1 /* crypto/ec/ectest.c */
2 /* ====================================================================
3 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in
14 * the documentation and/or other materials provided with the
17 * 3. All advertising materials mentioning features or use of this
18 * software must display the following acknowledgment:
19 * "This product includes software developed by the OpenSSL Project
20 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
22 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
23 * endorse or promote products derived from this software without
24 * prior written permission. For written permission, please contact
25 * openssl-core@openssl.org.
27 * 5. Products derived from this software may not be called "OpenSSL"
28 * nor may "OpenSSL" appear in their names without prior written
29 * permission of the OpenSSL Project.
31 * 6. Redistributions of any form whatsoever must retain the following
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
36 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
37 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
38 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
39 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
40 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
41 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
42 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
43 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
44 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
45 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
46 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
47 * OF THE POSSIBILITY OF SUCH DAMAGE.
48 * ====================================================================
50 * This product includes cryptographic software written by Eric Young
51 * (eay@cryptsoft.com). This product includes software written by Tim
52 * Hudson (tjh@cryptsoft.com).
68 int main(int argc
, char * argv
[]) { puts("Elliptic curves are disabled."); return 0; }
72 #include <openssl/ec.h>
73 #ifndef OPENSSL_NO_ENGINE
74 #include <openssl/engine.h>
76 #include <openssl/err.h>
80 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
81 ERR_print_errors_fp(stderr); \
86 static void timings(EC_GROUP
*group
, int multi
, BN_CTX
*ctx
)
95 if (s
== NULL
|| s0
== NULL
) ABORT
;
97 if (!EC_GROUP_get_curve_GFp(group
, s
, NULL
, NULL
, ctx
)) ABORT
;
98 fprintf(stdout
, "Timings for %d bit prime, ", (int)BN_num_bits(s
));
99 if (!EC_GROUP_get_order(group
, s
, ctx
)) ABORT
;
100 fprintf(stdout
, "%d bit scalars ", (int)BN_num_bits(s
));
103 P
= EC_POINT_new(group
);
104 if (P
== NULL
) ABORT
;
105 EC_POINT_copy(P
, EC_GROUP_get0_generator(group
));
108 for (i
= 0; i
< 10; i
++)
110 if (!BN_pseudo_rand(s
, BN_num_bits(s
), 0, 0)) ABORT
;
113 if (!BN_pseudo_rand(s0
, BN_num_bits(s
), 0, 0)) ABORT
;
115 for (j
= 0; j
< 10; j
++)
117 if (!EC_POINT_mul(group
, P
, s
, multi
? P
: NULL
, multi
? s0
: NULL
, ctx
)) ABORT
;
119 fprintf(stdout
, ".");
122 fprintf(stdout
, "\n");
124 clck
= clock() - clck
;
126 #ifdef CLOCKS_PER_SEC
127 /* "To determine the time in seconds, the value returned
128 * by the clock function should be divided by the value
129 * of the macro CLOCKS_PER_SEC."
133 /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
134 * -- cc on NeXTstep/OpenStep */
135 # define UNIT "units"
136 # define CLOCKS_PER_SEC 1
139 fprintf(stdout
, "%i %s in %.2f " UNIT
"\n", i
*j
,
140 multi
? "s*P+t*Q operations" : "point multiplications",
141 (double)clck
/CLOCKS_PER_SEC
);
142 fprintf(stdout
, "average: %.4f " UNIT
"\n", (double)clck
/(CLOCKS_PER_SEC
*i
*j
));
150 int main(int argc
, char *argv
[])
155 EC_GROUP
*P_192
= NULL
, *P_224
= NULL
, *P_256
= NULL
, *P_384
= NULL
, *P_521
= NULL
;
158 unsigned char buf
[100];
162 /* enable memory leak checking unless explicitly disabled */
163 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL
) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
165 CRYPTO_malloc_debug_init();
166 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL
);
170 /* OPENSSL_DEBUG_MEMORY=off */
171 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
173 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON
);
174 ERR_load_crypto_strings();
184 if (!p
|| !a
|| !b
) ABORT
;
186 if (!BN_hex2bn(&p
, "17")) ABORT
;
187 if (!BN_hex2bn(&a
, "1")) ABORT
;
188 if (!BN_hex2bn(&b
, "1")) ABORT
;
190 group
= EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
191 * so that the library gets to choose the EC_METHOD */
194 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
198 tmp
= EC_GROUP_new(EC_GROUP_method_of(group
));
200 if (!EC_GROUP_copy(tmp
, group
));
201 EC_GROUP_free(group
);
205 if (!EC_GROUP_get_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
207 fprintf(stdout
, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
208 BN_print_fp(stdout
, p
);
209 fprintf(stdout
, ")\n a = 0x");
210 BN_print_fp(stdout
, a
);
211 fprintf(stdout
, "\n b = 0x");
212 BN_print_fp(stdout
, b
);
213 fprintf(stdout
, "\n");
215 P
