ecdsa.c revision 1.2
1/* $OpenBSD: ecdsa.c,v 1.2 2023/07/05 12:27:36 tb Exp $ */
2/* ====================================================================
3 * Copyright (c) 2000-2002 The OpenSSL Project.  All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 *
9 * 1. Redistributions of source code must retain the above copyright
10 *    notice, this list of conditions and the following disclaimer.
11 *
12 * 2. Redistributions in binary form must reproduce the above copyright
13 *    notice, this list of conditions and the following disclaimer in
14 *    the documentation and/or other materials provided with the
15 *    distribution.
16 *
17 * 3. All advertising materials mentioning features or use of this
18 *    software must display the following acknowledgment:
19 *    "This product includes software developed by the OpenSSL Project
20 *    for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
21 *
22 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
23 *    endorse or promote products derived from this software without
24 *    prior written permission. For written permission, please contact
25 *    licensing@OpenSSL.org.
26 *
27 * 5. Products derived from this software may not be called "OpenSSL"
28 *    nor may "OpenSSL" appear in their names without prior written
29 *    permission of the OpenSSL Project.
30 *
31 * 6. Redistributions of any form whatsoever must retain the following
32 *    acknowledgment:
33 *    "This product includes software developed by the OpenSSL Project
34 *    for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
35 *
36 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
37 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
38 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
39 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
40 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
41 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
42 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
43 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
44 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
45 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
46 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
47 * OF THE POSSIBILITY OF SUCH DAMAGE.
48 * ====================================================================
49 *
50 * This product includes cryptographic software written by Eric Young
51 * (eay@cryptsoft.com).  This product includes software written by Tim
52 * Hudson (tjh@cryptsoft.com).
53 *
54 */
55
56#include <string.h>
57
58#include <openssl/opensslconf.h>
59
60#include <openssl/asn1t.h>
61#include <openssl/bn.h>
62#include <openssl/err.h>
63#include <openssl/evp.h>
64#include <openssl/objects.h>
65
66#include "bn_local.h"
67#include "ec_local.h"
68#include "ecdsa_local.h"
69
70static const ASN1_TEMPLATE ECDSA_SIG_seq_tt[] = {
71	{
72		.flags = 0,
73		.tag = 0,
74		.offset = offsetof(ECDSA_SIG, r),
75		.field_name = "r",
76		.item = &BIGNUM_it,
77	},
78	{
79		.flags = 0,
80		.tag = 0,
81		.offset = offsetof(ECDSA_SIG, s),
82		.field_name = "s",
83		.item = &BIGNUM_it,
84	},
85};
86
87const ASN1_ITEM ECDSA_SIG_it = {
88	.itype = ASN1_ITYPE_SEQUENCE,
89	.utype = V_ASN1_SEQUENCE,
90	.templates = ECDSA_SIG_seq_tt,
91	.tcount = sizeof(ECDSA_SIG_seq_tt) / sizeof(ASN1_TEMPLATE),
92	.funcs = NULL,
