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.
79 int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; }
83 #include <openssl/ec.h>
84 #include <openssl/engine.h>
85 #include <openssl/err.h>
86 #include <openssl/obj_mac.h>
90 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
91 ERR_print_errors_fp(stderr); \
95 void prime_field_tests(void);
96 void char2_field_tests(void);
99 static void timings(EC_GROUP *group, int multi, BN_CTX *ctx)
104 BIGNUM *r[10], *r0[10];
108 if (s == NULL) ABORT;
110 fprintf(stdout, "Timings for %d-bit field, ", EC_GROUP_get_degree(group));
111 if (!EC_GROUP_get_order(group, s, ctx)) ABORT;
112 fprintf(stdout, "%d-bit scalars ", (int)BN_num_bits(s));
115 P = EC_POINT_new(group);
116 if (P == NULL) ABORT;
117 EC_POINT_copy(P, EC_GROUP_get0_generator(group));
119 for (i = 0; i < 10; i++)
121 if ((r[i] = BN_new()) == NULL) ABORT;
122 if (!BN_pseudo_rand(r[i], BN_num_bits(s), 0, 0)) ABORT;
125 if ((r0[i] = BN_new()) == NULL) ABORT;
126 if (!BN_pseudo_rand(r0[i], BN_num_bits(s), 0, 0)) ABORT;
131 for (i = 0; i < 10; i++)
133 for (j = 0; j < 10; j++)
135 if (!EC_POINT_mul(group, P, r[i], multi ? P : NULL, multi ? r0[i] : NULL, ctx)) ABORT;
138 fprintf(stdout, "\n");
140 clck = clock() - clck;
142 #ifdef CLOCKS_PER_SEC
143 /* "To determine the time in seconds, the value returned
144 * by the clock function should be divided by the value
145 * of the macro CLOCKS_PER_SEC."
149 /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
150 * -- cc on NeXTstep/OpenStep */
151 # define UNIT "units"
152 # define CLOCKS_PER_SEC 1
155 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
156 multi ? "s*P+t*Q operations" : "point multiplications",
157 (double)clck/CLOCKS_PER_SEC);
158 fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
162 for (i = 0; i < 10; i++)
165 if (multi) BN_free(r0[i]);
170 void prime_field_tests()
175 EC_GROUP *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
178 unsigned char buf[100];
190 if (!p || !a || !b) ABORT;
192 if (!BN_hex2bn(&p, "17")) ABORT;
193 if (!BN_hex2bn(&a, "1")) ABORT;
194 if (!BN_hex2bn(&b, "1")) ABORT;
196 group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
197 * so that the library gets to choose the EC_METHOD */
200 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
204 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
206 if (!EC_GROUP_copy(tmp, group));
207 EC_GROUP_free(group);
211 if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;
213 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
214 BN_print_fp(stdout, p);
215 fprintf(stdout, ")\n a = 0x");
216 BN_print_fp(stdout, a);
217 fprintf(stdout, "\n b = 0x");
218 BN_print_fp(stdout, b);
219 fprintf(stdout, "\n");
221 P = EC_POINT_new(group);
222 Q = EC_POINT_new(group);
223 R = EC_POINT_new(group);
224 if (!P || !Q || !R) ABORT;
226 if (!EC_POINT_set_to_infinity(group, P)) ABORT;
227 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
230 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
232 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
233 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
238 if (!x || !y || !z) ABORT;
240 if (!BN_hex2bn(&x, "D")) ABORT;
241 if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
242 if (!EC_POINT_is_on_curve(group, Q, ctx))
244 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
245 fprintf(stderr, "Point is not on curve: x = 0x");
246 BN_print_fp(stderr, x);
247 fprintf(stderr, ", y = 0x");
248 BN_print_fp(stderr, y);
249 fprintf(stderr, "\n");
253 fprintf(stdout, "A cyclic subgroup:\n");
259 if (EC_POINT_is_at_infinity(group, P))
260 fprintf(stdout, " point at infinity\n");
263 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
265 fprintf(stdout, " x = 0x");
266 BN_print_fp(stdout, x);
267 fprintf(stdout, ", y = 0x");
268 BN_print_fp(stdout, y);
269 fprintf(stdout, "\n");
272 if (!EC_POINT_copy(R, P)) ABORT;
273 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
282 if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
287 while (!EC_POINT_is_at_infinity(group, P));
289 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
290 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
292 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
294 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
295 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
296 fprintf(stdout, "Generator as octect string, compressed form:\n ");
297 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
299 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
301 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
302 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
303 fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n ");
304 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
306 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
308 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
309 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
310 fprintf(stdout, "\nGenerator as octect string, hybrid form:\n ");
311 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
313 if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
314 fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
315 BN_print_fp(stdout, x);
316 fprintf(stdout, ", Y = 0x");
317 BN_print_fp(stdout, y);
318 fprintf(stdout, ", Z = 0x");
319 BN_print_fp(stdout, z);
320 fprintf(stdout, "\n");
322 if (!EC_POINT_invert(group, P, ctx)) ABORT;
323 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
326 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
328 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
329 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
330 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT;
331 if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT;
332 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
334 if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT;
335 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
336 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
337 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT;
338 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