= EC_POINT_new(group
);
216 Q
= EC_POINT_new(group
);
217 R
= EC_POINT_new(group
);
218 if (!P
|| !Q
|| !R
) ABORT
;
220 if (!EC_POINT_set_to_infinity(group
, P
)) ABORT
;
221 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
224 if (!EC_POINT_oct2point(group
, Q
, buf
, 1, ctx
)) ABORT
;
226 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
)) ABORT
;
227 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
232 if (!x
|| !y
|| !z
) ABORT
;
234 if (!BN_hex2bn(&x
, "D")) ABORT
;
235 if (!EC_POINT_set_compressed_coordinates_GFp(group
, Q
, x
, 1, ctx
)) ABORT
;
236 if (!EC_POINT_is_on_curve(group
, Q
, ctx
))
238 if (!EC_POINT_get_affine_coordinates_GFp(group
, Q
, x
, y
, ctx
)) ABORT
;
239 fprintf(stderr
, "Point is not on curve: x = 0x");
240 BN_print_fp(stderr
, x
);
241 fprintf(stderr
, ", y = 0x");
242 BN_print_fp(stderr
, y
);
243 fprintf(stderr
, "\n");
247 fprintf(stdout
, "A cyclic subgroup:\n");
253 if (EC_POINT_is_at_infinity(group
, P
))
254 fprintf(stdout
, " point at infinity\n");
257 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
259 fprintf(stdout
, " x = 0x");
260 BN_print_fp(stdout
, x
);
261 fprintf(stdout
, ", y = 0x");
262 BN_print_fp(stdout
, y
);
263 fprintf(stdout
, "\n");
266 if (!EC_POINT_copy(R
, P
)) ABORT
;
267 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
)) ABORT
;
276 if (!EC_POINTs_make_affine(group
, 2, points
, ctx
)) ABORT
;
281 while (!EC_POINT_is_at_infinity(group
, P
));
283 if (!EC_POINT_add(group
, P
, Q
, R
, ctx
)) ABORT
;
284 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
286 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_COMPRESSED
, buf
, sizeof buf
, ctx
);
288 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
289 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
290 fprintf(stdout
, "Generator as octect string, compressed form:\n ");
291 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
293 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_UNCOMPRESSED
, buf
, sizeof buf
, ctx
);
295 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
296 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
297 fprintf(stdout
, "\nGenerator as octect string, uncompressed form:\n ");
298 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
300 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_HYBRID
, buf
, sizeof buf
, ctx
);
302 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
303 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
304 fprintf(stdout
, "\nGenerator as octect string, hybrid form:\n ");
305 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
307 if (!EC_POINT_get_Jprojective_coordinates_GFp(group
, R
, x
, y
, z
, ctx
)) ABORT
;
308 fprintf(stdout
, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
309 BN_print_fp(stdout
, x
);
310 fprintf(stdout
, ", Y = 0x");
311 BN_print_fp(stdout
, y
);
312 fprintf(stdout
, ", Z = 0x");
313 BN_print_fp(stdout
, z
);
314 fprintf(stdout
, "\n");
316 if (!EC_POINT_invert(group
, P
, ctx
)) ABORT
;
317 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
)) ABORT
;
320 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
322 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT
;
323 if (1 != BN_is_prime(p
, BN_prime_checks
, 0, ctx
, NULL
)) ABORT
;
324 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT
;
325 if (!BN_hex2bn(&b
, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT
;
326 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
328 if (!BN_hex2bn(&x
, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT
;
329 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
)) ABORT
;
330 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
331 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT
;
332 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
334 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
335 fprintf(stdout
, "\nNIST curve P-192 -- Generator:\n x = 0x");
336 BN_print_fp(stdout
, x
);
337 fprintf(stdout
, "\n y = 0x");
338 BN_print_fp(stdout
, y
);
339 fprintf(stdout
, "\n");
340 /* G_y value taken from the standard: */
341 if (!BN_hex2bn(&z
, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT
;
342 if (0 != BN_cmp(y
, z
)) ABORT
;
344 fprintf(stdout
, "verify group order ...");
346 if (!EC_GROUP_get_order(group
, z
, ctx
)) ABORT
;
347 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
348 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
349 fprintf(stdout
, ".");
351 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
352 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
353 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
354 fprintf(stdout
, " ok\n");
356 if (!(P_192
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
357 if (!EC_GROUP_copy(P_192
, group
)) ABORT
;
360 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
362 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT
;
363 if (1 != BN_is_prime(p
, BN_prime_checks
, 0, ctx
, NULL
)) ABORT
;
364 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT
;
365 if (!BN_hex2bn(&b
, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT
