1 /* crypto/ec/ectest.c */
3 * Originally written by Bodo Moeller for the OpenSSL project.
5 /* ====================================================================
6 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
12 * 1. Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in
17 * the documentation and/or other materials provided with the
20 * 3. All advertising materials mentioning features or use of this
21 * software must display the following acknowledgment:
22 * "This product includes software developed by the OpenSSL Project
23 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
25 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
26 * endorse or promote products derived from this software without
27 * prior written permission. For written permission, please contact
28 * openssl-core@openssl.org.
30 * 5. Products derived from this software may not be called "OpenSSL"
31 * nor may "OpenSSL" appear in their names without prior written
32 * permission of the OpenSSL Project.
34 * 6. Redistributions of any form whatsoever must retain the following
36 * "This product includes software developed by the OpenSSL Project
37 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
39 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
40 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
41 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
42 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
43 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
44 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
45 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
46 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
48 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
49 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
50 * OF THE POSSIBILITY OF SUCH DAMAGE.
51 * ====================================================================
53 * This product includes cryptographic software written by Eric Young
54 * (eay@cryptsoft.com). This product includes software written by Tim
55 * Hudson (tjh@cryptsoft.com).
58 /* ====================================================================
59 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
61 * Portions of the attached software ("Contribution") are developed by
62 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
64 * The Contribution is licensed pursuant to the OpenSSL open source
65 * license provided above.
67 * The elliptic curve binary polynomial software is originally written by
68 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
84 int main(int argc
, char * argv
[]) { puts("Elliptic curves are disabled."); return 0; }
88 #include <openssl/ec.h>
89 #ifndef OPENSSL_NO_ENGINE
90 #include <openssl/engine.h>
92 #include <openssl/err.h>
93 #include <openssl/obj_mac.h>
94 #include <openssl/objects.h>
95 #include <openssl/rand.h>
96 #include <openssl/bn.h>
98 #if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12)
99 /* suppress "too big too optimize" warning */
100 #pragma warning(disable:4959)
105 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
106 ERR_print_errors_fp(stderr); \
110 void prime_field_tests(void);
111 void char2_field_tests(void);
112 void internal_curve_test(void);
114 #define TIMING_BASE_PT 0
115 #define TIMING_RAND_PT 1
116 #define TIMING_SIMUL 2
119 static void timings(EC_GROUP
*group
, int type
, BN_CTX
*ctx
)
124 BIGNUM
*r
[10], *r0
[10];
128 if (s
== NULL
) ABORT
;
130 fprintf(stdout
, "Timings for %d-bit field, ", EC_GROUP_get_degree(group
));
131 if (!EC_GROUP_get_order(group
, s
, ctx
)) ABORT
;
132 fprintf(stdout
, "%d-bit scalars ", (int)BN_num_bits(s
));
135 P
= EC_POINT_new(group
);
136 if (P
== NULL
) ABORT
;
137 EC_POINT_copy(P
, EC_GROUP_get0_generator(group
));
139 for (i
= 0; i
< 10; i
++)
141 if ((r
[i
] = BN_new()) == NULL
) ABORT
;
142 if (!BN_pseudo_rand(r
[i
], BN_num_bits(s
), 0, 0)) ABORT
;
143 if (type
!= TIMING_BASE_PT
)
145 if ((r0
[i
] = BN_new()) == NULL
) ABORT
;
146 if (!BN_pseudo_rand(r0
[i
], BN_num_bits(s
), 0, 0)) ABORT
;
151 for (i
= 0; i
< 10; i
++)
153 for (j
= 0; j
< 10; j
++)
155 if (!EC_POINT_mul(group
, P
, (type
!= TIMING_RAND_PT
) ? r
[i
] : NULL
,
156 (type
!= TIMING_BASE_PT
) ? P
: NULL
, (type
!= TIMING_BASE_PT
) ? r0
[i
] : NULL
, ctx
)) ABORT
;
159 clck
= clock() - clck
;
161 fprintf(stdout
, "\n");
163 #ifdef CLOCKS_PER_SEC
164 /* "To determine the time in seconds, the value returned
165 * by the clock function should be divided by the value
166 * of the macro CLOCKS_PER_SEC."
