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>
100 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
101 ERR_print_errors_fp(stderr); \
105 void prime_field_tests(void);
106 void char2_field_tests(void);
107 void internal_curve_test(void);
109 #define TIMING_BASE_PT 0
110 #define TIMING_RAND_PT 1
111 #define TIMING_SIMUL 2
114 static void timings(EC_GROUP
*group
, int type
, BN_CTX
*ctx
)
119 BIGNUM
*r
[10], *r0
[10];
123 if (s
== NULL
) ABORT
;
125 fprintf(stdout
, "Timings for %d-bit field, ", EC_GROUP_get_degree(group
));
126 if (!EC_GROUP_get_order(group
, s
, ctx
)) ABORT
;
127 fprintf(stdout
, "%d-bit scalars ", (int)BN_num_bits(s
));
130 P
= EC_POINT_new(group
);
131 if (P
== NULL
) ABORT
;
132 EC_POINT_copy(P
, EC_GROUP_get0_generator(group
));
134 for (i
= 0; i
< 10; i
++)
136 if ((r
[i
] = BN_new()) == NULL
) ABORT
;
137 if (!BN_pseudo_rand(r
[i
], BN_num_bits(s
), 0, 0)) ABORT
;
138 if (type
!= TIMING_BASE_PT
)
140 if ((r0
[i
] = BN_new()) == NULL
) ABORT
;
141 if (!BN_pseudo_rand(r0
[i
], BN_num_bits(s
), 0, 0)) ABORT
;
146 for (i
= 0; i
< 10; i
++)
148 for (j
= 0; j
< 10; j
++)
150 if (!EC_POINT_mul(group
, P
, (type
!= TIMING_RAND_PT
) ? r
[i
] : NULL
,
151 (type
!= TIMING_BASE_PT
) ? P
: NULL
, (type
!= TIMING_BASE_PT
) ? r0
[i
] : NULL
, ctx
)) ABORT
;
154 clck
= clock() - clck
;
156 fprintf(stdout
, "\n");
158 #ifdef CLOCKS_PER_SEC
159 /* "To determine the time in seconds, the value returned
160 * by the clock function should be divided by the value
161 * of the macro CLOCKS_PER_SEC."
165 /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
166 * -- cc on NeXTstep/OpenStep */
167 # define UNIT "units"
168 # define CLOCKS_PER_SEC 1
171 if (type
== TIMING_BASE_PT
) {
172 fprintf(stdout
, "%i %s in %.2f " UNIT
"\n", i
*j
,
173 "base point multiplications", (double)clck
/CLOCKS_PER_SEC
);
174 } else if (type
== TIMING_RAND_PT
) {
175 fprintf(stdout
, "%i %s in %.2f " UNIT
"\n", i
*j
,
176 "random point multiplications", (double)clck
/CLOCKS_PER_SEC
);
177 } else if (type
== TIMING_SIMUL
) {
178 fprintf(stdout
, "%i %s in %.2f " UNIT
"\n", i
*j
,
179 "s*P+t*Q operations", (double)clck
/CLOCKS_PER_SEC
);
181 fprintf(stdout
, "average: %.4f " UNIT
"\n", (double)clck
/(CLOCKS_PER_SEC
*i
*j
));
185 for (i
= 0; i
< 10; i
++)
188 if (type
!= TIMING_BASE_PT
) BN_free(r0
[i
]);
193 void prime_field_tests()
198 EC_GROUP
*P_160
= NULL
, *P_192
= NULL
, *P_224
= NULL
, *P_256
= NULL
, *P_384
= NULL
, *P_521
= NULL
;
201 unsigned char buf
[100];
213 if (!p
|| !a
|| !b
) ABORT
;
215 if (!BN_hex2bn(&p
, "17")) ABORT
;
216 if (!BN_hex2bn(&a
, "1")) ABORT
;
217 if (!BN_hex2bn(&b
, "1")) ABORT
;
219 group
= EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
220 * so that the library gets to choose the EC_METHOD */
223 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
227 tmp
= EC_GROUP_new(EC_GROUP_method_of(group
));
229 if (!EC_GROUP_copy(tmp
, group
));
230 EC_GROUP_free(group
);
234 if (!EC_GROUP_get_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
236 fprintf(stdout
, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
237 BN_print_fp(stdout
, p
);
238 fprintf(stdout
, ")\n a = 0x");
239 BN_print_fp(stdout
, a
);
240 fprintf(stdout
, "\n b = 0x");
241 BN_print_fp(stdout
, b
);
242 fprintf(stdout
, "\n");
244 P
= EC_POINT_new(group
);
245 Q
= EC_POINT_new(group
);
246 R
= EC_POINT_new(group
);
247 if (!P
|| !Q
|| !R
) ABORT
;
249 if (!EC_POINT_set_to_infinity(group
, P
)) ABORT
;
250 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
253 if (!EC_POINT_oct2point(group
, Q
, buf
, 1, ctx
)) ABORT
;
255 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
)) ABORT
;
256 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
261 if (!x
|| !y
|| !z
) ABORT
;
263 if (!BN_hex2bn(&x
, "D")) ABORT
;
264 if (!EC_POINT_set_compressed_coordinates_GFp(group
, Q
, x
, 1, ctx
)) ABORT
;
265 if (!EC_POINT_is_on_curve(group
, Q
, ctx
))
267 if (!EC_POINT_get_affine_coordinates_GFp(group
, Q
, x
, y
, ctx
)) ABORT
;
268 fprintf(stderr
, "Point is not on curve: x = 0x");
269 BN_print_fp(stderr
, x
);
270 fprintf(stderr
, ", y = 0x");
271 BN_print_fp(stderr
, y
);
272 fprintf(stderr
, "\n");
276 fprintf(stdout
, "A cyclic subgroup:\n");
282 if (EC_POINT_is_at_infinity(group
, P
))
283 fprintf(stdout
, " point at infinity\n");
286 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
288 fprintf(stdout
, " x = 0x");
289 BN_print_fp(stdout
, x
);
290 fprintf(stdout
, ", y = 0x");
291 BN_print_fp(stdout
, y
);
292 fprintf(stdout
, "\n");
295 if (!EC_POINT_copy(R
, P
)) ABORT
;
296 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
)) ABORT
;