;
366 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
368 if (!BN_hex2bn(&x
, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT
;
369 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 0, ctx
)) ABORT
;
370 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
371 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT
;
372 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
374 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
375 fprintf(stdout
, "\nNIST curve P-224 -- Generator:\n x = 0x");
376 BN_print_fp(stdout
, x
);
377 fprintf(stdout
, "\n y = 0x");
378 BN_print_fp(stdout
, y
);
379 fprintf(stdout
, "\n");
380 /* G_y value taken from the standard: */
381 if (!BN_hex2bn(&z
, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT
;
382 if (0 != BN_cmp(y
, z
)) ABORT
;
384 fprintf(stdout
, "verify group order ...");
386 if (!EC_GROUP_get_order(group
, z
, ctx
)) ABORT
;
387 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
388 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
389 fprintf(stdout
, ".");
391 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
392 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
393 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
394 fprintf(stdout
, " ok\n");
396 if (!(P_224
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
397 if (!EC_GROUP_copy(P_224
, group
)) ABORT
;
400 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
402 if (!BN_hex2bn(&p
, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT
;
403 if (1 != BN_is_prime(p
, BN_prime_checks
, 0, ctx
, NULL
)) ABORT
;
404 if (!BN_hex2bn(&a
, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT
;
405 if (!BN_hex2bn(&b
, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT
;
406 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
408 if (!BN_hex2bn(&x
, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT
;
409 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
)) ABORT
;
410 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
411 if (!BN_hex2bn(&z
, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
412 "84F3B9CAC2FC632551")) ABORT
;
413 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
415 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
416 fprintf(stdout
, "\nNIST curve P-256 -- Generator:\n x = 0x");
417 BN_print_fp(stdout
, x
);
418 fprintf(stdout
, "\n y = 0x");
419 BN_print_fp(stdout
, y
);
420 fprintf(stdout
, "\n");
421 /* G_y value taken from the standard: */
422 if (!BN_hex2bn(&z
, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT
;
423 if (0 != BN_cmp(y
, z
)) ABORT
;
425 fprintf(stdout
, "verify group order ...");
427 if (!EC_GROUP_get_order(group
, z
, ctx
)) ABORT
;
428 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
429 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
430 fprintf(stdout
, ".");
432 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
433 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
434 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
435 fprintf(stdout
, " ok\n");
437 if (!(P_256
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
438 if (!EC_GROUP_copy(P_256
, group
)) ABORT
;
441 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
443 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
444 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT
;
445 if (1 != BN_is_prime(p
, BN_prime_checks
, 0, ctx
, NULL
)) ABORT
;
446 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
447 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT
;
448 if (!BN_hex2bn(&b
, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
449 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT
;
450 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
452 if (!BN_hex2bn(&x
, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
453 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT
;
454 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
)) ABORT
;
455 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
456 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
457 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT
;
458 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
460 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
461 fprintf(stdout
, "\nNIST curve P-384 -- Generator:\n x = 0x");
462 BN_print_fp(stdout
, x
);
463 fprintf(stdout
, "\n y = 0x");
464 BN_print_fp(stdout
, y
);
465 fprintf(stdout
, "\n");
466 /* G_y value taken from the standard: */
467 if (!BN_hex2bn(&z
, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
468 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT
;
469 if (0 != BN_cmp(y
, z
)) ABORT
;
471 fprintf(stdout
, "verify group order ...");
473 if (!EC_GROUP_get_order(group
, z
, ctx
)) ABORT
;
474 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
475 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
476 fprintf(stdout
, ".");
478 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
479 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
480 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