170 /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
171 * -- cc on NeXTstep/OpenStep */
172 # define UNIT "units"
173 # define CLOCKS_PER_SEC 1
176 if (type
== TIMING_BASE_PT
) {
177 fprintf(stdout
, "%i %s in %.2f " UNIT
"\n", i
*j
,
178 "base point multiplications", (double)clck
/CLOCKS_PER_SEC
);
179 } else if (type
== TIMING_RAND_PT
) {
180 fprintf(stdout
, "%i %s in %.2f " UNIT
"\n", i
*j
,
181 "random point multiplications", (double)clck
/CLOCKS_PER_SEC
);
182 } else if (type
== TIMING_SIMUL
) {
183 fprintf(stdout
, "%i %s in %.2f " UNIT
"\n", i
*j
,
184 "s*P+t*Q operations", (double)clck
/CLOCKS_PER_SEC
);
186 fprintf(stdout
, "average: %.4f " UNIT
"\n", (double)clck
/(CLOCKS_PER_SEC
*i
*j
));
190 for (i
= 0; i
< 10; i
++)
193 if (type
!= TIMING_BASE_PT
) BN_free(r0
[i
]);
198 void prime_field_tests()
203 EC_GROUP
*P_160
= NULL
, *P_192
= NULL
, *P_224
= NULL
, *P_256
= NULL
, *P_384
= NULL
, *P_521
= NULL
;
206 unsigned char buf
[100];
218 if (!p
|| !a
|| !b
) ABORT
;
220 if (!BN_hex2bn(&p
, "17")) ABORT
;
221 if (!BN_hex2bn(&a
, "1")) ABORT
;
222 if (!BN_hex2bn(&b
, "1")) ABORT
;
224 group
= EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
225 * so that the library gets to choose the EC_METHOD */
228 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
232 tmp
= EC_GROUP_new(EC_GROUP_method_of(group
));
234 if (!EC_GROUP_copy(tmp
, group
)) ABORT
;
235 EC_GROUP_free(group
);
239 if (!EC_GROUP_get_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
241 fprintf(stdout
, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
242 BN_print_fp(stdout
, p
);
243 fprintf(stdout
, ")\n a = 0x");
244 BN_print_fp(stdout
, a
);
245 fprintf(stdout
, "\n b = 0x");
246 BN_print_fp(stdout
, b
);
247 fprintf(stdout
, "\n");
249 P
= EC_POINT_new(group
);
250 Q
= EC_POINT_new(group
);
251 R
= EC_POINT_new(group
);
252 if (!P
|| !Q
|| !R
) ABORT
;
254 if (!EC_POINT_set_to_infinity(group
, P
)) ABORT
;
255 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
258 if (!EC_POINT_oct2point(group
, Q
, buf
, 1, ctx
)) ABORT
;
260 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
)) ABORT
;
261 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
266 if (!x
|| !y
|| !z
) ABORT
;
268 if (!BN_hex2bn(&x
, "D")) ABORT
;
269 if (!EC_POINT_set_compressed_coordinates_GFp(group
, Q
, x
, 1, ctx
)) ABORT
;
270 if (!EC_POINT_is_on_curve(group
, Q
, ctx
))
272 if (!EC_POINT_get_affine_coordinates_GFp(group
, Q
, x
, y
, ctx
)) ABORT
;
273 fprintf(stderr
, "Point is not on curve: x = 0x");
274 BN_print_fp(stderr
, x
);
275 fprintf(stderr
, ", y = 0x");
276 BN_print_fp(stderr
, y
);
277 fprintf(stderr
, "\n");
281 fprintf(stdout
, "A cyclic subgroup:\n");
287 if (EC_POINT_is_at_infinity(group
, P
))
288 fprintf(stdout
, " point at infinity\n");
291 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
293 fprintf(stdout
, " x = 0x");
294 BN_print_fp(stdout
, x
);
295 fprintf(stdout
, ", y = 0x");
296 BN_print_fp(stdout
, y
);
297 fprintf(stdout
, "\n");
300 if (!EC_POINT_copy(R
, P
)) ABORT
;
301 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
)) ABORT
;
310 if (!EC_POINTs_make_affine(group
, 2, points
, ctx
)) ABORT
;
315 while (!EC_POINT_is_at_infinity(group
, P
));
317 if (!EC_POINT_add(group
, P
, Q
, R
, ctx
)) ABORT
;
318 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
320 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_COMPRESSED
, buf
, sizeof buf
, ctx
);
322 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
323 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
324 fprintf(stdout
, "Generator as octect string, compressed form:\n ");
325 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
327 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_UNCOMPRESSED
, buf
, sizeof buf
, ctx
);
329 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
330 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
331 fprintf(stdout
, "\nGenerator as octect string, uncompressed form:\n ");
332 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
334 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_HYBRID
, buf
, sizeof buf
, ctx
);
336 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
337 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
338 fprintf(stdout
, "\nGenerator as octect string, hybrid form:\n ");
339 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
341 if (!EC_POINT_get_Jprojective_coordinates_GFp(group
, R
, x
, y
, z
, ctx
)) ABORT
;
342 fprintf(stdout
, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
343 BN_print_fp(stdout
, x
);
344 fprintf(stdout
, ", Y = 0x");
345 BN_print_fp(stdout
, y
);
346 fprintf(stdout
, ", Z = 0x");
347 BN_print_fp(stdout
, z
);
348 fprintf(stdout
, "\n");
350 if (!EC_POINT_invert(group
, P
, ctx
)) ABORT
;
351 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
)) ABORT
;
354 /* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000)
355 * -- not a NIST curve, but commonly used */
357 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) ABORT
;