93	.size = sizeof(ECDSA_SIG),
94	.sname = "ECDSA_SIG",
95};
96
97ECDSA_SIG *ECDSA_SIG_new(void);
98void ECDSA_SIG_free(ECDSA_SIG *a);
99ECDSA_SIG *d2i_ECDSA_SIG(ECDSA_SIG **a, const unsigned char **in, long len);
100int i2d_ECDSA_SIG(const ECDSA_SIG *a, unsigned char **out);
101
102ECDSA_SIG *
103d2i_ECDSA_SIG(ECDSA_SIG **a, const unsigned char **in, long len)
104{
105	return (ECDSA_SIG *)ASN1_item_d2i((ASN1_VALUE **)a, in, len,
106	    &ECDSA_SIG_it);
107}
108
109int
110i2d_ECDSA_SIG(const ECDSA_SIG *a, unsigned char **out)
111{
112	return ASN1_item_i2d((ASN1_VALUE *)a, out, &ECDSA_SIG_it);
113}
114
115ECDSA_SIG *
116ECDSA_SIG_new(void)
117{
118	return (ECDSA_SIG *)ASN1_item_new(&ECDSA_SIG_it);
119}
120
121void
122ECDSA_SIG_free(ECDSA_SIG *a)
123{
124	ASN1_item_free((ASN1_VALUE *)a, &ECDSA_SIG_it);
125}
126
127void
128ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **pr, const BIGNUM **ps)
129{
130	if (pr != NULL)
131		*pr = sig->r;
132	if (ps != NULL)
133		*ps = sig->s;
134}
135
136const BIGNUM *
137ECDSA_SIG_get0_r(const ECDSA_SIG *sig)
138{
139	return sig->r;
140}
141
142const BIGNUM *
143ECDSA_SIG_get0_s(const ECDSA_SIG *sig)
144{
145	return sig->s;
146}
147
148int
149ECDSA_SIG_set0(ECDSA_SIG *sig, BIGNUM *r, BIGNUM *s)
150{
151	if (r == NULL || s == NULL)
152		return 0;
153
154	BN_free(sig->r);
155	BN_free(sig->s);
156	sig->r = r;
157	sig->s = s;
158	return 1;
159}
160
161int
162ECDSA_size(const EC_KEY *r)
163{
164	const EC_GROUP *group;
165	const BIGNUM *order = NULL;
166	ECDSA_SIG sig;
167	int ret = 0;
168
169	if (r == NULL)
170		goto err;
171
172	if ((group = EC_KEY_get0_group(r)) == NULL)
173		goto err;
174
175	if ((order = EC_GROUP_get0_order(group)) == NULL)
176		goto err;
177
178	sig.r = (BIGNUM *)order;
179	sig.s = (BIGNUM *)order;
180
181	if ((ret = i2d_ECDSA_SIG(&sig, NULL)) < 0)
182		ret = 0;
183
184 err:
185	return ret;
186}
187
188/*
189 * FIPS 186-5, section 6.4.1, step 2: convert hashed message into an integer.
190 * Use the order_bits leftmost bits if it exceeds the group order.
191 */
192static int
193ecdsa_prepare_digest(const unsigned char *digest, int digest_len,
194    const EC_KEY *key, BIGNUM *e)
195{
196	const EC_GROUP *group;
197	int digest_bits, order_bits;
198
199	if (!BN_bin2bn(digest, digest_len, e)) {
200		ECDSAerror(ERR_R_BN_LIB);
201		return 0;
202	}
203
204	if ((group = EC_KEY_get0_group(key)) == NULL)
205		return 0;
206	order_bits = EC_GROUP_order_bits(group);
207
208	digest_bits = 8 * digest_len;
209	if (digest_bits <= order_bits)
210		return 1;
211
212	return BN_rshift(e, e, digest_bits - order_bits);
213}
214
215int
216ecdsa_sign(int type, const unsigned char *digest, int digest_len,
217    unsigned char *signature, unsigned int *signature_len, const BIGNUM *kinv,
218    const BIGNUM *r, EC_KEY *key)
219{
220	ECDSA_SIG *sig;
221	int out_len = 0;
222	int ret = 0;
223
224	if ((sig = ECDSA_do_sign_ex(digest, digest_len, kinv, r, key)) == NULL)
225		goto err;
226
227	if ((out_len = i2d_ECDSA_SIG(sig, &signature)) < 0) {
228		out_len = 0;
229		goto err;
230	}
231
232	ret = 1;
233
234 err:
235	*signature_len = out_len;
236	ECDSA_SIG_free(sig);
237
238	return ret;
239}
240
241/*
242 * FIPS 186-5, section 6.4.1, steps 3-8 and 11: Generate k, calculate r and
243 * kinv, and clear it. If r == 0, try again with a new random k.
