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1 /* crypto/ec/ectest.c */
2 /*
3  * Originally written by Bodo Moeller for the OpenSSL project.
4  */
5 /* ====================================================================
6  * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
7  *
8  * Redistribution and use in source and binary forms, with or without
9  * modification, are permitted provided that the following conditions
10  * are met:
11  *
12  * 1. Redistributions of source code must retain the above copyright
13  *    notice, this list of conditions and the following disclaimer.
14  *
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
18  *    distribution.
19  *
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/)"
24  *
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.
29  *
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.
33  *
34  * 6. Redistributions of any form whatsoever must retain the following
35  *    acknowledgment:
36  *    "This product includes software developed by the OpenSSL Project
37  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
38  *
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  * ====================================================================
52  *
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).
56  *
57  */
58 /* ====================================================================
59  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
60  *
61  * Portions of the attached software ("Contribution") are developed by
62  * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
63  *
64  * The Contribution is licensed pursuant to the OpenSSL open source
65  * license provided above.
66  *
67  * The elliptic curve binary polynomial software is originally written by
68  * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
69  *
70  */
71 
72 #include <stdio.h>
73 #include <stdlib.h>
74 #ifdef FLAT_INC
75 #include "e_os.h"
76 #else
77 #include "../e_os.h"
78 #endif
79 #include <string.h>
80 #include <time.h>
81 
82 
83 #ifdef OPENSSL_NO_EC
main(int argc,char * argv[])84 int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; }
85 #else
86 
87 
88 #include <openssl/ec.h>
89 #ifndef OPENSSL_NO_ENGINE
90 #include <openssl/engine.h>
91 #endif
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>
97 
98 #if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12)
99 /* suppress "too big too optimize" warning */
100 #pragma warning(disable:4959)
101 #endif
102 
103 #define ABORT do { \
104 	fflush(stdout); \
105 	fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
106 	ERR_print_errors_fp(stderr); \
107 	EXIT(1); \
108 } while (0)
109 
110 void prime_field_tests(void);
111 void char2_field_tests(void);
112 void internal_curve_test(void);
113 
114 #define TIMING_BASE_PT 0
115 #define TIMING_RAND_PT 1
116 #define TIMING_SIMUL 2
117 
118 #if 0
119 static void timings(EC_GROUP *group, int type, BN_CTX *ctx)
120 	{
121 	clock_t clck;
122 	int i, j;
123 	BIGNUM *s;
124 	BIGNUM *r[10], *r0[10];
125 	EC_POINT *P;
126 
127 	s = BN_new();
128 	if (s == NULL) ABORT;
129 
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));
133 	fflush(stdout);
134 
135 	P = EC_POINT_new(group);
136 	if (P == NULL) ABORT;
137 	EC_POINT_copy(P, EC_GROUP_get0_generator(group));
138 
139 	for (i = 0; i < 10; i++)
140 		{
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)
144 			{
145 			if ((r0[i] = BN_new()) == NULL) ABORT;
146 			if (!BN_pseudo_rand(r0[i], BN_num_bits(s), 0, 0)) ABORT;
147 			}
148 		}
149 
150 	clck = clock();
151 	for (i = 0; i < 10; i++)
152 		{
153 		for (j = 0; j < 10; j++)
154 			{
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;
157 			}
158 		}
159 	clck = clock() - clck;
160 
161 	fprintf(stdout, "\n");
162 
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."