340 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
341 fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x");
342 BN_print_fp(stdout, x);
343 fprintf(stdout, "\n y = 0x");
344 BN_print_fp(stdout, y);
345 fprintf(stdout, "\n");
346 /* G_y value taken from the standard: */
347 if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT;
348 if (0 != BN_cmp(y, z)) ABORT;
350 fprintf(stdout, "verify degree ...");
351 if (EC_GROUP_get_degree(group) != 192) ABORT;
352 fprintf(stdout, " ok\n");
354 fprintf(stdout, "verify group order ...");
356 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
357 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
358 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
359 fprintf(stdout, ".");
361 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
362 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
363 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
364 fprintf(stdout, " ok\n");
366 if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
367 if (!EC_GROUP_copy(P_192, group)) ABORT;
370 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
372 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
373 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
374 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
375 if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
376 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
378 if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
379 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
380 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
381 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
382 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
384 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
385 fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x");
386 BN_print_fp(stdout, x);
387 fprintf(stdout, "\n y = 0x");
388 BN_print_fp(stdout, y);
389 fprintf(stdout, "\n");
390 /* G_y value taken from the standard: */
391 if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
392 if (0 != BN_cmp(y, z)) ABORT;
394 fprintf(stdout, "verify degree ...");
395 if (EC_GROUP_get_degree(group) != 224) ABORT;
396 fprintf(stdout, " ok\n");
398 fprintf(stdout, "verify group order ...");
400 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
401 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
402 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
403 fprintf(stdout, ".");
405 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
406 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
407 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
408 fprintf(stdout, " ok\n");
410 if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
411 if (!EC_GROUP_copy(P_224, group)) ABORT;
414 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
416 if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
417 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
418 if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
419 if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT;
420 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
422 if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT;
423 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
424 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
425 if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
426 "84F3B9CAC2FC632551")) ABORT;
427 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
429 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
430 fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x");
431 BN_print_fp(stdout, x);
432 fprintf(stdout, "\n y = 0x");
433 BN_print_fp(stdout, y);
434 fprintf(stdout, "\n");
435 /* G_y value taken from the standard: */
436 if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT;
437 if (0 != BN_cmp(y, z)) ABORT;
439 fprintf(stdout, "verify degree ...");
440 if (EC_GROUP_get_degree(group) != 256) ABORT;
441 fprintf(stdout, " ok\n");
443 fprintf(stdout, "verify group order ...");
445 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
446 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
447 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
448 fprintf(stdout, ".");
450 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
451 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
452 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
453 fprintf(stdout, " ok\n");
455 if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
456 if (!EC_GROUP_copy(P_256, group)) ABORT;
459 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
461 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
462 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT;
463 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
464 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
465 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT;
466 if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
467 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT;
468 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
470 if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
471 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
472 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
473 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
474 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
475 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT;
476 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
478 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
479 fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x");
480 BN_print_fp(stdout, x);
481 fprintf(stdout, "\n y = 0x");
482 BN_print_fp(stdout, y);
483 fprintf(stdout, "\n");
484 /* G_y value taken from the standard: */
485 if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
486 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT;
487 if (0 != BN_cmp(y, z)) ABORT;
489 fprintf(stdout, "verify degree ...");
490 if (EC_GROUP_get_degree(group) != 384) ABORT;
491 fprintf(stdout, " ok\n");
493 fprintf(stdout, "verify group order ...");
495 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
496 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