305 if (!EC_POINTs_make_affine(group
, 2, points
, ctx
)) ABORT
;
310 while (!EC_POINT_is_at_infinity(group
, P
));
312 if (!EC_POINT_add(group
, P
, Q
, R
, ctx
)) ABORT
;
313 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
315 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_COMPRESSED
, buf
, sizeof buf
, ctx
);
317 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
318 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
319 fprintf(stdout
, "Generator as octect string, compressed form:\n ");
320 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
322 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_UNCOMPRESSED
, buf
, sizeof buf
, ctx
);
324 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
325 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
326 fprintf(stdout
, "\nGenerator as octect string, uncompressed form:\n ");
327 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
329 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_HYBRID
, buf
, sizeof buf
, ctx
);
331 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
332 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
333 fprintf(stdout
, "\nGenerator as octect string, hybrid form:\n ");
334 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
336 if (!EC_POINT_get_Jprojective_coordinates_GFp(group
, R
, x
, y
, z
, ctx
)) ABORT
;
337 fprintf(stdout
, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
338 BN_print_fp(stdout
, x
);
339 fprintf(stdout
, ", Y = 0x");
340 BN_print_fp(stdout
, y
);
341 fprintf(stdout
, ", Z = 0x");
342 BN_print_fp(stdout
, z
);
343 fprintf(stdout
, "\n");
345 if (!EC_POINT_invert(group
, P
, ctx
)) ABORT
;
346 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
)) ABORT
;
349 /* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000)
350 * -- not a NIST curve, but commonly used */
352 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) ABORT
;
353 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
)) ABORT
;
354 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) ABORT
;
355 if (!BN_hex2bn(&b
, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) ABORT
;
356 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
358 if (!BN_hex2bn(&x
, "4A96B5688EF573284664698968C38BB913CBFC82")) ABORT
;
359 if (!BN_hex2bn(&y
, "23a628553168947d59dcc912042351377ac5fb32")) ABORT
;
360 if (!EC_POINT_set_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
361 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
362 if (!BN_hex2bn(&z
, "0100000000000000000001F4C8F927AED3CA752257")) ABORT
;
363 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
365 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
366 fprintf(stdout
, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x");
367 BN_print_fp(stdout
, x
);
368 fprintf(stdout
, "\n y = 0x");
369 BN_print_fp(stdout
, y
);
370 fprintf(stdout
, "\n");
371 /* G_y value taken from the standard: */
372 if (!BN_hex2bn(&z
, "23a628553168947d59dcc912042351377ac5fb32")) ABORT
;
373 if (0 != BN_cmp(y
, z
)) ABORT
;
375 fprintf(stdout
, "verify degree ...");
376 if (EC_GROUP_get_degree(group
) != 160) ABORT
;
377 fprintf(stdout
, " ok\n");
379 fprintf(stdout
, "verify group order ...");
381 if (!EC_GROUP_get_order(group
, z
, ctx
)) ABORT
;
382 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
383 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
384 fprintf(stdout
, ".");
386 if (!EC_GROUP_precompute_mult(group
, 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
, " ok\n");
391 if (!(P_160
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
392 if (!EC_GROUP_copy(P_160
, group
)) ABORT
;
395 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
397 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT
;
398 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
)) ABORT
;
399 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT
;
400 if (!BN_hex2bn(&b
, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT
;
401 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
403 if (!BN_hex2bn(&x
, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT
;
404 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
)) ABORT
;
405 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
406 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) 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
, "\nNIST curve P-192 -- 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
, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT
;
417 if (0 != BN_cmp(y
, z
)) ABORT
;
419 fprintf(stdout
, "verify degree ...");
420 if (EC_GROUP_get_degree(group
) != 192) ABORT
;
421 fprintf(stdout
, " ok\n");
423 fprintf(stdout
