2bn(&z, _order)) ABORT; \
757 if (!BN_hex2bn(&cof, _cof)) ABORT; \
758 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
759 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
760 BN_print_fp(stdout, x); \
761 fprintf(stdout, "\n y = 0x"); \
762 BN_print_fp(stdout, y); \
763 fprintf(stdout, "\n");
766 #define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
767 if (!BN_hex2bn(&p, _p)) ABORT; \
768 if (!BN_hex2bn(&a, _a)) ABORT; \
769 if (!BN_hex2bn(&b, _b)) ABORT; \
770 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
771 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
772 fprintf(stdout, "verify degree ..."); \
773 if (EC_GROUP_get_degree(group) != _degree) ABORT; \
774 fprintf(stdout, " ok\n"); \
775 group_order_tests(group); \
776 if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \
777 if (!EC_GROUP_copy(_variable, group)) ABORT; \
780 static void char2_field_tests()
785 EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = NULL, *C2_K571 = NULL;
786 EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = NULL, *C2_B571 = NULL;
788 BIGNUM *x, *y, *z, *cof;
789 unsigned char buf[100];
801 if (!p || !a || !b) ABORT;
803 if (!BN_hex2bn(&p, "13")) ABORT;
804 if (!BN_hex2bn(&a, "3")) ABORT;
805 if (!BN_hex2bn(&b, "1")) ABORT;
807 group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m
808 * so that the library gets to choose the EC_METHOD */
810 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT;
814 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
816 if (!EC_GROUP_copy(tmp, group)) ABORT;
817 EC_GROUP_free(group);
821 if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT;
823 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x");
824 BN_print_fp(stdout, p);
825 fprintf(stdout, ")\n a = 0x");
826 BN_print_fp(stdout, a);
827 fprintf(stdout, "\n b = 0x");
828 BN_print_fp(stdout, b);
829 fprintf(stdout, "\n(0x... means binary polynomial)\n");
831 P = EC_POINT_new(group);
832 Q = EC_POINT_new(group);
833 R = EC_POINT_new(group);
834 if (!P || !Q || !R) ABORT;
836 if (!EC_POINT_set_to_infinity(group, P)) ABORT;
837 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
840 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
842 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
843 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
849 if (!x || !y || !z || !cof) ABORT;
851 if (!BN_hex2bn(&x, "6")) ABORT;
852 /* Change test based on whether binary point compression is enabled or not. */
853 #ifdef OPENSSL_EC_BIN_PT_COMP
854 if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT;
856 if (!BN_hex2bn(&y, "8")) ABORT;
857 if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
859 if (!EC_POINT_is_on_curve(group, Q, ctx))
861 /* Change test based on whether binary point compression is enabled or not. */
862 #ifdef OPENSSL_EC_BIN_PT_COMP
863 if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
865 fprintf(stderr, "Point is not on curve: x = 0x");
866 BN_print_fp(stderr, x);
867 fprintf(stderr, ", y = 0x");
868 BN_print_fp(stderr, y);
869 fprintf(stderr, "\n");
873 fprintf(stdout, "A cyclic subgroup:\n");
879 if (EC_POINT_is_at_infinity(group, P))
880 fprintf(stdout, " point at infinity\n");
883 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT;
885 fprintf(stdout, " x = 0x");
886 BN_print_fp(stdout, x);
887 fprintf(stdout, ", y = 0x");
888 BN_print_fp(stdout, y);
889 fprintf(stdout, "\n");
892 if (!EC_POINT_copy(R, P)) ABORT;
893 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
895 while (!EC_POINT_is_at_infinity(group, P));
897 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
898 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
900 /* Change test based on whether binary point compression is enabled or not. */
901 #ifdef OPENSSL_EC_BIN_PT_COMP
902 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
904 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
905 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
906 fprintf(stdout, "Generator as octet string, compressed form:\n ");
907 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
910 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
912 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
913 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
914 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n ");
915 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