167 	 *                                       -- ISO/IEC 9899 */
168 #	define UNIT "s"
169 #else
170 	/* "`CLOCKS_PER_SEC' undeclared (first use this function)"
171 	 *                            -- cc on NeXTstep/OpenStep */
172 #	define UNIT "units"
173 #	define CLOCKS_PER_SEC 1
174 #endif
175 
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);
185 	}
186 	fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
187 
188 	EC_POINT_free(P);
189 	BN_free(s);
190 	for (i = 0; i < 10; i++)
191 		{
192 		BN_free(r[i]);
193 		if (type != TIMING_BASE_PT) BN_free(r0[i]);
194 		}
195 	}
196 #endif
197 
prime_field_tests()198 void prime_field_tests()
199 	{
200 	BN_CTX *ctx = NULL;
201 	BIGNUM *p, *a, *b;
202 	EC_GROUP *group;
203 	EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
204 	EC_POINT *P, *Q, *R;
205 	BIGNUM *x, *y, *z;
206 	unsigned char buf[100];
207 	size_t i, len;
208 	int k;
209 
210 #if 1 /* optional */
211 	ctx = BN_CTX_new();
212 	if (!ctx) ABORT;
213 #endif
214 
215 	p = BN_new();
216 	a = BN_new();
217 	b = BN_new();
218 	if (!p || !a || !b) ABORT;
219 
220 	if (!BN_hex2bn(&p, "17")) ABORT;
221 	if (!BN_hex2bn(&a, "1")) ABORT;
222 	if (!BN_hex2bn(&b, "1")) ABORT;
223 
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 */
226 	if (!group) ABORT;
227 
228 	if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
229 
230 	{
231 		EC_GROUP *tmp;
232 		tmp = EC_GROUP_new(EC_GROUP_method_of(group));
233 		if (!tmp) ABORT;
234 		if (!EC_GROUP_copy(tmp, group)) ABORT;
235 		EC_GROUP_free(group);
236 		group = tmp;
237 	}
238 
239 	if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;
240 
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");
248 
249 	P = EC_POINT_new(group);
250 	Q = EC_POINT_new(group);
251 	R = EC_POINT_new(group);
252 	if (!P || !Q || !R) ABORT;
253 
254 	if (!EC_POINT_set_to_infinity(group, P)) ABORT;
255 	if (!EC_POINT_is_at_infinity(group, P)) ABORT;
256 
257 	buf[0] = 0;
258 	if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
259 
260 	if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
261 	if (!EC_POINT_is_at_infinity(group, P)) ABORT;
262 
263 	x = BN_new();
264 	y = BN_new();
265 	z = BN_new();
266 	if (!x || !y || !z) ABORT;
267 
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))
271 		{
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");
278 		ABORT;
279 		}
280 
281 	fprintf(stdout, "A cyclic subgroup:\n");
282 	k = 100;
283 	do
284 		{
285 		if (k-- == 0) ABORT;
286 
287 		if (EC_POINT_is_at_infinity(group, P))
288 			fprintf(stdout, "     point at infinity\n");
289 		else
290 			{
291 			if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
292 
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");
298 			}
299 
300 		if (!EC_POINT_copy(R, P)) ABORT;
301 		if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
302 
303 #if 0 /* optional */
304 		{
305 			EC_POINT *points[3];
306 
307 			points[0] = R;
308 			points[1] = Q;
309 			points[2] = P;
310 			if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
311 		}
312 #endif
313 
314 		}
315 	while (!EC_POINT_is_at_infinity(group, P));
316 
317 	if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
318 	if (!EC_POINT_is_at_infinity(group, P)) ABORT;
319 
320 	len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
321 	if (len == 0) ABORT;
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]);
326 
327 	len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
328 	if (len == 0) ABORT;
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]);
333 
334 	len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
335 	if (len == 0) ABORT;
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]);
340 
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");
349 
350 	if (!EC_POINT_invert(group, P, ctx)) ABORT;
351 	if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
352 
353 
354 	/* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000)
355 	 * -- not a NIST curve, but commonly used */
356 
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;
362 
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;
369 
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;
379 
380 	fprintf(stdout, "verify degree ...");
381 	if (EC_GROUP_get_degree(group) != 160) ABORT;
382 	fprintf(stdout, " ok\n");
383 
384 	fprintf(stdout, "verify group order ...");
385 	fflush(stdout);
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, ".");
390 	fflush(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");
395 