, "verify group order ...");
425 if (!EC_GROUP_get_order(group
, z
, ctx
)) ABORT
;
426 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
427 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
428 fprintf(stdout
, ".");
430 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
431 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
432 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
433 fprintf(stdout
, " ok\n");
435 if (!(P_192
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
436 if (!EC_GROUP_copy(P_192
, group
)) ABORT
;
439 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
441 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT
;
442 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
)) ABORT
;
443 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT
;
444 if (!BN_hex2bn(&b
, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT
;
445 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
447 if (!BN_hex2bn(&x
, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT
;
448 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 0, ctx
)) ABORT
;
449 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
450 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT
;
451 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
453 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
454 fprintf(stdout
, "\nNIST curve P-224 -- Generator:\n x = 0x");
455 BN_print_fp(stdout
, x
);
456 fprintf(stdout
, "\n y = 0x");
457 BN_print_fp(stdout
, y
);
458 fprintf(stdout
, "\n");
459 /* G_y value taken from the standard: */
460 if (!BN_hex2bn(&z
, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT
;
461 if (0 != BN_cmp(y
, z
)) ABORT
;
463 fprintf(stdout
, "verify degree ...");
464 if (EC_GROUP_get_degree(group
) != 224) ABORT
;
465 fprintf(stdout
, " ok\n");
467 fprintf(stdout
, "verify group order ...");
469 if (!EC_GROUP_get_order(group
, z
, ctx
)) ABORT
;
470 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
471 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
472 fprintf(stdout
, ".");
474 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
475 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
476 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
477 fprintf(stdout
, " ok\n");
479 if (!(P_224
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
480 if (!EC_GROUP_copy(P_224
, group
)) ABORT
;
483 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
485 if (!BN_hex2bn(&p
, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT
;
486 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
)) ABORT
;
487 if (!BN_hex2bn(&a
, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT
;
488 if (!BN_hex2bn(&b
, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT
;
489 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
491 if (!BN_hex2bn(&x
, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT
;
492 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
)) ABORT
;
493 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
494 if (!BN_hex2bn(&z
, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
495 "84F3B9CAC2FC632551")) ABORT
;
496 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
498 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
499 fprintf(stdout
, "\nNIST curve P-256 -- Generator:\n x = 0x");
500 BN_print_fp(stdout
, x
);
501 fprintf(stdout
, "\n y = 0x");
502 BN_print_fp(stdout
, y
);
503 fprintf(stdout
, "\n");
504 /* G_y value taken from the standard: */
505 if (!BN_hex2bn(&z
, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT
;
506 if (0 != BN_cmp(y
, z
)) ABORT
;
508 fprintf(stdout
, "verify degree ...");
509 if (EC_GROUP_get_degree(group
) != 256) ABORT
;
510 fprintf(stdout
, " ok\n");
512 fprintf(stdout
, "verify group order ...");
514 if (!EC_GROUP_get_order(group
, z
, ctx
)) ABORT
;
515 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
516 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
517 fprintf(stdout
, ".");
519 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
520 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
521 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
522 fprintf(stdout
, " ok\n");
524 if (!(P_256
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
525 if (!EC_GROUP_copy(P_256
, group
)) ABORT
;
528 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
530 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
531 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT
;
532 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
)) ABORT
;
533 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
534 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT
;