244 */
245
246int
247ecdsa_sign_setup(EC_KEY *key, BN_CTX *in_ctx, BIGNUM **out_kinv, BIGNUM **out_r)
248{
249	const EC_GROUP *group;
250	EC_POINT *point = NULL;
251	BN_CTX *ctx = NULL;
252	BIGNUM *k = NULL, *r = NULL;
253	const BIGNUM *order;
254	BIGNUM *x;
255	int order_bits;
256	int ret = 0;
257
258	BN_free(*out_kinv);
259	*out_kinv = NULL;
260
261	BN_free(*out_r);
262	*out_r = NULL;
263
264	if (key == NULL) {
265		ECDSAerror(ERR_R_PASSED_NULL_PARAMETER);
266		goto err;
267	}
268	if ((group = EC_KEY_get0_group(key)) == NULL) {
269		ECDSAerror(ERR_R_PASSED_NULL_PARAMETER);
270		goto err;
271	}
272
273	if ((k = BN_new()) == NULL)
274		goto err;
275	if ((r = BN_new()) == NULL)
276		goto err;
277
278	if ((ctx = in_ctx) == NULL)
279		ctx = BN_CTX_new();
280	if (ctx == NULL) {
281		ECDSAerror(ERR_R_MALLOC_FAILURE);
282		goto err;
283	}
284
285	BN_CTX_start(ctx);
286
287	if ((x = BN_CTX_get(ctx)) == NULL)
288		goto err;
289
290	if ((point = EC_POINT_new(group)) == NULL) {
291		ECDSAerror(ERR_R_EC_LIB);
292		goto err;
293	}
294	if ((order = EC_GROUP_get0_order(group)) == NULL) {
295		ECDSAerror(ERR_R_EC_LIB);
296		goto err;
297	}
298
299	if (BN_cmp(order, BN_value_one()) <= 0) {
300		ECDSAerror(EC_R_INVALID_GROUP_ORDER);
301		goto err;
302	}
303
304	/* Reject curves with an order that is smaller than 80 bits. */
305	if ((order_bits = BN_num_bits(order)) < 80) {
306		ECDSAerror(EC_R_INVALID_GROUP_ORDER);
307		goto err;
308	}
309
310	/* Preallocate space. */
311	if (!BN_set_bit(k, order_bits) ||
312	    !BN_set_bit(r, order_bits) ||
313	    !BN_set_bit(x, order_bits))
314		goto err;
315
316	/* Step 11: repeat until r != 0. */
317	do {
318		/* Step 3: generate random k. */
319		if (!bn_rand_interval(k, BN_value_one(), order)) {
320			ECDSAerror(ECDSA_R_RANDOM_NUMBER_GENERATION_FAILED);
321			goto err;
322		}
323
324		/*
325		 * We do not want timing information to leak the length of k,
326		 * so we compute G * k using an equivalent scalar of fixed
327		 * bit-length.
328		 *
329		 * We unconditionally perform both of these additions to prevent
330		 * a small timing information leakage.  We then choose the sum
331		 * that is one bit longer than the order.  This guarantees the
332		 * code path used in the constant time implementations
333		 * elsewhere.
334		 *
335		 * TODO: revisit the bn_copy aiming for a memory access agnostic
336		 * conditional copy.
337		 */
338		if (!BN_add(r, k, order) ||
339		    !BN_add(x, r, order) ||
340		    !bn_copy(k, BN_num_bits(r) > order_bits ? r : x))
341			goto err;
342
343		BN_set_flags(k, BN_FLG_CONSTTIME);
344
345		/* Step 5: P = k * G. */
346		if (!EC_POINT_mul(group, point, k, NULL, NULL, ctx)) {
347			ECDSAerror(ERR_R_EC_LIB);
348			goto err;
349		}
350		/* Steps 6 (and 7): from P = (x, y) retain the x-coordinate. */
351		if (!EC_POINT_get_affine_coordinates(group, point, x, NULL,
352		    ctx)) {
353			ECDSAerror(ERR_R_EC_LIB);
354			goto err;
355		}
356		/* Step 8: r = x (mod order). */
357		if (!BN_nnmod(r, x, order, ctx)) {
358			ECDSAerror(ERR_R_BN_LIB);
359			goto err;
360		}
361	} while (BN_is_zero(r));
362
363	/* Step 4: calculate kinv. */
364	if (BN_mod_inverse_ct(k, k, order, ctx) == NULL) {
365		ECDSAerror(ERR_R_BN_LIB);
366		goto err;
367	}
368
369	*out_kinv = k;
370	k = NULL;
371
372	*out_r = r;
373	r = NULL;
374
375	ret = 1;
376
377 err:
378	BN_CTX_end(ctx);
379	if (ctx != in_ctx)
380		BN_CTX_free(ctx);
381	BN_free(k);
382	BN_free(r);
383	EC_POINT_free(point);
384
385	return ret;
386}
387
388/*
389 * FIPS 186-5, section 6.4.1, step 9: compute s = inv(k)(e + xr) mod order.