917 /* Change test based on whether binary point compression is enabled or not. */
918 #ifdef OPENSSL_EC_BIN_PT_COMP
919 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
921 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
922 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
923 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n ");
924 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
927 fprintf(stdout, "\n");
929 if (!EC_POINT_invert(group, P, ctx)) ABORT;
930 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
933 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
937 "0800000000000000000000000000000000000000C9",
940 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
941 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
943 "04000000000000000000020108A2E0CC0D99F8A5EF",
949 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
953 "0800000000000000000000000000000000000000C9",
955 "020A601907B8C953CA1481EB10512F78744A3205FD",
956 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
957 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
959 "040000000000000000000292FE77E70C12A4234C33",
965 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
969 "020000000000000000000000000000000000000004000000000000000001",
972 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
973 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
975 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
981 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
985 "020000000000000000000000000000000000000004000000000000000001",
986 "000000000000000000000000000000000000000000000000000000000001",
987 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
988 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
989 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
991 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
997 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
1001 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1004 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
1005 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
1007 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
1013 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
1017 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1018 "000000000000000000000000000000000000000000000000000000000000000000000001",
1019 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
1020 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
1021 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1023 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
1029 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
1033 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1036 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
1037 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1039 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
1045 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
1049 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1050 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1051 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
1052 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
1053 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1055 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
1061 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
1065 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1068 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1069 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1071 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1077 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
1081 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1082 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1083 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1084 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1085 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1087 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1093 /* more tests using the last curve */
1095 if (!EC_POINT_copy(Q, P)) ABORT;
1096 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
1097 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
1098 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
1099 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
1101 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