535 if (!BN_hex2bn(&b
, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
536 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT
;
537 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
539 if (!BN_hex2bn(&x
, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
540 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT
;
541 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
)) ABORT
;
542 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
543 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
544 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT
;
545 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
547 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
548 fprintf(stdout
, "\nNIST curve P-384 -- Generator:\n x = 0x");
549 BN_print_fp(stdout
, x
);
550 fprintf(stdout
, "\n y = 0x");
551 BN_print_fp(stdout
, y
);
552 fprintf(stdout
, "\n");
553 /* G_y value taken from the standard: */
554 if (!BN_hex2bn(&z
, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
555 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT
;
556 if (0 != BN_cmp(y
, z
)) ABORT
;
558 fprintf(stdout
, "verify degree ...");
559 if (EC_GROUP_get_degree(group
) != 384) ABORT
;
560 fprintf(stdout
, " ok\n");
562 fprintf(stdout
, "verify group order ...");
564 if (!EC_GROUP_get_order(group
, z
, ctx
)) ABORT
;
565 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
566 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
567 fprintf(stdout
, ".");
569 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
570 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
571 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
572 fprintf(stdout
, " ok\n");
574 if (!(P_384
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
575 if (!EC_GROUP_copy(P_384
, group
)) ABORT
;
578 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
580 if (!BN_hex2bn(&p
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
581 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
582 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT
;
583 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
)) ABORT
;
584 if (!BN_hex2bn(&a
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
585 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
586 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT
;
587 if (!BN_hex2bn(&b
, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
588 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
589 "DF883D2C34F1EF451FD46B503F00")) ABORT
;
590 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
592 if (!BN_hex2bn(&x
, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
593 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
594 "3C1856A429BF97E7E31C2E5BD66")) ABORT
;
595 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 0, ctx
)) ABORT
;
596 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
597 if (!BN_hex2bn(&z
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
598 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
599 "C9B8899C47AEBB6FB71E91386409")) ABORT
;
600 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
602 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
603 fprintf(stdout
, "\nNIST curve P-521 -- Generator:\n x = 0x");
604 BN_print_fp(stdout
, x
);
605 fprintf(stdout
, "\n y = 0x");
606 BN_print_fp(stdout
, y
);
607 fprintf(stdout
, "\n");
608 /* G_y value taken from the standard: */
609 if (!BN_hex2bn(&z
, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
610 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
611 "7086A272C24088BE94769FD16650")) ABORT
;
612 if (0 != BN_cmp(y
, z
)) ABORT
;
614 fprintf(stdout
, "verify degree ...");
615 if (EC_GROUP_get_degree(group
) != 521) ABORT
;
616 fprintf(stdout
, " ok\n");
618 fprintf(stdout
, "verify group order ...");
620 if (!EC_GROUP_get_order(group
, z
, ctx
)) ABORT
;
621 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
622 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
623 fprintf(stdout
, ".");
625 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
626 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
627 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
628 fprintf(stdout
, " ok\n");
630 if (!(P_521
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
631 if (!EC_GROUP_copy(P_521
, group
)) ABORT
;
634 /* more tests using the last curve */
636 if (!EC_POINT_copy(Q
, P
)) ABORT
;
637 if (EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
638 if (!EC_POINT_dbl(group
, P
, P
, ctx
)) ABORT
;
639 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
640 if (!EC_POINT_invert(group
, Q
, ctx
)) ABORT
; /* P = -2Q */
642 if (!EC_POINT_add(group