497 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
498 fprintf(stdout, ".");
500 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
501 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
502 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
503 fprintf(stdout, " ok\n");
505 if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
506 if (!EC_GROUP_copy(P_384, group)) ABORT;
509 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
511 if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
512 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
513 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
514 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
515 if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
516 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
517 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
518 if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
519 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
520 "DF883D2C34F1EF451FD46B503F00")) ABORT;
521 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
523 if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
524 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
525 "3C1856A429BF97E7E31C2E5BD66")) ABORT;
526 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
527 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
528 if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
529 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
530 "C9B8899C47AEBB6FB71E91386409")) ABORT;
531 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
533 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
534 fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x");
535 BN_print_fp(stdout, x);
536 fprintf(stdout, "\n y = 0x");
537 BN_print_fp(stdout, y);
538 fprintf(stdout, "\n");
539 /* G_y value taken from the standard: */
540 if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
541 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
542 "7086A272C24088BE94769FD16650")) ABORT;
543 if (0 != BN_cmp(y, z)) ABORT;
545 fprintf(stdout, "verify degree ...");
546 if (EC_GROUP_get_degree(group) != 521) ABORT;
547 fprintf(stdout, " ok\n");
549 fprintf(stdout, "verify group order ...");
551 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
552 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
553 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
554 fprintf(stdout, ".");
556 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
557 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
558 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
559 fprintf(stdout, " ok\n");
561 if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
562 if (!EC_GROUP_copy(P_521, group)) ABORT;
565 /* more tests using the last curve */
567 if (!EC_POINT_copy(Q, P)) ABORT;
568 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
569 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
570 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
571 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
573 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
574 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
575 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
578 const EC_POINT *points[3];
579 const BIGNUM *scalars[3];
581 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
586 if (!BN_add(y, z, BN_value_one())) ABORT;
587 if (BN_is_odd(y)) ABORT;
588 if (!BN_rshift1(y, y)) ABORT;
589 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
592 fprintf(stdout, "combined multiplication ...");
595 /* z is still the group order */
596 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
597 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
598 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
599 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
601 fprintf(stdout, ".");
604 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
605 if (!BN_add(z, z, y)) ABORT;
608 scalars[1] = z; /* z = -(order + y) */
610 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
611 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
613 fprintf(stdout, ".");
616 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
617 if (!BN_add(z, x, y)) ABORT;
621 scalars[2] = z; /* z = -(x+y) */
623 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
624 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
626 fprintf(stdout, " ok\n\n");
631 timings(P_192, 0, ctx);
632 timings(P_192, 1, ctx);
633 timings(P_224, 0, ctx);
634 timings(P_224, 1, ctx);
635 timings(P_256, 0, ctx);
636 timings(P_256, 1, ctx);
637 timings(P_384, 0, ctx);
638 timings(P_384, 1, ctx);
639 timings(P_521, 0, ctx);
640 timings(P_521, 1, ctx);
646 BN_free(p); BN_free(a); BN_free(b);
647 EC_GROUP_free(group);
651 BN_free(x); BN_free(y); BN_free(z);
653 if (P_192) EC_GROUP_free(P_192);
654 if (P_224) EC_GROUP_free(P_224);
655 if (P_256) EC_GROUP_free(P_256);
656 if (P_384) EC_GROUP_free(P_384);
657 if (P_521) EC_GROUP_free(P_521);
661 /* Change test based on whether binary point compression is enabled or not. */
662 #ifdef OPENSSL_EC_BIN_PT_COMP
663 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
664 if (!BN_hex2bn(&x, _x)) ABORT; \
665 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
666 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
667 if (!BN_hex2bn(&z, _order)) ABORT; \
668 if (!BN_hex2bn(&cof, _cof)) ABORT; \
669 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
670 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
671 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
672 BN_print_fp(stdout, x); \
673 fprintf(stdout, "\n y = 0x"); \
674 BN_print_fp(stdout, y); \
675 fprintf(stdout, "\n"); \
676 /* G_y value taken from the standard: */ \
677 if (!BN_hex2bn(&z, _y)) ABORT; \
678 if (0 != BN_cmp(y, z)) ABORT;
680 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
681 if (!BN_hex2bn(&x, _x)) ABORT; \
682 if (!BN_hex2bn(&y, _y)) ABORT; \
683 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
684 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
685 if (!BN_hex2bn(&z, _order)) ABORT; \
686 if (!BN_hex2bn(&cof, _cof)) ABORT; \