358 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
)) ABORT
;
359 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) ABORT
;
360 if (!BN_hex2bn(&b
, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) ABORT
;
361 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
363 if (!BN_hex2bn(&x
, "4A96B5688EF573284664698968C38BB913CBFC82")) ABORT
;
364 if (!BN_hex2bn(&y
, "23a628553168947d59dcc912042351377ac5fb32")) ABORT
;
365 if (!EC_POINT_set_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
366 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
367 if (!BN_hex2bn(&z
, "0100000000000000000001F4C8F927AED3CA752257")) ABORT
;
368 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
370 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
371 fprintf(stdout
, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x");
372 BN_print_fp(stdout
, x
);
373 fprintf(stdout
, "\n y = 0x");
374 BN_print_fp(stdout
, y
);
375 fprintf(stdout
, "\n");
376 /* G_y value taken from the standard: */
377 if (!BN_hex2bn(&z
, "23a628553168947d59dcc912042351377ac5fb32")) ABORT
;
378 if (0 != BN_cmp(y
, z
)) ABORT
;
380 fprintf(stdout
, "verify degree ...");
381 if (EC_GROUP_get_degree(group
) != 160) ABORT
;
382 fprintf(stdout
, " ok\n");
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_160
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
397 if (!EC_GROUP_copy(P_160
, group
)) ABORT
;
400 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
402 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT
;
403 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
)) ABORT
;
404 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT
;
405 if (!BN_hex2bn(&b
, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT
;
406 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
408 if (!BN_hex2bn(&x
, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) 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
, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT
;
412 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
414 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
415 fprintf(stdout
, "\nNIST curve P-192 -- Generator:\n x = 0x");
416 BN_print_fp(stdout
, x
);
417 fprintf(stdout
, "\n y = 0x");
418 BN_print_fp(stdout
, y
);
419 fprintf(stdout
, "\n");
420 /* G_y value taken from the standard: */
421 if (!BN_hex2bn(&z
, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT
;
422 if (0 != BN_cmp(y
, z
)) ABORT
;
424 fprintf(stdout
, "verify degree ...");
425 if (EC_GROUP_get_degree(group
) != 192) ABORT
;
426 fprintf(stdout
, " ok\n");
428 fprintf(stdout
, "verify group order ...");
430 if (!EC_GROUP_get_order(group
, z
, 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
, ".");
435 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
436 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
437 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
438 fprintf(stdout
, " ok\n");
440 if (!(P_192
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
441 if (!EC_GROUP_copy(P_192
, group
)) ABORT
;
444 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
446 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT
;
447 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
)) ABORT
;
448 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT
;
449 if (!BN_hex2bn(&b
, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT
;
450 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
452 if (!BN_hex2bn(&x
, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT
;
453 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 0, ctx
)) ABORT
;
454 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
455 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT
;
456 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
458 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
459 fprintf(stdout
, "\nNIST curve P-224 -- Generator:\n x = 0x");
460 BN_print_fp(stdout
, x
);
461 fprintf(stdout
, "\n y = 0x");
462 BN_print_fp(stdout
, y
);
463 fprintf(stdout
, "\n");
464 /* G_y value taken from the standard: */
465 if (!BN_hex2bn(&z
, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT
;
466 if (0 != BN_cmp(y
, z
)) ABORT
;
468 fprintf(stdout
, "verify degree ...");
469 if (EC_GROUP_get_degree(group
) != 224) ABORT
;
470 fprintf(stdout
, " ok\n");
472 fprintf(stdout
, "verify group order ...");
474 if (!EC_GROUP_get_order(group
, z
, 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
, ".");
479 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
480 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
481 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
482 fprintf(stdout
, " ok\n");
484 if (!(P_224
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
485 if (!EC_GROUP_copy(P_224
, group
)) ABORT
;
488 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
490 if (!BN_hex2bn(&p
, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT
;
491 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
)) ABORT
;
492 if (!BN_hex2bn(&a
, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT
;
493 if (!BN_hex2bn(&b
, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT
;
494 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
496 if (!BN_hex2bn(&x
, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT
;
497 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
)) ABORT
;
498 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
499 if (!BN_hex2bn(&z
, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
500 "84F3B9CAC2FC632551")) ABORT
;
501 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
503 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
504 fprintf(stdout
, "\nNIST curve P-256 -- Generator:\n x = 0x");
505 BN_print_fp(stdout
, x
);
506 fprintf(stdout
, "\n y = 0x");
507 BN_print_fp(stdout
, y
);
508 fprintf(stdout
, "\n");
509 /* G_y value taken from the standard: */
510 if (!BN_hex2bn(&z
, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT
;
511 if (0 != BN_cmp(y
, z
)) ABORT
;
513 fprintf(stdout
, "verify degree ...");
514 if (EC_GROUP_get_degree(group
) != 256) ABORT
;
515 fprintf(stdout
, " ok\n");
517 fprintf(stdout
, "verify group order ...");
519 if (!EC_GROUP_get_order(group
, z
, 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
, ".");
524 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
525 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
526 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
527 fprintf(stdout
, " ok\n");
529 if (!(P_256
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
530 if (!EC_GROUP_copy(P_256
, group
)) ABORT
;
533 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
535 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
536 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT
;
537 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
)) ABORT
;
538 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
539 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT
;
540 if (!BN_hex2bn(&b
, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
541 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT
;
542 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
544 if (!BN_hex2bn(&x
, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
545 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT
;
546 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
)) ABORT
;
547 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
548 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
549 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT
;
550 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
552 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
553 fprintf(stdout
, "\nNIST curve P-384 -- Generator:\n x = 0x");
554 BN_print_fp(stdout
, x
);
555 fprintf(stdout
, "\n y = 0x");
556 BN_print_fp(stdout
, y
);
557 fprintf(stdout
, "\n");
558 /* G_y value taken from the standard: */
559 if (!BN_hex2bn(&z
, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
560 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT
;
561 if (0 != BN_cmp(y
, z
)) ABORT
;
563 fprintf(stdout
, "verify degree ...");
564 if (EC_GROUP_get_degree(group
) != 384) ABORT
;
565 fprintf(stdout
, " ok\n");
567 fprintf(stdout
, "verify group order ...");
569 if (!EC_GROUP_get_order(group
, z
, 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
, ".");
574 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
575 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
576 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
577 fprintf(stdout
, " ok\n");
579 if (!(P_384
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
580 if (!EC_GROUP_copy(P_384
, group
)) ABORT
;
583 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
585 if (!BN_hex2bn(&p
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
586 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
587 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT
;
588 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
)) ABORT
;
589 if (!BN_hex2bn(&a
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
590 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
591 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT
;
592 if (!BN_hex2bn(&b
, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
593 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
594 "DF883D2C34F1EF451FD46B503F00")) ABORT
;
595 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
)) ABORT
;
597 if (!BN_hex2bn(&x
, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
598 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
599 "3C1856A429BF97E7E31C2E5BD66")) ABORT
;
600 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 0, ctx
)) ABORT
;
601 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
602 if (!BN_hex2bn(&z
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
603 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
604 "C9B8899C47AEBB6FB71E91386409")) ABORT
;
605 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one())) ABORT
;
607 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
)) ABORT
;
608 fprintf(stdout
, "\nNIST curve P-521 -- Generator:\n x = 0x");