, R
, P
, Q
, ctx
)) ABORT
;
643 if (!EC_POINT_add(group
, R
, R
, Q
, ctx
)) ABORT
;
644 if (!EC_POINT_is_at_infinity(group
, R
)) ABORT
; /* R = P + 2Q */
647 const EC_POINT
*points
[3];
648 const BIGNUM
*scalars
[3];
650 if (EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
655 if (!BN_add(y
, z
, BN_value_one())) ABORT
;
656 if (BN_is_odd(y
)) ABORT
;
657 if (!BN_rshift1(y
, y
)) ABORT
;
658 scalars
[0] = y
; /* (group order + 1)/2, so y*Q + y*Q = Q */
661 fprintf(stdout
, "combined multiplication ...");
664 /* z is still the group order */
665 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
)) ABORT
;
666 if (!EC_POINTs_mul(group
, R
, z
, 2, points
, scalars
, ctx
)) ABORT
;
667 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
)) ABORT
;
668 if (0 != EC_POINT_cmp(group
, R
, Q
, ctx
)) ABORT
;
670 fprintf(stdout
, ".");
673 if (!BN_pseudo_rand(y
, BN_num_bits(y
), 0, 0)) ABORT
;
674 if (!BN_add(z
, z
, y
)) ABORT
;
677 scalars
[1] = z
; /* z = -(order + y) */
679 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
)) ABORT
;
680 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
682 fprintf(stdout
, ".");
685 if (!BN_pseudo_rand(x
, BN_num_bits(y
) - 1, 0, 0)) ABORT
;
686 if (!BN_add(z
, x
, y
)) ABORT
;
690 scalars
[2] = z
; /* z = -(x+y) */
692 if (!EC_POINTs_mul(group
, P
, NULL
, 3, points
, scalars
, ctx
)) ABORT
;
693 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
695 fprintf(stdout
, " ok\n\n");
700 timings(P_160
, TIMING_BASE_PT
, ctx
);
701 timings(P_160
, TIMING_RAND_PT
, ctx
);
702 timings(P_160
, TIMING_SIMUL
, ctx
);
703 timings(P_192
, TIMING_BASE_PT
, ctx
);
704 timings(P_192
, TIMING_RAND_PT
, ctx
);
705 timings(P_192
, TIMING_SIMUL
, ctx
);
706 timings(P_224
, TIMING_BASE_PT
, ctx
);
707 timings(P_224
, TIMING_RAND_PT
, ctx
);
708 timings(P_224
, TIMING_SIMUL
, ctx
);
709 timings(P_256
, TIMING_BASE_PT
, ctx
);
710 timings(P_256
, TIMING_RAND_PT
, ctx
);
711 timings(P_256
, TIMING_SIMUL
, ctx
);
712 timings(P_384
, TIMING_BASE_PT
, ctx
);
713 timings(P_384
, TIMING_RAND_PT
, ctx
);
714 timings(P_384
, TIMING_SIMUL
, ctx
);
715 timings(P_521
, TIMING_BASE_PT
, ctx
);
716 timings(P_521
, TIMING_RAND_PT
, ctx
);
717 timings(P_521
, TIMING_SIMUL
, ctx
);
723 BN_free(p
); BN_free(a
); BN_free(b
);
724 EC_GROUP_free(group
);
728 BN_free(x
); BN_free(y
); BN_free(z
);
730 if (P_160
) EC_GROUP_free(P_160
);
731 if (P_192
) EC_GROUP_free(P_192
);
732 if (P_224
) EC_GROUP_free(P_224
);
733 if (P_256
) EC_GROUP_free(P_256
);
734 if (P_384
) EC_GROUP_free(P_384
);
735 if (P_521
) EC_GROUP_free(P_521
);
739 /* Change test based on whether binary point compression is enabled or not. */
740 #ifdef OPENSSL_EC_BIN_PT_COMP
741 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
742 if (!BN_hex2bn(&x, _x)) ABORT; \
743 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
744 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
745 if (!BN_hex2bn(&z, _order)) ABORT; \
746 if (!BN_hex2bn(&cof, _cof)) ABORT; \
747 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
748 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
749 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
750 BN_print_fp(stdout, x); \
751 fprintf(stdout, "\n y = 0x"); \
752 BN_print_fp(stdout, y); \
753 fprintf(stdout, "\n"); \
754 /* G_y value taken from the standard: */ \
755 if (!BN_hex2bn(&z, _y)) ABORT; \
756 if (0 != BN_cmp(y, z)) ABORT;
758 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
759 if (!BN_hex2bn(&x, _x)) ABORT; \
760 if (!BN_hex2bn(&y, _y)) ABORT; \
761 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
762 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
763 if (!BN_hex2bn(&z, _order)) ABORT; \
764 if (!BN_hex2bn(&cof, _cof)) ABORT; \
765 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
766 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
767 BN_print_fp(stdout, x); \
768 fprintf(stdout, "\n y = 0x"); \
769 BN_print_fp(stdout, y); \
770 fprintf(stdout, "\n");
773 #define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
774 if (!BN_hex2bn(&p, _p)) ABORT; \
775 if (!BN_hex2bn(&a, _a)) ABORT; \
776 if (!BN_hex2bn(&b, _b)) ABORT; \
777 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
778 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
779 fprintf(stdout, "verify degree ..."); \
780 if (EC_GROUP_get_degree(group) != _degree) ABORT; \
781 fprintf(stdout, " ok\n"); \
782 fprintf(stdout, "verify group order ..."); \
784 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; \
785 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \
786 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \
787 fprintf(stdout, "."); \
789 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; \
790 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \
791 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \
792 fprintf(stdout, " ok\n"); \
793 if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \
794 if (!EC_GROUP_copy(_variable, group)) ABORT;
796 void char2_field_tests()
801 EC_GROUP
*C2_K163
= NULL
, *C2_K233
= NULL
, *C2_K283
= NULL
, *C2_K409
= NULL
, *C2_K571
= NULL
;
802 EC_GROUP
*C2_B163
= NULL
, *C2_B233
= NULL
, *C2_B283
= NULL
, *C2_B409
= NULL
, *C2_B571
= NULL
;
804 BIGNUM
*x
, *y
, *z
, *cof
;
805 unsigned char buf
[100];
817 if (!p
|| !a
|| !b
) ABORT
;
819 if (!BN_hex2bn(&p
, "13")) ABORT
;
820 if (!BN_hex2bn(&a
, "3")) ABORT
;
821 if (!BN_hex2bn(&b
, "1")) ABORT
;
823 group
= EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m
824 * so that the library gets to choose the EC_METHOD */
826 if (!EC_GROUP_set_curve_GF2m(group
, p
, a
, b
, ctx
)) ABORT
;
830 tmp
= EC_GROUP_new(EC_GROUP_method_of(group
));
832 if (!EC_GROUP_copy(tmp
, group
));
833 EC_GROUP_free(group
);
837 if (!EC_GROUP_get_curve_GF2m(group
, p
, a
, b
, ctx
)) ABORT
;
839 fprintf(stdout
, "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x");
840 BN_print_fp(stdout
, p
);
841 fprintf(stdout
, ")\n a = 0x");
842 BN_print_fp(stdout
, a
);
843 fprintf(stdout
, "\n b = 0x");
844 BN_print_fp(stdout
, b
);
845 fprintf(stdout
, "\n(0x... means binary polynomial)\n");
847 P
= EC_POINT_new(group
);
848 Q
= EC_POINT_new(group
);
849 R
= EC_POINT_new(group
);
850 if (!P
|| !Q
|| !R
) ABORT
;
852 if (!EC_POINT_set_to_infinity(group
, P
)) ABORT
;
853 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
856 if (!EC_POINT_oct2point(group
, Q
, buf
, 1, ctx
)) ABORT
;
858 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
)) ABORT
;
859 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
865 if (!x
|| !y
|| !z
|| !cof
) ABORT
;
867 if (!BN_hex2bn(&x
, "6")) ABORT
;
868 /* Change test based on whether binary point compression is enabled or not. */
869 #ifdef OPENSSL_EC_BIN_PT_COMP
870 if (!EC_POINT_set_compressed_coordinates_GF2m(group
, Q
, x
, 1, ctx
)) ABORT
;
872 if (!BN_hex2bn(&y
, "8")) ABORT
;
873 if (!EC_POINT_set_affine_coordinates_GF2m(group
, Q
, x
, y
, ctx
)) ABORT
;
875 if (!EC_POINT_is_on_curve(group
, Q
, ctx
))
877 /* Change test based on whether binary point compression is enabled or not. */
878 #ifdef OPENSSL_EC_BIN_PT_COMP
879 if (!EC_POINT_get_affine_coordinates_GF2m(group
, Q
, x
, y
, ctx
)) ABORT
;
881 fprintf(stderr
, "Point is not on curve: x = 0x");
882 BN_print_fp(stderr
, x
);
883 fprintf(stderr
, ", y = 0x");
884 BN_print_fp(stderr
, y
);
885 fprintf(stderr
, "\n");
889 fprintf(stdout
, "A cyclic subgroup:\n");
895 if (EC_POINT_is_at_infinity(group
, P
))
896 fprintf(stdout
, " point at infinity\n");
899 if (!EC_POINT_get_affine_coordinates_GF2m(group
, P
, x
, y
, ctx
)) ABORT
;
901 fprintf(stdout
, " x = 0x");
902 BN_print_fp(stdout
, x
);
903 fprintf(stdout
, ", y = 0x");
904 BN_print_fp(stdout
, y
);
905 fprintf(stdout
, "\n");
908 if (!EC_POINT_copy(R
, P
)) ABORT
;
909 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
)) ABORT
;
911 while (!EC_POINT_is_at_infinity(group
, P
));
913 if (!EC_POINT_add(group
, P
, Q
, R
, ctx
)) ABORT
;
914 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
916 /* Change test based on whether binary point compression is enabled or not. */
917 #ifdef OPENSSL_EC_BIN_PT_COMP
918 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_COMPRESSED
, buf
, sizeof buf
, ctx
);
920 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
921 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
922 fprintf(stdout
, "Generator as octet string, compressed form:\n ");
923 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
926 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_UNCOMPRESSED
, buf
, sizeof buf
, ctx
);
928 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
929 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
930 fprintf(stdout
, "\nGenerator as octet string, uncompressed form:\n ");
931 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
933 /* Change test based on whether binary point compression is enabled or not. */
934 #ifdef OPENSSL_EC_BIN_PT_COMP
935 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_HYBRID
, buf
, sizeof buf
, ctx
);
937 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
938 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
939 fprintf(stdout
, "\nGenerator as octet string, hybrid form:\n ");
940 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
943 fprintf(stdout
, "\n");