390 * In order to reduce the possibility of a side-channel attack, the following
391 * is calculated using a random blinding value b in [1, order):
392 * s = inv(b)(be + bxr)inv(k) mod order.
393 */
394
395static int
396ecdsa_compute_s(BIGNUM **out_s, const BIGNUM *e, const BIGNUM *kinv,
397    const BIGNUM *r, const EC_KEY *key, BN_CTX *ctx)
398{
399	const EC_GROUP *group;
400	const BIGNUM *order, *priv_key;
401	BIGNUM *b, *binv, *be, *bxr;
402	BIGNUM *s = NULL;
403	int ret = 0;
404
405	*out_s = NULL;
406
407	BN_CTX_start(ctx);
408
409	if ((group = EC_KEY_get0_group(key)) == NULL) {
410		ECDSAerror(ERR_R_PASSED_NULL_PARAMETER);
411		goto err;
412	}
413	if ((order = EC_GROUP_get0_order(group)) == NULL) {
414		ECDSAerror(ERR_R_EC_LIB);
415		goto err;
416	}
417	if ((priv_key = EC_KEY_get0_private_key(key)) == NULL) {
418		ECDSAerror(ERR_R_PASSED_NULL_PARAMETER);
419		goto err;
420	}
421
422	if ((b = BN_CTX_get(ctx)) == NULL)
423		goto err;
424	if ((binv = BN_CTX_get(ctx)) == NULL)
425		goto err;
426	if ((be = BN_CTX_get(ctx)) == NULL)
427		goto err;
428	if ((bxr = BN_CTX_get(ctx)) == NULL)
429		goto err;
430
431	if ((s = BN_new()) == NULL)
432		goto err;
433
434	/*
435	 * In a valid ECDSA signature, r must be in [1, order). Since r can be
436	 * caller provided - either directly or by replacing sign_setup() - we
437	 * can't rely on this being the case.
438	 */
439	if (BN_cmp(r, BN_value_one()) < 0 || BN_cmp(r, order) >= 0) {
440		ECDSAerror(ECDSA_R_BAD_SIGNATURE);
441		goto err;
442	}
443
444	if (!bn_rand_interval(b, BN_value_one(), order)) {
445		ECDSAerror(ERR_R_BN_LIB);
446		goto err;
447	}
448
449	if (BN_mod_inverse_ct(binv, b, order, ctx) == NULL) {
450		ECDSAerror(ERR_R_BN_LIB);
451		goto err;
452	}
453
454	if (!BN_mod_mul(bxr, b, priv_key, order, ctx)) {
455		ECDSAerror(ERR_R_BN_LIB);
456		goto err;
457	}
458	if (!BN_mod_mul(bxr, bxr, r, order, ctx)) {
459		ECDSAerror(ERR_R_BN_LIB);
460		goto err;
461	}
462	if (!BN_mod_mul(be, b, e, order, ctx)) {
463		ECDSAerror(ERR_R_BN_LIB);
464		goto err;
465	}
466	if (!BN_mod_add(s, be, bxr, order, ctx)) {
467		ECDSAerror(ERR_R_BN_LIB);
468		goto err;
469	}
470	/* s = b(e + xr)k^-1 */
471	if (!BN_mod_mul(s, s, kinv, order, ctx)) {
472		ECDSAerror(ERR_R_BN_LIB);
473		goto err;
474	}
475	/* s = (e + xr)k^-1 */
476	if (!BN_mod_mul(s, s, binv, order, ctx)) {
477		ECDSAerror(ERR_R_BN_LIB);
478		goto err;
479	}
480
481	/* Step 11: if s == 0 start over. */
482	if (!BN_is_zero(s)) {
483		*out_s = s;
484		s = NULL;
485	}
486
487	ret = 1;
488
489 err:
490	BN_CTX_end(ctx);
491	BN_free(s);
492
493	return ret;
494}
495
496/*
497 * It is too expensive to check curve parameters on every sign operation.