1102 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
1103 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
1106 const EC_POINT *points[3];
1107 const BIGNUM *scalars[3];
1109 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
1114 if (!BN_add(y, z, BN_value_one())) ABORT;
1115 if (BN_is_odd(y)) ABORT;
1116 if (!BN_rshift1(y, y)) ABORT;
1117 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
1120 fprintf(stdout, "combined multiplication ...");
1123 /* z is still the group order */
1124 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
1125 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
1126 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
1127 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
1129 fprintf(stdout, ".");
1132 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
1133 if (!BN_add(z, z, y)) ABORT;
1134 BN_set_negative(z, 1);
1136 scalars[1] = z; /* z = -(order + y) */
1138 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
1139 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1141 fprintf(stdout, ".");
1144 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
1145 if (!BN_add(z, x, y)) ABORT;
1146 BN_set_negative(z, 1);
1149 scalars[2] = z; /* z = -(x+y) */
1151 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
1152 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1154 fprintf(stdout, " ok\n\n");
1159 timings(C2_K163, TIMING_BASE_PT, ctx);
1160 timings(C2_K163, TIMING_RAND_PT, ctx);
1161 timings(C2_K163, TIMING_SIMUL, ctx);
1162 timings(C2_B163, TIMING_BASE_PT, ctx);
1163 timings(C2_B163, TIMING_RAND_PT, ctx);
1164 timings(C2_B163, TIMING_SIMUL, ctx);
1165 timings(C2_K233, TIMING_BASE_PT, ctx);
1166 timings(C2_K233, TIMING_RAND_PT, ctx);
1167 timings(C2_K233, TIMING_SIMUL, ctx);
1168 timings(C2_B233, TIMING_BASE_PT, ctx);
1169 timings(C2_B233, TIMING_RAND_PT, ctx);
1170 timings(C2_B233, TIMING_SIMUL, ctx);
1171 timings(C2_K283, TIMING_BASE_PT, ctx);
1172 timings(C2_K283, TIMING_RAND_PT, ctx);
1173 timings(C2_K283, TIMING_SIMUL, ctx);
1174 timings(C2_B283, TIMING_BASE_PT, ctx);
1175 timings(C2_B283, TIMING_RAND_PT, ctx);
1176 timings(C2_B283, TIMING_SIMUL, ctx);
1177 timings(C2_K409, TIMING_BASE_PT, ctx);
1178 timings(C2_K409, TIMING_RAND_PT, ctx);
1179 timings(C2_K409, TIMING_SIMUL, ctx);
1180 timings(C2_B409, TIMING_BASE_PT, ctx);
1181 timings(C2_B409, TIMING_RAND_PT, ctx);
1182 timings(C2_B409, TIMING_SIMUL, ctx);
1183 timings(C2_K571, TIMING_BASE_PT, ctx);
1184 timings(C2_K571, TIMING_RAND_PT, ctx);
1185 timings(C2_K571, TIMING_SIMUL, ctx);
1186 timings(C2_B571, TIMING_BASE_PT, ctx);
1187 timings(C2_B571, TIMING_RAND_PT, ctx);
1188 timings(C2_B571, TIMING_SIMUL, ctx);
1194 BN_free(p); BN_free(a); BN_free(b);
1195 EC_GROUP_free(group);
1199 BN_free(x); BN_free(y); BN_free(z); BN_free(cof);
1201 if (C2_K163) EC_GROUP_free(C2_K163);
1202 if (C2_B163) EC_GROUP_free(C2_B163);
1203 if (C2_K233) EC_GROUP_free(C2_K233);
1204 if (C2_B233) EC_GROUP_free(C2_B233);
1205 if (C2_K283) EC_GROUP_free(C2_K283);
1206 if (C2_B283) EC_GROUP_free(C2_B283);
1207 if (C2_K409) EC_GROUP_free(C2_K409);
1208 if (C2_B409) EC_GROUP_free(C2_B409);
1209 if (C2_K571) EC_GROUP_free(C2_K571);
1210 if (C2_B571) EC_GROUP_free(C2_B571);
1214 static void internal_curve_test(void)
1216 EC_builtin_curve *curves = NULL;
1217 size_t crv_len = 0, n = 0;
1220 crv_len = EC_get_builtin_curves(NULL, 0);
1222 curves = OPENSSL_malloc(sizeof(EC_builtin_curve) * crv_len);
1227 if (!EC_get_builtin_curves(curves, crv_len))
1229 OPENSSL_free(curves);
1233 fprintf(stdout, "testing internal curves: ");
1235 for (n = 0; n < crv_len; n++)
1237 EC_GROUP *group = NULL;
1238 int nid = curves[n].nid;
1239 if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL)
1242 fprintf(stdout, "\nEC_GROUP_new_curve_name() failed with"
1243 " curve %s\n", OBJ_nid2sn(nid));
1244 /* try next curve */
1247 if (!EC_GROUP_check(group, NULL))
1250 fprintf(stdout, "\nEC_GROUP_check() failed with"
1251 " curve %s\n", OBJ_nid2sn(nid));
1252 EC_GROUP_free(group);
1253 /* try the next curve */
1256 fprintf(stdout, ".");
1258 EC_GROUP_free(group);
1261 fprintf(stdout, " ok\n\n");
1263 fprintf(stdout, " failed\n\n");
1264 OPENSSL_free(curves);
1268 #ifdef EC_NISTP224_64_GCC_128
1269 void nistp224_test()
1271 fprintf(stdout, "\nNIST curve P-224 (optimised implementation):\n");
1272 BIGNUM *p, *a, *b, *x, *y, *n, *m, *order;
1276 x = BN_new(); y = BN_new();