945 if (!EC_POINT_invert(group
, P
, ctx
)) ABORT
;
946 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
)) ABORT
;
949 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
953 "0800000000000000000000000000000000000000C9",
956 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
957 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
959 "04000000000000000000020108A2E0CC0D99F8A5EF",
965 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
969 "0800000000000000000000000000000000000000C9",
971 "020A601907B8C953CA1481EB10512F78744A3205FD",
972 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
973 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
975 "040000000000000000000292FE77E70C12A4234C33",
981 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
985 "020000000000000000000000000000000000000004000000000000000001",
988 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
989 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
991 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
997 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
1001 "020000000000000000000000000000000000000004000000000000000001",
1002 "000000000000000000000000000000000000000000000000000000000001",
1003 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
1004 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
1005 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
1007 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
1013 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
1017 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1020 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
1021 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
1023 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
1029 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
1033 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1034 "000000000000000000000000000000000000000000000000000000000000000000000001",
1035 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
1036 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
1037 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1039 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
1045 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
1049 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1052 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
1053 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1055 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
1061 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
1065 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1066 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1067 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
1068 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
1069 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1071 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
1077 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
1081 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1084 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1085 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1087 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1093 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
1097 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1098 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1099 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1100 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1101 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1103 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1109 /* more tests using the last curve */
1111 if (!EC_POINT_copy(Q
, P
)) ABORT
;
1112 if (EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
1113 if (!EC_POINT_dbl(group
, P
, P
, ctx
)) ABORT
;
1114 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
1115 if (!EC_POINT_invert(group
, Q
, ctx
)) ABORT
; /* P = -2Q */
1117 if (!EC_POINT_add(group
, R
, P
, Q
, ctx
)) ABORT
;
1118 if (!EC_POINT_add(group
, R
, R
, Q
, ctx
)) ABORT
;
1119 if (!EC_POINT_is_at_infinity(group
, R
)) ABORT
; /* R = P + 2Q */
1122 const EC_POINT
*points
[3];
1123 const BIGNUM
*scalars
[3];
1125 if (EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
1130 if (!BN_add(y
, z
, BN_value_one())) ABORT
;
1131 if (BN_is_odd(y
)) ABORT
;
1132 if (!BN_rshift1(y
, y
)) ABORT
;
1133 scalars
[0] = y
; /* (group order + 1)/2, so y*Q + y*Q = Q */
1136 fprintf(stdout
, "combined multiplication ...");
1139 /* z is still the group order */
1140 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
)) ABORT
;
1141 if (!EC_POINTs_mul(group
, R
, z
, 2, points
, scalars
, ctx
)) ABORT
;