609 BN_print_fp(stdout
, x
);
610 fprintf(stdout
, "\n y = 0x");
611 BN_print_fp(stdout
, y
);
612 fprintf(stdout
, "\n");
613 /* G_y value taken from the standard: */
614 if (!BN_hex2bn(&z
, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
615 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
616 "7086A272C24088BE94769FD16650")) ABORT
;
617 if (0 != BN_cmp(y
, z
)) ABORT
;
619 fprintf(stdout
, "verify degree ...");
620 if (EC_GROUP_get_degree(group
) != 521) ABORT
;
621 fprintf(stdout
, " ok\n");
623 fprintf(stdout
, "verify group order ...");
625 if (!EC_GROUP_get_order(group
, z
, 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
, ".");
630 if (!EC_GROUP_precompute_mult(group
, ctx
)) ABORT
;
631 if (!EC_POINT_mul(group
, Q
, z
, NULL
, NULL
, ctx
)) ABORT
;
632 if (!EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
633 fprintf(stdout
, " ok\n");
635 if (!(P_521
= EC_GROUP_new(EC_GROUP_method_of(group
)))) ABORT
;
636 if (!EC_GROUP_copy(P_521
, group
)) ABORT
;
639 /* more tests using the last curve */
641 if (!EC_POINT_copy(Q
, P
)) ABORT
;
642 if (EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
643 if (!EC_POINT_dbl(group
, P
, P
, ctx
)) ABORT
;
644 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
645 if (!EC_POINT_invert(group
, Q
, ctx
)) ABORT
; /* P = -2Q */
647 if (!EC_POINT_add(group
, R
, P
, Q
, ctx
)) ABORT
;
648 if (!EC_POINT_add(group
, R
, R
, Q
, ctx
)) ABORT
;
649 if (!EC_POINT_is_at_infinity(group
, R
)) ABORT
; /* R = P + 2Q */
652 const EC_POINT
*points
[4];
653 const BIGNUM
*scalars
[4];
656 if (EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
662 if (!BN_add(y
, z
, BN_value_one())) ABORT
;
663 if (BN_is_odd(y
)) ABORT
;
664 if (!BN_rshift1(y
, y
)) ABORT
;
665 scalars
[0] = y
; /* (group order + 1)/2, so y*Q + y*Q = Q */
668 fprintf(stdout
, "combined multiplication ...");
671 /* z is still the group order */
672 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
)) ABORT
;
673 if (!EC_POINTs_mul(group
, R
, z
, 2, points
, scalars
, ctx
)) ABORT
;
674 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
)) ABORT
;
675 if (0 != EC_POINT_cmp(group
, R
, Q
, ctx
)) ABORT
;
677 fprintf(stdout
, ".");
680 if (!BN_pseudo_rand(y
, BN_num_bits(y
), 0, 0)) ABORT
;
681 if (!BN_add(z
, z
, y
)) ABORT
;
682 BN_set_negative(z
, 1);
684 scalars
[1] = z
; /* z = -(order + y) */
686 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
)) ABORT
;
687 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
689 fprintf(stdout
, ".");
692 if (!BN_pseudo_rand(x
, BN_num_bits(y
) - 1, 0, 0)) ABORT
;
693 if (!BN_add(z
, x
, y
)) ABORT
;
694 BN_set_negative(z
, 1);
697 scalars
[2] = z
; /* z = -(x+y) */
701 scalars
[3] = &scalar3
;
703 if (!EC_POINTs_mul(group
, P
, NULL
, 4, points
, scalars
, ctx
)) ABORT
;
704 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
706 fprintf(stdout
, " ok\n\n");
713 timings(P_160
, TIMING_BASE_PT
, ctx
);
714 timings(P_160
, TIMING_RAND_PT
, ctx
);
715 timings(P_160
, TIMING_SIMUL
, ctx
);
716 timings(P_192
, TIMING_BASE_PT
, ctx
);
717 timings(P_192
, TIMING_RAND_PT
, ctx
);
718 timings(P_192
, TIMING_SIMUL
, ctx
);
719 timings(P_224
, TIMING_BASE_PT
, ctx
);
720 timings(P_224
, TIMING_RAND_PT
, ctx
);
721 timings(P_224
, TIMING_SIMUL
, ctx
);
722 timings(P_256
, TIMING_BASE_PT
, ctx
);
723 timings(P_256
, TIMING_RAND_PT
, ctx
);
724 timings(P_256
, TIMING_SIMUL
, ctx
);
725 timings(P_384
, TIMING_BASE_PT
, ctx
);
726 timings(P_384
, TIMING_RAND_PT
, ctx
);
727 timings(P_384
, TIMING_SIMUL
, ctx
);
728 timings(P_521
, TIMING_BASE_PT
, ctx
);
729 timings(P_521
, TIMING_RAND_PT
, ctx
);
730 timings(P_521
, TIMING_SIMUL
, ctx
);
736 BN_free(p
); BN_free(a
); BN_free(b
);
737 EC_GROUP_free(group
);
741 BN_free(x
); BN_free(y
); BN_free(z
);
743 if (P_160
) EC_GROUP_free(P_160
);
744 if (P_192
) EC_GROUP_free(P_192
);
745 if (P_224
) EC_GROUP_free(P_224
);
746 if (P_256
) EC_GROUP_free(P_256
);
747 if (P_384
) EC_GROUP_free(P_384
);
748 if (P_521
) EC_GROUP_free(P_521
);
752 /* Change test based on whether binary point compression is enabled or not. */
753 #ifdef OPENSSL_EC_BIN_PT_COMP
754 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
755 if (!BN_hex2bn(&x, _x)) ABORT; \
756 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
757 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
758 if (!BN_hex2bn(&z, _order)) ABORT; \
759 if (!BN_hex2bn(&cof, _cof)) ABORT; \
760 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
761 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
762 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
763 BN_print_fp(stdout, x); \
764 fprintf(stdout, "\n y = 0x"); \
765 BN_print_fp(stdout, y); \
766 fprintf(stdout, "\n"); \
767 /* G_y value taken from the standard: */ \
768 if (!BN_hex2bn(&z, _y)) ABORT; \
769 if (0 != BN_cmp(y, z)) ABORT;
771 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
772 if (!BN_hex2bn(&x, _x)) ABORT; \
773 if (!BN_hex2bn(&y, _y)) ABORT; \
774 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