498 * Instead, cap the number of retries. A single retry is very unlikely, so
499 * allowing 32 retries is amply enough.
500 */
501#define ECDSA_MAX_SIGN_ITERATIONS		32
502
503/*
504 * FIPS 186-5: Section 6.4.1: ECDSA signature generation, steps 2-12.
505 * The caller provides the hash of the message, thus performs step 1.
506 * Step 10, zeroing k and kinv, is done by BN_free().
507 */
508
509ECDSA_SIG *
510ecdsa_sign_sig(const unsigned char *digest, int digest_len,
511    const BIGNUM *in_kinv, const BIGNUM *in_r, EC_KEY *key)
512{
513	BN_CTX *ctx = NULL;
514	BIGNUM *kinv = NULL, *r = NULL, *s = NULL;
515	BIGNUM *e;
516	int caller_supplied_values = 0;
517	int attempts = 0;
518	ECDSA_SIG *sig = NULL;
519
520	if ((ctx = BN_CTX_new()) == NULL) {
521		ECDSAerror(ERR_R_MALLOC_FAILURE);
522		goto err;
523	}
524
525	BN_CTX_start(ctx);
526
527	if ((e = BN_CTX_get(ctx)) == NULL)
528		goto err;
529
530	/* Step 2: convert hash into an integer. */
531	if (!ecdsa_prepare_digest(digest, digest_len, key, e))
532		goto err;
533
534	if (in_kinv != NULL && in_r != NULL) {
535		/*
536		 * Use the caller's kinv and r. Don't call ECDSA_sign_setup().
537		 * If we're unable to compute a valid signature, the caller
538		 * must provide new values.
539		 */
540		caller_supplied_values = 1;
541
542		if ((kinv = BN_dup(in_kinv)) == NULL) {
543			ECDSAerror(ERR_R_MALLOC_FAILURE);
544			goto err;
545		}
546		if ((r = BN_dup(in_r)) == NULL) {
547			ECDSAerror(ERR_R_MALLOC_FAILURE);
548			goto err;
549		}
550	}
551
552	do {
553		/* Steps 3-8: calculate kinv and r. */
554		if (!caller_supplied_values) {
555			if (!ECDSA_sign_setup(key, ctx, &kinv, &r)) {
556				ECDSAerror(ERR_R_ECDSA_LIB);
557				goto err;
558			}
559		}
560
561		/*
562		 * Steps 9 and 11: if s is non-NULL, we have a valid signature.
563		 */
564		if (!ecdsa_compute_s(&s, e, kinv, r, key, ctx))
565			goto err;
566		if (s != NULL)
567			break;
568
569		if (caller_supplied_values) {
570			ECDSAerror(ECDSA_R_NEED_NEW_SETUP_VALUES);
571			goto err;
572		}
573
574		if (++attempts > ECDSA_MAX_SIGN_ITERATIONS) {
575			ECDSAerror(EC_R_WRONG_CURVE_PARAMETERS);
576			goto err;
577		}
578	} while (1);
579
580	/* Step 12: output (r, s). */
581	if ((sig = ECDSA_SIG_new()) == NULL) {
582		ECDSAerror(ERR_R_MALLOC_FAILURE);
583		goto err;
584	}
585	if (!ECDSA_SIG_set0(sig, r, s)) {
586		ECDSA_SIG_free(sig);
587		goto err;
588	}
589	r = NULL;
590	s = NULL;
591
592 err:
593	BN_CTX_end(ctx);
594	BN_CTX_free(ctx);
595	BN_free(kinv);
596	BN_free(r);
597	BN_free(s);
598
599	return sig;
600}
601
602int
603ecdsa_verify(int type, const unsigned char *digest, int digest_len,
604    const unsigned char *sigbuf, int sig_len, EC_KEY *key)
605{
606	ECDSA_SIG *s;
607	unsigned char *der = NULL;
608	const unsigned char *p;
609	int der_len = 0;
610	int ret = -1;
611
612	if ((s = ECDSA_SIG_new()) == NULL)
613		goto err;
614
615	p = sigbuf;
616	if (d2i_ECDSA_SIG(&s, &p, sig_len) == NULL)
617		goto err;
618
619	/* Ensure signature uses DER and doesn't have trailing garbage */
620	if ((der_len = i2d_ECDSA_SIG(s, &der)) != sig_len)
621		goto err;
622	if (timingsafe_memcmp(sigbuf, der, der_len))
623		goto err;
624
625	ret = ECDSA_do_verify(digest, digest_len, s, key);
626
627 err:
628	freezero(der, der_len);
629	ECDSA_SIG_free(s);
630
631	return ret;
632}
633
634/*
635 * FIPS 186-5, section 6.4.2: ECDSA signature verification.