687 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
688 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
689 BN_print_fp(stdout, x); \
690 fprintf(stdout, "\n y = 0x"); \
691 BN_print_fp(stdout, y); \
692 fprintf(stdout, "\n");
695 #define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
696 if (!BN_hex2bn(&p, _p)) ABORT; \
697 if (!BN_hex2bn(&a, _a)) ABORT; \
698 if (!BN_hex2bn(&b, _b)) ABORT; \
699 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
700 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
701 fprintf(stdout, "verify degree ..."); \
702 if (EC_GROUP_get_degree(group) != _degree) ABORT; \
703 fprintf(stdout, " ok\n"); \
704 fprintf(stdout, "verify group order ..."); \
706 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; \
707 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \
708 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \
709 fprintf(stdout, "."); \
711 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; \
712 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \
713 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \
714 fprintf(stdout, " ok\n"); \
715 if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \
716 if (!EC_GROUP_copy(_variable, group)) ABORT;
718 void char2_field_tests()
723 EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = NULL, *C2_K571 = NULL;
724 EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = NULL, *C2_B571 = NULL;
726 BIGNUM *x, *y, *z, *cof;
727 unsigned char buf[100];
739 if (!p || !a || !b) ABORT;
741 if (!BN_hex2bn(&p, "13")) ABORT;
742 if (!BN_hex2bn(&a, "3")) ABORT;
743 if (!BN_hex2bn(&b, "1")) ABORT;
745 group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m
746 * so that the library gets to choose the EC_METHOD */
748 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT;
752 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
754 if (!EC_GROUP_copy(tmp, group));
755 EC_GROUP_free(group);
759 if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT;
761 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x");
762 BN_print_fp(stdout, p);
763 fprintf(stdout, ")\n a = 0x");
764 BN_print_fp(stdout, a);
765 fprintf(stdout, "\n b = 0x");
766 BN_print_fp(stdout, b);
767 fprintf(stdout, "\n(0x... means binary polynomial)\n");
769 P = EC_POINT_new(group);
770 Q = EC_POINT_new(group);
771 R = EC_POINT_new(group);
772 if (!P || !Q || !R) ABORT;
774 if (!EC_POINT_set_to_infinity(group, P)) ABORT;
775 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
778 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
780 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
781 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
787 if (!x || !y || !z || !cof) ABORT;
789 if (!BN_hex2bn(&x, "6")) ABORT;
790 /* Change test based on whether binary point compression is enabled or not. */
791 #ifdef OPENSSL_EC_BIN_PT_COMP
792 if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT;
794 if (!BN_hex2bn(&y, "8")) ABORT;
795 if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
797 if (!EC_POINT_is_on_curve(group, Q, ctx))
799 /* Change test based on whether binary point compression is enabled or not. */
800 #ifdef OPENSSL_EC_BIN_PT_COMP
801 if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
803 fprintf(stderr, "Point is not on curve: x = 0x");
804 BN_print_fp(stderr, x);
805 fprintf(stderr, ", y = 0x");
806 BN_print_fp(stderr, y);
807 fprintf(stderr, "\n");
811 fprintf(stdout, "A cyclic subgroup:\n");
817 if (EC_POINT_is_at_infinity(group, P))
818 fprintf(stdout, " point at infinity\n");
821 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT;
823 fprintf(stdout, " x = 0x");
824 BN_print_fp(stdout, x);
825 fprintf(stdout, ", y = 0x");
826 BN_print_fp(stdout, y);
827 fprintf(stdout, "\n");
830 if (!EC_POINT_copy(R, P)) ABORT;
831 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
833 while (!EC_POINT_is_at_infinity(group, P));
835 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
836 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
838 /* Change test based on whether binary point compression is enabled or not. */
839 #ifdef OPENSSL_EC_BIN_PT_COMP
840 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
842 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
843 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
844 fprintf(stdout, "Generator as octet string, compressed form:\n ");
845 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
848 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
850 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
851 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
852 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n ");
853 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
855 /* Change test based on whether binary point compression is enabled or not. */
856 #ifdef OPENSSL_EC_BIN_PT_COMP
857 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
859 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
860 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
861 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n ");
862 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
865 fprintf(stdout, "\n");
867 if (!EC_POINT_invert(group, P, ctx)) ABORT;
868 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
871 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
875 "0800000000000000000000000000000000000000C9",
878 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
879 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
881 "04000000000000000000020108A2E0CC0D99F8A5EF",
887 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
891 "0800000000000000000000000000000000000000C9",
893 "020A601907B8C953CA1481EB10512F78744A3205FD",
894 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
895 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
897 "040000000000000000000292FE77E70C12A4234C33",
903 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
907 "020000000000000000000000000000000000000004000000000000000001",
910 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
911 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