775 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
776 if (!BN_hex2bn(&z, _order)) ABORT; \
777 if (!BN_hex2bn(&cof, _cof)) ABORT; \
778 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
779 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
780 BN_print_fp(stdout, x); \
781 fprintf(stdout, "\n y = 0x"); \
782 BN_print_fp(stdout, y); \
783 fprintf(stdout, "\n");
786 #define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
787 if (!BN_hex2bn(&p, _p)) ABORT; \
788 if (!BN_hex2bn(&a, _a)) ABORT; \
789 if (!BN_hex2bn(&b, _b)) ABORT; \
790 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
791 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
792 fprintf(stdout, "verify degree ..."); \
793 if (EC_GROUP_get_degree(group) != _degree) ABORT; \
794 fprintf(stdout, " ok\n"); \
795 fprintf(stdout, "verify group order ..."); \
797 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; \
798 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \
799 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \
800 fprintf(stdout, "."); \
802 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; \
803 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \
804 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \
805 fprintf(stdout, " ok\n"); \
806 if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \
807 if (!EC_GROUP_copy(_variable, group)) ABORT;
809 void char2_field_tests()
814 EC_GROUP
*C2_K163
= NULL
, *C2_K233
= NULL
, *C2_K283
= NULL
, *C2_K409
= NULL
, *C2_K571
= NULL
;
815 EC_GROUP
*C2_B163
= NULL
, *C2_B233
= NULL
, *C2_B283
= NULL
, *C2_B409
= NULL
, *C2_B571
= NULL
;
817 BIGNUM
*x
, *y
, *z
, *cof
;
818 unsigned char buf
[100];
830 if (!p
|| !a
|| !b
) ABORT
;
832 if (!BN_hex2bn(&p
, "13")) ABORT
;
833 if (!BN_hex2bn(&a
, "3")) ABORT
;
834 if (!BN_hex2bn(&b
, "1")) ABORT
;
836 group
= EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m
837 * so that the library gets to choose the EC_METHOD */
839 if (!EC_GROUP_set_curve_GF2m(group
, p
, a
, b
, ctx
)) ABORT
;
843 tmp
= EC_GROUP_new(EC_GROUP_method_of(group
));
845 if (!EC_GROUP_copy(tmp
, group
)) ABORT
;
846 EC_GROUP_free(group
);
850 if (!EC_GROUP_get_curve_GF2m(group
, p
, a
, b
, ctx
)) ABORT
;
852 fprintf(stdout
, "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x");
853 BN_print_fp(stdout
, p
);
854 fprintf(stdout
, ")\n a = 0x");
855 BN_print_fp(stdout
, a
);
856 fprintf(stdout
, "\n b = 0x");
857 BN_print_fp(stdout
, b
);
858 fprintf(stdout
, "\n(0x... means binary polynomial)\n");
860 P
= EC_POINT_new(group
);
861 Q
= EC_POINT_new(group
);
862 R
= EC_POINT_new(group
);
863 if (!P
|| !Q
|| !R
) ABORT
;
865 if (!EC_POINT_set_to_infinity(group
, P
)) ABORT
;
866 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
869 if (!EC_POINT_oct2point(group
, Q
, buf
, 1, ctx
)) ABORT
;
871 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
)) ABORT
;
872 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
878 if (!x
|| !y
|| !z
|| !cof
) ABORT
;
880 if (!BN_hex2bn(&x
, "6")) ABORT
;
881 /* Change test based on whether binary point compression is enabled or not. */
882 #ifdef OPENSSL_EC_BIN_PT_COMP
883 if (!EC_POINT_set_compressed_coordinates_GF2m(group
, Q
, x
, 1, ctx
)) ABORT
;
885 if (!BN_hex2bn(&y
, "8")) ABORT
;
886 if (!EC_POINT_set_affine_coordinates_GF2m(group
, Q
, x
, y
, ctx
)) ABORT
;
888 if (!EC_POINT_is_on_curve(group
, Q
, ctx
))
890 /* Change test based on whether binary point compression is enabled or not. */
891 #ifdef OPENSSL_EC_BIN_PT_COMP
892 if (!EC_POINT_get_affine_coordinates_GF2m(group
, Q
, x
, y
, ctx
)) ABORT
;
894 fprintf(stderr
, "Point is not on curve: x = 0x");
895 BN_print_fp(stderr
, x
);
896 fprintf(stderr
, ", y = 0x");
897 BN_print_fp(stderr
, y
);
898 fprintf(stderr
, "\n");
902 fprintf(stdout
, "A cyclic subgroup:\n");
908 if (EC_POINT_is_at_infinity(group
, P
))
909 fprintf(stdout
, " point at infinity\n");
912 if (!EC_POINT_get_affine_coordinates_GF2m(group
, P
, x
, y
, ctx
)) ABORT
;
914 fprintf(stdout
, " x = 0x");
915 BN_print_fp(stdout
, x
);
916 fprintf(stdout
, ", y = 0x");
917 BN_print_fp(stdout
, y
);
918 fprintf(stdout
, "\n");
921 if (!EC_POINT_copy(R
, P
)) ABORT
;
922 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
)) ABORT
;
924 while (!EC_POINT_is_at_infinity(group
, P
));
926 if (!EC_POINT_add(group
, P
, Q
, R
, ctx
)) ABORT
;
927 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
929 /* Change test based on whether binary point compression is enabled or not. */
930 #ifdef OPENSSL_EC_BIN_PT_COMP
931 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_COMPRESSED
, buf
, sizeof buf
, ctx
);
933 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
934 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
935 fprintf(stdout
, "Generator as octet string, compressed form:\n ");
936 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
939 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_UNCOMPRESSED
, buf
, sizeof buf
, ctx
);
941 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