636 * The caller provides us with the hash of the message, so has performed step 2.
637 */
638
639int
640ecdsa_verify_sig(const unsigned char *digest, int digest_len,
641    const ECDSA_SIG *sig, EC_KEY *key)
642{
643	const EC_GROUP *group;
644	const EC_POINT *pub_key;
645	EC_POINT *point = NULL;
646	const BIGNUM *order;
647	BN_CTX *ctx = NULL;
648	BIGNUM *e, *sinv, *u, *v, *x;
649	int ret = -1;
650
651	if (key == NULL || sig == NULL) {
652		ECDSAerror(ECDSA_R_MISSING_PARAMETERS);
653		goto err;
654	}
655	if ((group = EC_KEY_get0_group(key)) == NULL) {
656		ECDSAerror(ECDSA_R_MISSING_PARAMETERS);
657		goto err;
658	}
659	if ((pub_key = EC_KEY_get0_public_key(key)) == NULL) {
660		ECDSAerror(ECDSA_R_MISSING_PARAMETERS);
661		goto err;
662	}
663
664	if ((ctx = BN_CTX_new()) == NULL) {
665		ECDSAerror(ERR_R_MALLOC_FAILURE);
666		goto err;
667	}
668
669	BN_CTX_start(ctx);
670
671	if ((e = BN_CTX_get(ctx)) == NULL)
672		goto err;
673	if ((sinv = BN_CTX_get(ctx)) == NULL)
674		goto err;
675	if ((u = BN_CTX_get(ctx)) == NULL)
676		goto err;
677	if ((v = BN_CTX_get(ctx)) == NULL)
678		goto err;
679	if ((x = BN_CTX_get(ctx)) == NULL)
680		goto err;
681
682	if ((order = EC_GROUP_get0_order(group)) == NULL) {
683		ECDSAerror(ERR_R_EC_LIB);
684		goto err;
685	}
686
687	/* Step 1: verify that r and s are in the range [1, order). */
688	if (BN_cmp(sig->r, BN_value_one()) < 0 || BN_cmp(sig->r, order) >= 0) {
689		ECDSAerror(ECDSA_R_BAD_SIGNATURE);
690		ret = 0;
691		goto err;
692	}
693	if (BN_cmp(sig->s, BN_value_one()) < 0 || BN_cmp(sig->s, order) >= 0) {
694		ECDSAerror(ECDSA_R_BAD_SIGNATURE);
695		ret = 0;
696		goto err;
697	}
698
699	/* Step 3: convert the hash into an integer. */
700	if (!ecdsa_prepare_digest(digest, digest_len, key, e))
701		goto err;
702
703	/* Step 4: compute the inverse of s modulo order. */
704	if (BN_mod_inverse_ct(sinv, sig->s, order, ctx) == NULL) {
705		ECDSAerror(ERR_R_BN_LIB);
706		goto err;
707	}
708	/* Step 5: compute u = s^-1 * e and v = s^-1 * r (modulo order). */
709	if (!BN_mod_mul(u, e, sinv, order, ctx)) {
710		ECDSAerror(ERR_R_BN_LIB);
711		goto err;
712	}
713	if (!BN_mod_mul(v, sig->r, sinv, order, ctx)) {
714		ECDSAerror(ERR_R_BN_LIB);
715		goto err;
716	}
717
718	/*
719	 * Steps 6 and 7: compute R = G * u + pub_key * v = (x, y). Reject if
720	 * it's the point at infinity - getting affine coordinates fails. Keep
721	 * the x coordinate.