481 fprintf(stdout
, " ok\n");
483 if (!(P_384
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
484 if (!EC_GROUP_copy(P_384
, group
)) ABORT
;
487 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
489 if (!BN_hex2bn(&p
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
490 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
491 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT
;
492 if (1 != BN_is_prime(p
, BN_prime_checks
, 0, ctx
, NULL
)) ABORT
;
493 if (!BN_hex2bn(&a
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
494 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
495 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT
;
496 if (!BN_hex2bn(&b
, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
497 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
498 "DF883D2C34F1EF451FD46B503F00")) ABORT
;
499 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
501 if (!BN_hex2bn(&x
, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
502 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
503 "3C1856A429BF97E7E31C2E5BD66")) ABORT
;
504 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 0, ctx
)) ABORT
;
505 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
506 if (!BN_hex2bn(&z
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
507 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
508 "C9B8899C47AEBB6FB71E91386409")) ABORT
;
509 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
511 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
512 fprintf(stdout
, "\nNIST curve P-521 -- Generator:\n x = 0x");
513 BN_print_fp(stdout
, x
);
514 fprintf(stdout
, "\n y = 0x");
515 BN_print_fp(stdout
, y
);
516 fprintf(stdout
, "\n");
517 /* G_y value taken from the standard: */
518 if (!BN_hex2bn(&z
, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
519 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
520 "7086A272C24088BE94769FD16650")) ABORT
;
521 if (0 != BN_cmp(y
, z
)) ABORT
;
523 fprintf(stdout
, "verify group order ...");
525 if (!EC_GROUP_get_order(group
, z
, ctx
)) ABORT
;
526 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
527 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
528 fprintf(stdout
, ".");
530 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
531 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
532 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
533 fprintf(stdout
, " ok\n");
535 if (!(P_521
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
536 if (!EC_GROUP_copy(P_521
, group
)) ABORT
;
539 /* more tests using the last curve */
541 if (!EC_POINT_copy(Q
, P
)) ABORT
;
542 if (EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
543 if (!EC_POINT_dbl(group
, P
, P
, ctx
)) ABORT
;
544 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
545 if (!EC_POINT_invert(group
, Q
, ctx
)) ABORT
; /* P = -2Q */
547 if (!EC_POINT_add(group
, R
, P
, Q
, ctx
)) ABORT
;
548 if (!EC_POINT_add(group
, R
, R
, Q
, ctx
)) ABORT
;
549 if (!EC_POINT_is_at_infinity(group
, R
)) ABORT
; /* R = P + 2Q */
552 const EC_POINT
*points
[3];
553 const BIGNUM
*scalars
[3];
555 if (EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
560 if (!BN_add(y
, z
, BN_value_one())) ABORT
;
561 if (BN_is_odd(y
)) ABORT
;
562 if (!BN_rshift1(y
, y
)) ABORT
;
563 scalars
[0] = y
; /* (group order + 1)/2, so y*Q + y*Q = Q */
566 fprintf(stdout
, "combined multiplication ...");
569 /* z is still the group order */
570 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
)) ABORT
;
571 if (!EC_POINTs_mul(group
, R
, z
, 2, points
, scalars
, ctx
)) ABORT
;
572 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
)) ABORT
;
573 if (0 != EC_POINT_cmp(group
, R
, Q
, ctx
)) ABORT
;
575 fprintf(stdout
, ".");
578 if (!BN_pseudo_rand(y
, BN_num_bits(y
), 0, 0)) ABORT
;
579 if (!BN_add(z
, z
, y
)) ABORT
;
582 scalars
[1] = z
; /* z = -(order + y) */
584 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
)) ABORT
;
585 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
587 fprintf(stdout
, ".");
590 if (!BN_pseudo_rand(x
, BN_num_bits(y
) - 1, 0, 0)) ABORT
;
591 if (!BN_add(z
, x
, y
)) ABORT
;
595 scalars
[2] = z
; /* z = -(x+y) */
597 if (!EC_POINTs_mul(group
, P
, NULL
, 3, points
, scalars
, ctx
)) ABORT
;
598 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
600 fprintf(stdout
, " ok\n\n");
605 timings(P_192
, 0, ctx
);
606 timings(P_192
, 1, ctx
);
607 timings(P_224
, 0, ctx
);
608 timings(P_224
, 1, ctx
);
609 timings(P_256
, 0, ctx
);
610 timings(P_256
, 1, ctx
);
611 timings(P_384
, 0, ctx
);
612 timings(P_384
, 1, ctx
);
613 timings(P_521
, 0, ctx
);
614 timings(P_521
, 1, ctx
);
620 BN_free(p
); BN_free(a
); BN_free(b
);
621 EC_GROUP_free(group
);
625 BN_free(x
); BN_free(y
); BN_free(z
);
627 if (P_192
) EC_GROUP_free(P_192
);
628 if (P_224
) EC_GROUP_free(P_224
);
629 if (P_256
) EC_GROUP_free(P_256
);
630 if (P_384
) EC_GROUP_free(P_384
);
631 if (P_521
) EC_GROUP_free(P_521
);
633 #ifndef OPENSSL_NO_ENGINE
636 CRYPTO_cleanup_all_ex_data();
639 CRYPTO_mem_leaks_fp(stderr
);