396 	if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
397 	if (!EC_GROUP_copy(P_160, group)) ABORT;
398 
399 
400 	/* Curve P-192 (FIPS PUB 186-2, App. 6) */
401 
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;
407 
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;
413 
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;
423 
424 	fprintf(stdout, "verify degree ...");
425 	if (EC_GROUP_get_degree(group) != 192) ABORT;
426 	fprintf(stdout, " ok\n");
427 
428 	fprintf(stdout, "verify group order ...");
429 	fflush(stdout);
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, ".");
434 	fflush(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");
439 
440 	if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
441 	if (!EC_GROUP_copy(P_192, group)) ABORT;
442 
443 
444 	/* Curve P-224 (FIPS PUB 186-2, App. 6) */
445 
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;
451 
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;
457 
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;
467 
468 	fprintf(stdout, "verify degree ...");
469 	if (EC_GROUP_get_degree(group) != 224) ABORT;
470 	fprintf(stdout, " ok\n");
471 
472 	fprintf(stdout, "verify group order ...");
473 	fflush(stdout);
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, ".");
478 	fflush(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");
483 
484 	if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
485 	if (!EC_GROUP_copy(P_224, group)) ABORT;
486 
487 
488 	/* Curve P-256 (FIPS PUB 186-2, App. 6) */
489 
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;
495 
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;
502 
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;
512 
513 	fprintf(stdout, "verify degree ...");
514 	if (EC_GROUP_get_degree(group) != 256) ABORT;
515 	fprintf(stdout, " ok\n");
516 
517 	fprintf(stdout, "verify group order ...");
518 	fflush(stdout);
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, ".");
523 	fflush(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");
528 
529 	if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
530 	if (!EC_GROUP_copy(P_256, group)) ABORT;
531 
532 
533 	/* Curve P-384 (FIPS PUB 186-2, App. 6) */
534 
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;
543 
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;
551 
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;
562 
563 	fprintf(stdout, "verify degree ...");
564 	if (EC_GROUP_get_degree(group) != 384) ABORT;
565 	fprintf(stdout, " ok\n");
566 
567 	fprintf(stdout, "verify group order ...");
568 	fflush(stdout);
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, ".");
573 	fflush(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");
578 
579 	if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
580 	if (!EC_GROUP_copy(P_384, group)) ABORT;
581 
582 
583 	/* Curve P-521 (FIPS PUB 186-2, App. 6) */
584 
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;
596 
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;
606 
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;
618 
619 	fprintf(stdout, "verify degree ...");
620 	if (EC_GROUP_get_degree(group) != 521) ABORT;
621 	fprintf(stdout, " ok\n");
622 
623 	fprintf(stdout, "verify group order ...");
624 	fflush(stdout);
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, ".");
629 	fflush(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");
634 
635 	if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
636 	if (!EC_GROUP_copy(P_521, group)) ABORT;
637 
638 
639 	/* more tests using the last curve */
640 
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 */
646 
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 */
650 
651 	{
652 		const EC_POINT *points[4];
653 		const BIGNUM *scalars[4];
654 		BIGNUM scalar3;
655 
656 		if (EC_POINT_is_at_infinity(group, Q)) ABORT;
657 		points[0] = Q;
658 		points[1] = Q;
659 		points[2] = Q;
660 		points[3] = Q;
661 
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 */
666 		scalars[1] = y;
667 
668 		fprintf(stdout, "combined multiplication ...");
669 		fflush(stdout);
670 
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;
676 
677 		fprintf(stdout, ".");
678 		fflush(stdout);
679 
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);
683 		scalars[0] = y;
684 		scalars[1] = z; /* z = -(order + y) */
685 
686 		if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
687 		if (!EC_POINT_is_at_infinity(group, P)) ABORT;
688 
689 		fprintf(stdout, ".");