913 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
919 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
923 "020000000000000000000000000000000000000004000000000000000001",
924 "000000000000000000000000000000000000000000000000000000000001",
925 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
926 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
927 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
929 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
935 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
939 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
942 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
943 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
945 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
951 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
955 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
956 "000000000000000000000000000000000000000000000000000000000000000000000001",
957 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
958 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
959 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
961 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
967 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
971 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
974 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
975 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
977 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
983 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
987 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
988 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
989 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
990 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
991 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
993 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
999 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
1003 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1006 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1007 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1009 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1015 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
1019 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1020 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1021 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1022 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1023 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1025 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1031 /* more tests using the last curve */
1033 if (!EC_POINT_copy(Q, P)) ABORT;
1034 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
1035 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
1036 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
1037 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
1039 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
1040 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
1041 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
1044 const EC_POINT *points[3];
1045 const BIGNUM *scalars[3];
1047 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
1052 if (!BN_add(y, z, BN_value_one())) ABORT;
1053 if (BN_is_odd(y)) ABORT;
1054 if (!BN_rshift1(y, y)) ABORT;
1055 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
1058 fprintf(stdout, "combined multiplication ...");
1061 /* z is still the group order */
1062 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
1063 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
1064 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
1065 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
1067 fprintf(stdout, ".");
1070 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
1071 if (!BN_add(z, z, y)) ABORT;
1074 scalars[1] = z; /* z = -(order + y) */
1076 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
1077 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1079 fprintf(stdout, ".");
1082 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
1083 if (!BN_add(z, x, y)) ABORT;
1087 scalars[2] = z; /* z = -(x+y) */
1089 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
1090 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1092 fprintf(stdout, " ok\n\n");
1097 timings(C2_K163, 0, ctx);
1098 timings(C2_K163, 1, ctx);
1099 timings(C2_B163, 0, ctx);
1100 timings(C2_B163, 1, ctx);
1101 timings(C2_K233, 0, ctx);
1102 timings(C2_K233, 1, ctx);
1103 timings(C2_B233, 0, ctx);
1104 timings(C2_B233, 1, ctx);
1105 timings(C2_K283, 0, ctx);
1106 timings(C2_K283, 1, ctx);
1107 timings(C2_B283, 0, ctx);
1108 timings(C2_B283, 1, ctx);
1109 timings(C2_K409, 0, ctx);
1110 timings(C2_K409, 1, ctx);
1111 timings(C2_B409, 0, ctx);
1112 timings(C2_B409, 1, ctx);
1113 timings(C2_K571, 0, ctx);
1114 timings(C2_K571, 1, ctx);
1115 timings(C2_B571, 0, ctx);
1116 timings(C2_B571, 1, ctx);
1122 BN_free(p); BN_free(a); BN_free(b);
1123 EC_GROUP_free(group);
1127 BN_free(x); BN_free(y); BN_free(z); BN_free(cof);
1129 if (C2_K163) EC_GROUP_free(C2_K163);
1130 if (C2_B163) EC_GROUP_free(C2_B163);
1131 if (C2_K233) EC_GROUP_free(C2_K233);
1132 if (C2_B233) EC_GROUP_free(C2_B233);
1133 if (C2_K283) EC_GROUP_free(C2_K283);
1134 if (C2_B283) EC_GROUP_free(C2_B283);
1135 if (C2_K409) EC_GROUP_free(C2_K409);
1136 if (C2_B409) EC_GROUP_free(C2_B409);
1137 if (C2_K571) EC_GROUP_free(C2_K571);
1138 if (C2_B571) EC_GROUP_free(C2_B571);
1142 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
1144 int main(int argc, char *argv[])
1147 /* enable memory leak checking unless explicitly disabled */
1148 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
1150 CRYPTO_malloc_debug_init();
1151 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL);
1155 /* OPENSSL_DEBUG_MEMORY=off */
1156 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
1158 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
1159 ERR_load_crypto_strings();
1161 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
1163 prime_field_tests();
1165 char2_field_tests();
1168 CRYPTO_cleanup_all_ex_data();
1170 ERR_remove_state(0);
1171 CRYPTO_mem_leaks_fp(stderr);