722	 */
723	if ((point = EC_POINT_new(group)) == NULL) {
724		ECDSAerror(ERR_R_MALLOC_FAILURE);
725		goto err;
726	}
727	if (!EC_POINT_mul(group, point, u, pub_key, v, ctx)) {
728		ECDSAerror(ERR_R_EC_LIB);
729		goto err;
730	}
731	if (!EC_POINT_get_affine_coordinates(group, point, x, NULL, ctx)) {
732		ECDSAerror(ERR_R_EC_LIB);
733		goto err;
734	}
735	/* Step 8: convert x to a number in [0, order). */
736	if (!BN_nnmod(x, x, order, ctx)) {
737		ECDSAerror(ERR_R_BN_LIB);
738		goto err;
739	}
740
741	/* Step 9: the signature is valid iff the x-coordinate is equal to r. */
742	ret = (BN_cmp(x, sig->r) == 0);
743
744 err:
745	BN_CTX_end(ctx);
746	BN_CTX_free(ctx);
747	EC_POINT_free(point);
748
749	return ret;
750}
751
752ECDSA_SIG *
753ECDSA_do_sign(const unsigned char *digest, int digest_len, EC_KEY *key)
754{
755	return ECDSA_do_sign_ex(digest, digest_len, NULL, NULL, key);
756}
757
758ECDSA_SIG *
759ECDSA_do_sign_ex(const unsigned char *digest, int digest_len,
760    const BIGNUM *kinv, const BIGNUM *out_r, EC_KEY *key)
761{
762	if (key->meth->sign_sig == NULL) {
763		ECDSAerror(EVP_R_METHOD_NOT_SUPPORTED);
764		return 0;
765	}
766	return key->meth->sign_sig(digest, digest_len, kinv, out_r, key);
767}
768
769int
770ECDSA_sign(int type, const unsigned char *digest, int digest_len,
771    unsigned char *signature, unsigned int *signature_len, EC_KEY *key)
772{
773	return ECDSA_sign_ex(type, digest, digest_len, signature, signature_len,
774	    NULL, NULL, key);
775}
776
777int
778ECDSA_sign_ex(int type, const unsigned char *digest, int digest_len,
779    unsigned char *signature, unsigned int *signature_len, const BIGNUM *kinv,
780    const BIGNUM *r, EC_KEY *key)
781{
782	if (key->meth->sign == NULL) {
783		ECDSAerror(EVP_R_METHOD_NOT_SUPPORTED);
784		return 0;
785	}
786	return key->meth->sign(type, digest, digest_len, signature,
787	    signature_len, kinv, r, key);
788}
789
790int
791ECDSA_sign_setup(EC_KEY *key, BN_CTX *in_ctx, BIGNUM **out_kinv,
792    BIGNUM **out_r)
793{
794	if (key->meth->sign_setup == NULL) {
795		ECDSAerror(EVP_R_METHOD_NOT_SUPPORTED);
796		return 0;
797	}
798	return key->meth->sign_setup(key, in_ctx, out_kinv, out_r);
799}
800
801int
802ECDSA_do_verify(const unsigned char *digest, int digest_len,
803    const ECDSA_SIG *sig, EC_KEY *key)
804{
805	if (key->meth->verify_sig == NULL) {
806		ECDSAerror(EVP_R_METHOD_NOT_SUPPORTED);
807		return 0;
808	}
809	return key->meth->verify_sig(digest, digest_len, sig, key);
810}
811
812int
813ECDSA_verify(int type, const unsigned char *digest, int digest_len,
814    const unsigned char *sigbuf, int sig_len, EC_KEY *key)
815{
816	if (key->meth->verify == NULL) {
817		ECDSAerror(EVP_R_METHOD_NOT_SUPPORTED);
818		return 0;
819	}
820	return key->meth->verify(type, digest, digest_len, sigbuf, sig_len, key);
821}
822