690 		fflush(stdout);
691 
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);
695 		scalars[0] = x;
696 		scalars[1] = y;
697 		scalars[2] = z; /* z = -(x+y) */
698 
699 		BN_init(&scalar3);
700 		BN_zero(&scalar3);
701 		scalars[3] = &scalar3;
702 
703 		if (!EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx)) ABORT;
704 		if (!EC_POINT_is_at_infinity(group, P)) ABORT;
705 
706 		fprintf(stdout, " ok\n\n");
707 
708 		BN_free(&scalar3);
709 	}
710 
711 
712 #if 0
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);
731 #endif
732 
733 
734 	if (ctx)
735 		BN_CTX_free(ctx);
736 	BN_free(p); BN_free(a);	BN_free(b);
737 	EC_GROUP_free(group);
738 	EC_POINT_free(P);
739 	EC_POINT_free(Q);
740 	EC_POINT_free(R);
741 	BN_free(x); BN_free(y); BN_free(z);
742 
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);
749 
750 	}
751 
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;
770 #else
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");
784 #endif
785 
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 ..."); \
796 	fflush(stdout); \
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, "."); \
801 	fflush(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;
808 
char2_field_tests()809 void char2_field_tests()
810 	{
811 	BN_CTX *ctx = NULL;
812 	BIGNUM *p, *a, *b;
813 	EC_GROUP *group;
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;
816 	EC_POINT *P, *Q, *R;
817 	BIGNUM *x, *y, *z, *cof;
818 	unsigned char buf[100];
819 	size_t i, len;
820 	int k;
821 
822 #if 1 /* optional */
823 	ctx = BN_CTX_new();
824 	if (!ctx) ABORT;
825 #endif
826 
827 	p = BN_new();
828 	a = BN_new();
829 	b = BN_new();
830 	if (!p || !a || !b) ABORT;
831 
832 	if (!BN_hex2bn(&p, "13")) ABORT;
833 	if (!BN_hex2bn(&a, "3")) ABORT;
834 	if (!BN_hex2bn(&b, "1")) ABORT;
835 
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 */
838 	if (!group) ABORT;
839 	if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT;
840 
841 	{
842 		EC_GROUP *tmp;
843 		tmp = EC_GROUP_new(EC_GROUP_method_of(group));
844 		if (!tmp) ABORT;
845 		if (!EC_GROUP_copy(tmp, group)) ABORT;
846 		EC_GROUP_free(group);
847 		group = tmp;
848 	}
849 
850 	if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT;
851 
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");
859 
860 	P = EC_POINT_new(group);
861 	Q = EC_POINT_new(group);
862 	R = EC_POINT_new(group);
863 	if (!P || !Q || !R) ABORT;
864 
865 	if (!EC_POINT_set_to_infinity(group, P)) ABORT;
866 	if (!EC_POINT_is_at_infinity(group, P)) ABORT;
867 
868 	buf[0] = 0;
869 	if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
870 
871 	if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
872 	if (!EC_POINT_is_at_infinity(group, P)) ABORT;
873 
874 	x = BN_new();
875 	y = BN_new();
876 	z = BN_new();
877 	cof = BN_new();
878 	if (!x || !y || !z || !cof) ABORT;
879 
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;
884 #else
885 	if (!BN_hex2bn(&y, "8")) ABORT;
886 	if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
887 #endif
888 	if (!EC_POINT_is_on_curve(group, Q, ctx))
889 		{
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;
893 #endif
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");
899 		ABORT;
900 		}
901 
902 	fprintf(stdout, "A cyclic subgroup:\n");
903 	k = 100;
904 	do
905 		{
906 		if (k-- == 0) ABORT;
907 
908 		if (EC_POINT_is_at_infinity(group, P))
909 			fprintf(stdout, "     point at infinity\n");
910 		else
911 			{
912 			if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT;
913 
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");
919 			}
920 
921 		if (!EC_POINT_copy(R, P)) ABORT;
922 		if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
923 		}
924 	while (!EC_POINT_is_at_infinity(group, P));
925 
926 	if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
927 	if (!EC_POINT_is_at_infinity(group, P)) ABORT;
928 
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);
932 	if (len == 0) ABORT;
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]);
937 #endif
938 
939 	len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
940 	if (len == 0) ABORT;
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]);
945 
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);
949 	if (len == 0) ABORT;
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]);
954 #endif
955 
956 	fprintf(stdout, "\n");
957 
958 	if (!EC_POINT_invert(group, P, ctx)) ABORT;
959 	if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
960 
961 