1277 m = BN_new(); n = BN_new(); order = BN_new();
1278 BN_CTX *ctx = BN_CTX_new();
1280 EC_POINT *G, *P, *Q, *Q_CHECK;
1282 NISTP224 = EC_GROUP_new(EC_GFp_nistp224_method());
1283 if(!NISTP224) ABORT;
1284 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
1285 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
1286 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
1287 if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
1288 if (!EC_GROUP_set_curve_GFp(NISTP224, p, a, b, ctx)) ABORT;
1289 G = EC_POINT_new(NISTP224);
1290 P = EC_POINT_new(NISTP224);
1291 Q = EC_POINT_new(NISTP224);
1292 Q_CHECK = EC_POINT_new(NISTP224);
1293 if(!BN_hex2bn(&x, "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E")) ABORT;
1294 if(!BN_hex2bn(&y, "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555")) ABORT;
1295 if(!EC_POINT_set_affine_coordinates_GFp(NISTP224, Q_CHECK, x, y, ctx)) ABORT;
1296 if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
1297 if (!BN_hex2bn(&y, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
1298 if (!EC_POINT_set_affine_coordinates_GFp(NISTP224, G, x, y, ctx)) ABORT;
1299 if (!BN_hex2bn(&order, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
1300 if (!EC_GROUP_set_generator(NISTP224, G, order, BN_value_one())) ABORT;
1302 fprintf(stdout, "verify degree ... ");
1303 if (EC_GROUP_get_degree(NISTP224) != 224) ABORT;
1304 fprintf(stdout, "ok\n");
1306 fprintf(stdout, "NIST test vectors ... ");
1307 if (!BN_hex2bn(&n, "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8")) ABORT;
1308 /* fixed point multiplication */
1309 EC_POINT_mul(NISTP224, Q, n, NULL, NULL, ctx);
1310 if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
1311 /* random point multiplication */
1312 EC_POINT_mul(NISTP224, Q, NULL, G, n, ctx);
1313 if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
1315 /* set generator to P = 2*G, where G is the standard generator */
1316 if (!EC_POINT_dbl(NISTP224, P, G, ctx)) ABORT;
1317 if (!EC_GROUP_set_generator(NISTP224, P, order, BN_value_one())) ABORT;
1318 /* set the scalar to m=n/2, where n is the NIST test scalar */
1319 if (!BN_rshift(m, n, 1)) ABORT;
1321 /* test the non-standard generator */
1322 /* fixed point multiplication */
1323 EC_POINT_mul(NISTP224, Q, m, NULL, NULL, ctx);
1324 if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
1325 /* random point multiplication */
1326 EC_POINT_mul(NISTP224, Q, NULL, P, m, ctx);
1327 if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
1329 /* now repeat all tests with precomputation */
1330 if (!EC_GROUP_precompute_mult(NISTP224, ctx)) ABORT;
1332 /* fixed point multiplication */
1333 EC_POINT_mul(NISTP224, Q, m, NULL, NULL, ctx);
1334 if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
1335 /* random point multiplication */
1336 EC_POINT_mul(NISTP224, Q, NULL, P, m, ctx);
1337 if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
1339 /* reset generator */
1340 if (!EC_GROUP_set_generator(NISTP224, G, order, BN_value_one())) ABORT;
1341 /* fixed point multiplication */
1342 EC_POINT_mul(NISTP224, Q, n, NULL, NULL, ctx);
1343 if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
1344 /* random point multiplication */
1345 EC_POINT_mul(NISTP224, Q, NULL, G, n, ctx);
1346 if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
1348 fprintf(stdout, "ok\n");
1349 group_order_tests(NISTP224);
1351 timings(NISTP224, TIMING_BASE_PT, ctx);
1352 timings(NISTP224, TIMING_RAND_PT, ctx);
1354 EC_GROUP_free(NISTP224);
1358 EC_POINT_free(Q_CHECK);
1371 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
1373 int main(int argc, char *argv[])
1376 /* enable memory leak checking unless explicitly disabled */
1377 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
1379 CRYPTO_malloc_debug_init();
1380 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL);
1384 /* OPENSSL_DEBUG_MEMORY=off */
1385 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
1387 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
1388 ERR_load_crypto_strings();
1390 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
1392 prime_field_tests();
1394 char2_field_tests();
1395 #ifdef EC_NISTP224_64_GCC_128
1398 /* test the internal curves */
1399 internal_curve_test();
1401 #ifndef OPENSSL_NO_ENGINE
1404 CRYPTO_cleanup_all_ex_data();
1406 ERR_remove_thread_state(NULL);
1407 CRYPTO_mem_leaks_fp(stderr);