1142 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
)) ABORT
;
1143 if (0 != EC_POINT_cmp(group
, R
, Q
, ctx
)) ABORT
;
1145 fprintf(stdout
, ".");
1148 if (!BN_pseudo_rand(y
, BN_num_bits(y
), 0, 0)) ABORT
;
1149 if (!BN_add(z
, z
, y
)) ABORT
;
1152 scalars
[1] = z
; /* z = -(order + y) */
1154 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
)) ABORT
;
1155 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
1157 fprintf(stdout
, ".");
1160 if (!BN_pseudo_rand(x
, BN_num_bits(y
) - 1, 0, 0)) ABORT
;
1161 if (!BN_add(z
, x
, y
)) ABORT
;
1165 scalars
[2] = z
; /* z = -(x+y) */
1167 if (!EC_POINTs_mul(group
, P
, NULL
, 3, points
, scalars
, ctx
)) ABORT
;
1168 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
1170 fprintf(stdout
, " ok\n\n");
1175 timings(C2_K163
, TIMING_BASE_PT
, ctx
);
1176 timings(C2_K163
, TIMING_RAND_PT
, ctx
);
1177 timings(C2_K163
, TIMING_SIMUL
, ctx
);
1178 timings(C2_B163
, TIMING_BASE_PT
, ctx
);
1179 timings(C2_B163
, TIMING_RAND_PT
, ctx
);
1180 timings(C2_B163
, TIMING_SIMUL
, ctx
);
1181 timings(C2_K233
, TIMING_BASE_PT
, ctx
);
1182 timings(C2_K233
, TIMING_RAND_PT
, ctx
);
1183 timings(C2_K233
, TIMING_SIMUL
, ctx
);
1184 timings(C2_B233
, TIMING_BASE_PT
, ctx
);
1185 timings(C2_B233
, TIMING_RAND_PT
, ctx
);
1186 timings(C2_B233
, TIMING_SIMUL
, ctx
);
1187 timings(C2_K283
, TIMING_BASE_PT
, ctx
);
1188 timings(C2_K283
, TIMING_RAND_PT
, ctx
);
1189 timings(C2_K283
, TIMING_SIMUL
, ctx
);
1190 timings(C2_B283
, TIMING_BASE_PT
, ctx
);
1191 timings(C2_B283
, TIMING_RAND_PT
, ctx
);
1192 timings(C2_B283
, TIMING_SIMUL
, ctx
);
1193 timings(C2_K409
, TIMING_BASE_PT
, ctx
);
1194 timings(C2_K409
, TIMING_RAND_PT
, ctx
);
1195 timings(C2_K409
, TIMING_SIMUL
, ctx
);
1196 timings(C2_B409
, TIMING_BASE_PT
, ctx
);
1197 timings(C2_B409
, TIMING_RAND_PT
, ctx
);
1198 timings(C2_B409
, TIMING_SIMUL
, ctx
);
1199 timings(C2_K571
, TIMING_BASE_PT
, ctx
);
1200 timings(C2_K571
, TIMING_RAND_PT
, ctx
);
1201 timings(C2_K571
, TIMING_SIMUL
, ctx
);
1202 timings(C2_B571
, TIMING_BASE_PT
, ctx
);
1203 timings(C2_B571
, TIMING_RAND_PT
, ctx
);
1204 timings(C2_B571
, TIMING_SIMUL
, ctx
);
1210 BN_free(p
); BN_free(a
); BN_free(b
);
1211 EC_GROUP_free(group
);
1215 BN_free(x
); BN_free(y
); BN_free(z
); BN_free(cof
);
1217 if (C2_K163
) EC_GROUP_free(C2_K163
);
1218 if (C2_B163
) EC_GROUP_free(C2_B163
);
1219 if (C2_K233
) EC_GROUP_free(C2_K233
);
1220 if (C2_B233
) EC_GROUP_free(C2_B233
);
1221 if (C2_K283
) EC_GROUP_free(C2_K283
);
1222 if (C2_B283
) EC_GROUP_free(C2_B283
);
1223 if (C2_K409
) EC_GROUP_free(C2_K409
);
1224 if (C2_B409
) EC_GROUP_free(C2_B409
);
1225 if (C2_K571
) EC_GROUP_free(C2_K571
);
1226 if (C2_B571
) EC_GROUP_free(C2_B571
);
1230 void internal_curve_test(void)
1232 EC_builtin_curve
*curves
= NULL
;
1233 size_t crv_len
= 0, n
= 0;
1236 crv_len
= EC_get_builtin_curves(NULL
, 0);
1238 curves
= OPENSSL_malloc(sizeof(EC_builtin_curve
) * crv_len
);
1243 if (!EC_get_builtin_curves(curves
, crv_len
))
1245 OPENSSL_free(curves
);
1249 fprintf(stdout
, "testing internal curves: ");
1251 for (n
= 0; n
< crv_len
; n
++)
1253 EC_GROUP
*group
= NULL
;
1254 int nid
= curves
[n
].nid
;
1255 if ((group
= EC_GROUP_new_by_nid(nid
)) == NULL
)
1258 fprintf(stdout
, "\nEC_GROUP_new_by_nid() failed with"
1259 " curve %s\n", OBJ_nid2sn(nid
));
1260 /* try next curve */
1263 if (!EC_GROUP_check(group
, NULL
))
1266 fprintf(stdout
, "\nEC_GROUP_check() failed with"
1267 " curve %s\n", OBJ_nid2sn(nid
));
1268 EC_GROUP_free(group
);
1269 /* try the next curve */
1272 fprintf(stdout
, ".");
1274 EC_GROUP_free(group
);
1277 fprintf(stdout
, " ok\n");
1279 fprintf(stdout
, " failed\n");
1280 OPENSSL_free(curves
);
1284 static const char rnd_seed
[] = "string to make the random number generator think it has entropy";
1286 int main(int argc
, char *argv
[])
1289 /* enable memory leak checking unless explicitly disabled */
1290 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL
) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
1292 CRYPTO_malloc_debug_init();
1293 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL
);
1297 /* OPENSSL_DEBUG_MEMORY=off */
1298 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
1300 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON
);
1301 ERR_load_crypto_strings();
1303 RAND_seed(rnd_seed
, sizeof rnd_seed
); /* or BN_generate_prime may fail */
1305 prime_field_tests();
1307 char2_field_tests();
1308 /* test the internal curves */
1309 internal_curve_test();
1311 #ifndef OPENSSL_NO_ENGINE
1314 CRYPTO_cleanup_all_ex_data();
1316 ERR_remove_state(0);
1317 CRYPTO_mem_leaks_fp(stderr
);