962 	/* Curve K-163 (FIPS PUB 186-2, App. 6) */
963 	CHAR2_CURVE_TEST
964 		(
965 		"NIST curve K-163",
966 		"0800000000000000000000000000000000000000C9",
967 		"1",
968 		"1",
969 		"02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
970 		"0289070FB05D38FF58321F2E800536D538CCDAA3D9",
971 		1,
972 		"04000000000000000000020108A2E0CC0D99F8A5EF",
973 		"2",
974 		163,
975 		C2_K163
976 		);
977 
978 	/* Curve B-163 (FIPS PUB 186-2, App. 6) */
979 	CHAR2_CURVE_TEST
980 		(
981 		"NIST curve B-163",
982 		"0800000000000000000000000000000000000000C9",
983 		"1",
984 		"020A601907B8C953CA1481EB10512F78744A3205FD",
985 		"03F0EBA16286A2D57EA0991168D4994637E8343E36",
986 		"00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
987 		1,
988 		"040000000000000000000292FE77E70C12A4234C33",
989 		"2",
990 		163,
991 		C2_B163
992 		);
993 
994 	/* Curve K-233 (FIPS PUB 186-2, App. 6) */
995 	CHAR2_CURVE_TEST
996 		(
997 		"NIST curve K-233",
998 		"020000000000000000000000000000000000000004000000000000000001",
999 		"0",
1000 		"1",
1001 		"017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
1002 		"01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
1003 		0,
1004 		"008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
1005 		"4",
1006 		233,
1007 		C2_K233
1008 		);
1009 
1010 	/* Curve B-233 (FIPS PUB 186-2, App. 6) */
1011 	CHAR2_CURVE_TEST
1012 		(
1013 		"NIST curve B-233",
1014 		"020000000000000000000000000000000000000004000000000000000001",
1015 		"000000000000000000000000000000000000000000000000000000000001",
1016 		"0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
1017 		"00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
1018 		"01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
1019 		1,
1020 		"01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
1021 		"2",
1022 		233,
1023 		C2_B233
1024 		);
1025 
1026 	/* Curve K-283 (FIPS PUB 186-2, App. 6) */
1027 	CHAR2_CURVE_TEST
1028 		(
1029 		"NIST curve K-283",
1030 		"0800000000000000000000000000000000000000000000000000000000000000000010A1",
1031 		"0",
1032 		"1",
1033 		"0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
1034 		"01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
1035 		0,
1036 		"01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
1037 		"4",
1038 		283,
1039 		C2_K283
1040 		);
1041 
1042 	/* Curve B-283 (FIPS PUB 186-2, App. 6) */
1043 	CHAR2_CURVE_TEST
1044 		(
1045 		"NIST curve B-283",
1046 		"0800000000000000000000000000000000000000000000000000000000000000000010A1",
1047 		"000000000000000000000000000000000000000000000000000000000000000000000001",
1048 		"027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
1049 		"05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
1050 		"03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1051 		1,
1052 		"03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
1053 		"2",
1054 		283,
1055 		C2_B283
1056 		);
1057 
1058 	/* Curve K-409 (FIPS PUB 186-2, App. 6) */
1059 	CHAR2_CURVE_TEST
1060 		(
1061 		"NIST curve K-409",
1062 		"02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1063 		"0",
1064 		"1",
1065 		"0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
1066 		"01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1067 		1,
1068 		"007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
1069 		"4",
1070 		409,
1071 		C2_K409
1072 		);
1073 
1074 	/* Curve B-409 (FIPS PUB 186-2, App. 6) */
1075 	CHAR2_CURVE_TEST
1076 		(
1077 		"NIST curve B-409",
1078 		"02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1079 		"00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1080 		"0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
1081 		"015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
1082 		"0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1083 		1,
1084 		"010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
1085 		"2",
1086 		409,
1087 		C2_B409
1088 		);
1089 
1090 	/* Curve K-571 (FIPS PUB 186-2, App. 6) */
1091 	CHAR2_CURVE_TEST
1092 		(
1093 		"NIST curve K-571",
1094 		"80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1095 		"0",
1096 		"1",
1097 		"026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1098 		"0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1099 		0,
1100 		"020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1101 		"4",
1102 		571,
1103 		C2_K571
1104 		);
1105 
1106 	/* Curve B-571 (FIPS PUB 186-2, App. 6) */
1107 	CHAR2_CURVE_TEST
1108 		(
1109 		"NIST curve B-571",