942 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
943 fprintf(stdout
, "\nGenerator as octet string, uncompressed form:\n ");
944 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
946 /* Change test based on whether binary point compression is enabled or not. */
947 #ifdef OPENSSL_EC_BIN_PT_COMP
948 len
= EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_HYBRID
, buf
, sizeof buf
, ctx
);
950 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
)) ABORT
;
951 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
)) ABORT
;
952 fprintf(stdout
, "\nGenerator as octet string, hybrid form:\n ");
953 for (i
= 0; i
< len
; i
++) fprintf(stdout
, "%02X", buf
[i
]);
956 fprintf(stdout
, "\n");
958 if (!EC_POINT_invert(group
, P
, ctx
)) ABORT
;
959 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
)) ABORT
;
962 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
966 "0800000000000000000000000000000000000000C9",
969 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
970 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
972 "04000000000000000000020108A2E0CC0D99F8A5EF",
978 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
982 "0800000000000000000000000000000000000000C9",
984 "020A601907B8C953CA1481EB10512F78744A3205FD",
985 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
986 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
988 "040000000000000000000292FE77E70C12A4234C33",
994 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
998 "020000000000000000000000000000000000000004000000000000000001",
1001 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
1002 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
1004 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
1010 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
1014 "020000000000000000000000000000000000000004000000000000000001",
1015 "000000000000000000000000000000000000000000000000000000000001",
1016 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
1017 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
1018 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
1020 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
1026 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
1030 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1033 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
1034 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
1036 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
1042 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
1046 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1047 "000000000000000000000000000000000000000000000000000000000000000000000001",
1048 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
1049 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
1050 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1052 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
1058 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
1062 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1065 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
1066 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1068 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
1074 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
1078 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1079 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1080 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
1081 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
1082 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1084 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
1090 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
1094 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1097 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1098 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1100 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1106 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
1110 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1111 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1112 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1113 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1114 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1116 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1122 /* more tests using the last curve */
1124 if (!EC_POINT_copy(Q
, P
)) ABORT
;
1125 if (EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
1126 if (!EC_POINT_dbl(group
, P
, P
, ctx
)) ABORT
;
1127 if (!EC_POINT_is_on_curve(group
, P
, ctx
)) ABORT
;
1128 if (!EC_POINT_invert(group
, Q
, ctx
)) ABORT
; /* P = -2Q */
1130 if (!EC_POINT_add(group
, R
, P
, Q
, ctx
)) ABORT
;
1131 if (!EC_POINT_add(group
, R
, R
, Q
, ctx
)) ABORT
;
1132 if (!EC_POINT_is_at_infinity(group
, R
)) ABORT
; /* R = P + 2Q */
1135 const EC_POINT
*points
[3];
1136 const BIGNUM
*scalars
[3];
1138 if (EC_POINT_is_at_infinity(group
, Q
)) ABORT
;
1143 if (!BN_add(y
, z
, BN_value_one())) ABORT
;
1144 if (BN_is_odd(y
)) ABORT
;
1145 if (!BN_rshift1(y
, y
)) ABORT
;
1146 scalars
[0] = y
; /* (group order + 1)/2, so y*Q + y*Q = Q */
1149 fprintf(stdout
, "combined multiplication ...");
1152 /* z is still the group order */
1153 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
)) ABORT
;
1154 if (!EC_POINTs_mul(group
, R
, z
, 2, points
, scalars
, ctx
)) ABORT
;
1155 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
)) ABORT
;
1156 if (0 != EC_POINT_cmp(group
, R
, Q
, ctx
)) ABORT
;
1158 fprintf(stdout
, ".");
1161 if (!BN_pseudo_rand(y
, BN_num_bits(y
), 0, 0)) ABORT
;
1162 if (!BN_add(z
, z
, y
)) ABORT
;
1163 BN_set_negative(z
, 1);
1165 scalars
[1] = z
; /* z = -(order + y) */
1167 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
)) ABORT
;
1168 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
1170 fprintf(stdout
, ".");
1173 if (!BN_pseudo_rand(x
, BN_num_bits(y
) - 1, 0, 0)) ABORT
;
1174 if (!BN_add(z
, x
, y
)) ABORT
;
1175 BN_set_negative(z
, 1);
1178 scalars
[2] = z
; /* z = -(x+y) */
1180 if (!EC_POINTs_mul(group
, P
, NULL
, 3, points
, scalars
, ctx
)) ABORT
;
1181 if (!EC_POINT_is_at_infinity(group
, P
)) ABORT
;
1183 fprintf(stdout
, " ok\n\n");
1188 timings(C2_K163
, TIMING_BASE_PT
, ctx
);
1189 timings(C2_K163
, TIMING_RAND_PT
, ctx
);
1190 timings(C2_K163
, TIMING_SIMUL
, ctx
);
1191 timings(C2_B163
, TIMING_BASE_PT
, ctx
);
1192 timings(C2_B163
, TIMING_RAND_PT
, ctx
);
1193 timings(C2_B163
, TIMING_SIMUL
, ctx
);
1194 timings(C2_K233
, TIMING_BASE_PT
, ctx
);
1195 timings(C2_K233
, TIMING_RAND_PT
, ctx
);
1196 timings(C2_K233
, TIMING_SIMUL
, ctx
);
1197 timings(C2_B233
, TIMING_BASE_PT
, ctx
);
1198 timings(C2_B233
, TIMING_RAND_PT
, ctx
);
1199 timings(C2_B233
, TIMING_SIMUL
, ctx
);
1200 timings(C2_K283
, TIMING_BASE_PT
, ctx
);
1201 timings(C2_K283
, TIMING_RAND_PT
, ctx
);
1202 timings(C2_K283
, TIMING_SIMUL
, ctx
);
1203 timings(C2_B283
, TIMING_BASE_PT
, ctx
);
1204 timings(C2_B283
, TIMING_RAND_PT
, ctx
);
1205 timings(C2_B283
, TIMING_SIMUL
, ctx
);
1206 timings(C2_K409
, TIMING_BASE_PT
, ctx
);
1207 timings(C2_K409
, TIMING_RAND_PT
, ctx
);
1208 timings(C2_K409
, TIMING_SIMUL
, ctx
);
1209 timings(C2_B409
, TIMING_BASE_PT
, ctx
);
1210 timings(C2_B409
, TIMING_RAND_PT
, ctx
);
1211 timings(C2_B409
, TIMING_SIMUL
, ctx
);
1212 timings(C2_K571
, TIMING_BASE_PT
, ctx
);
1213 timings(C2_K571
, TIMING_RAND_PT
, ctx
);
1214 timings(C2_K571
, TIMING_SIMUL
, ctx
);
1215 timings(C2_B571
, TIMING_BASE_PT
, ctx
);
1216 timings(C2_B571
, TIMING_RAND_PT
, ctx
);
1217 timings(C2_B571
, TIMING_SIMUL
, ctx
);
1223 BN_free(p
); BN_free(a
); BN_free(b
);
1224 EC_GROUP_free(group
);
1228 BN_free(x
); BN_free(y
); BN_free(z
); BN_free(cof
);
1230 if (C2_K163
) EC_GROUP_free(C2_K163
);
1231 if (C2_B163
) EC_GROUP_free(C2_B163
);
1232 if (C2_K233
) EC_GROUP_free(C2_K233
);
1233 if (C2_B233
) EC_GROUP_free(C2_B233
);
1234 if (C2_K283
) EC_GROUP_free(C2_K283
);
1235 if (C2_B283
) EC_GROUP_free(C2_B283
);
1236 if (C2_K409
) EC_GROUP_free(C2_K409
);
1237 if (C2_B409
) EC_GROUP_free(C2_B409
);
1238 if (C2_K571
) EC_GROUP_free(C2_K571
);
1239 if (C2_B571
) EC_GROUP_free(C2_B571
);
1243 void internal_curve_test(void)
1245 EC_builtin_curve
*curves
= NULL
;
1246 size_t crv_len
= 0, n
= 0;
1249 crv_len
= EC_get_builtin_curves(NULL
, 0);
1251 curves
= OPENSSL_malloc(sizeof(EC_builtin_curve
) * crv_len
);
1256 if (!EC_get_builtin_curves(curves
, crv_len
))
1258 OPENSSL_free(curves
);
1262 fprintf(stdout
, "testing internal curves: ");
1264 for (n
= 0; n
< crv_len
; n
++)
1266 EC_GROUP
*group
= NULL
;
1267 int nid
= curves
[n
].nid
;
1268 if ((group
= EC_GROUP_new_by_curve_name(nid
)) == NULL
)
1271 fprintf(stdout
, "\nEC_GROUP_new_curve_name() failed with"
1272 " curve %s\n", OBJ_nid2sn(nid
));
1273 /* try next curve */
1276 if (!EC_GROUP_check(group
, NULL
))
1279 fprintf(stdout
, "\nEC_GROUP_check() failed with"
1280 " curve %s\n", OBJ_nid2sn(nid
));
1281 EC_GROUP_free(group
);
1282 /* try the next curve */
1285 fprintf(stdout
, ".");
1287 EC_GROUP_free(group
);
1290 fprintf(stdout
, " ok\n");
1292 fprintf(stdout
, " failed\n");
1293 OPENSSL_free(curves
);
1297 static const char rnd_seed
[] = "string to make the random number generator think it has entropy";
1299 int main(int argc
, char *argv
[])
1302 /* enable memory leak checking unless explicitly disabled */
1303 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL
) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
1305 CRYPTO_malloc_debug_init();
1306 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL
);
1310 /* OPENSSL_DEBUG_MEMORY=off */
1311 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
1313 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON
);
1314 ERR_load_crypto_strings();
1316 RAND_seed(rnd_seed
, sizeof rnd_seed
); /* or BN_generate_prime may fail */
1318 prime_field_tests();
1320 char2_field_tests();
1321 /* test the internal curves */
1322 internal_curve_test();
1324 #ifndef OPENSSL_NO_ENGINE
1327 CRYPTO_cleanup_all_ex_data();
1329 ERR_remove_thread_state(NULL
);
1330 CRYPTO_mem_leaks_fp(stderr
);