1110 		"80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1111 		"000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1112 		"02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1113 		"0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1114 		"037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1115 		1,
1116 		"03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1117 		"2",
1118 		571,
1119 		C2_B571
1120 		);
1121 
1122 	/* more tests using the last curve */
1123 
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 */
1129 
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 */
1133 
1134 	{
1135 		const EC_POINT *points[3];
1136 		const BIGNUM *scalars[3];
1137 
1138 		if (EC_POINT_is_at_infinity(group, Q)) ABORT;
1139 		points[0] = Q;
1140 		points[1] = Q;
1141 		points[2] = Q;
1142 
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 */
1147 		scalars[1] = y;
1148 
1149 		fprintf(stdout, "combined multiplication ...");
1150 		fflush(stdout);
1151 
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;
1157 
1158 		fprintf(stdout, ".");
1159 		fflush(stdout);
1160 
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);
1164 		scalars[0] = y;
1165 		scalars[1] = z; /* z = -(order + y) */
1166 
1167 		if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
1168 		if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1169 
1170 		fprintf(stdout, ".");
1171 		fflush(stdout);
1172 
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);
1176 		scalars[0] = x;
1177 		scalars[1] = y;
1178 		scalars[2] = z; /* z = -(x+y) */
1179 
1180 		if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
1181 		if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1182 
1183 		fprintf(stdout, " ok\n\n");
1184 	}
1185 
1186 
1187 #if 0
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);
1218 #endif
1219 
1220 
1221 	if (ctx)
1222 		BN_CTX_free(ctx);
1223 	BN_free(p); BN_free(a);	BN_free(b);
1224 	EC_GROUP_free(group);
1225 	EC_POINT_free(P);
1226 	EC_POINT_free(Q);
1227 	EC_POINT_free(R);
1228 	BN_free(x); BN_free(y); BN_free(z); BN_free(cof);
1229 
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);
1240 
1241 	}
1242 
internal_curve_test(void)1243 void internal_curve_test(void)
1244 	{
1245 	EC_builtin_curve *curves = NULL;
1246 	size_t crv_len = 0, n = 0;
1247 	int    ok = 1;
1248 
1249 	crv_len = EC_get_builtin_curves(NULL, 0);
1250 
1251 	curves = OPENSSL_malloc(sizeof(EC_builtin_curve) * crv_len);
1252 
1253 	if (curves == NULL)
1254 		return;
1255 
1256 	if (!EC_get_builtin_curves(curves, crv_len))
1257 		{
1258 		OPENSSL_free(curves);
1259 		return;
1260 		}
1261 
1262 	fprintf(stdout, "testing internal curves: ");
1263 
1264 	for (n = 0; n < crv_len; n++)
1265 		{
1266 		EC_GROUP *group = NULL;
1267 		int nid = curves[n].nid;
1268 		if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL)
1269 			{
1270 			ok = 0;
1271 			fprintf(stdout, "\nEC_GROUP_new_curve_name() failed with"
1272 				" curve %s\n", OBJ_nid2sn(nid));
1273 			/* try next curve */
1274 			continue;
1275 			}
1276 		if (!EC_GROUP_check(group, NULL))
1277 			{
1278 			ok = 0;
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 */
1283 			continue;
1284 			}
1285 		fprintf(stdout, ".");
1286 		fflush(stdout);
1287 		EC_GROUP_free(group);
1288 		}
1289 	if (ok)
1290 		fprintf(stdout, " ok\n");
1291 	else
1292 		fprintf(stdout, " failed\n");
1293 	OPENSSL_free(curves);
1294 	return;
1295 	}
1296 
1297 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
1298 
main(int argc,char * argv[])1299 int main(int argc, char *argv[])
1300 	{
1301 
1302 	/* enable memory leak checking unless explicitly disabled */
1303 	if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
1304 		{
1305 		CRYPTO_malloc_debug_init();
1306 		CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL);
1307 		}
1308 	else
1309 		{
1310 		/* OPENSSL_DEBUG_MEMORY=off */
1311 		CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
1312 		}
1313 	CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
1314 	ERR_load_crypto_strings();
1315 
1316 	RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
1317 
1318 	prime_field_tests();
1319 	puts("");
1320 	char2_field_tests();
1321 	/* test the internal curves */
1322 	internal_curve_test();
1323 
1324 #ifndef OPENSSL_NO_ENGINE
1325 	ENGINE_cleanup();
1326 #endif
1327 	CRYPTO_cleanup_all_ex_data();
1328 	ERR_free_strings();
1329 	ERR_remove_thread_state(NULL);
1330 	CRYPTO_mem_leaks_fp(stderr);
1331 
1332 	return 0;
1333 	}
1334 #endif
1335