xref: /freebsd/crypto/libecc/src/sig/ecdsa_common.c (revision f0865ec9906d5a18fa2a3b61381f22ce16e606ad)
1 /*
2  *  Copyright (C) 2017 - This file is part of libecc project
3  *
4  *  Authors:
5  *      Ryad BENADJILA <ryadbenadjila@gmail.com>
6  *      Arnaud EBALARD <arnaud.ebalard@ssi.gouv.fr>
7  *      Jean-Pierre FLORI <jean-pierre.flori@ssi.gouv.fr>
8  *
9  *  Contributors:
10  *      Nicolas VIVET <nicolas.vivet@ssi.gouv.fr>
11  *      Karim KHALFALLAH <karim.khalfallah@ssi.gouv.fr>
12  *
13  *  This software is licensed under a dual BSD and GPL v2 license.
14  *  See LICENSE file at the root folder of the project.
15  */
16 #include <libecc/lib_ecc_config.h>
17 #if defined(WITH_SIG_ECDSA) || defined(WITH_SIG_DECDSA)
18 
19 #include <libecc/nn/nn_rand.h>
20 #include <libecc/nn/nn_mul_public.h>
21 #include <libecc/nn/nn_logical.h>
22 
23 #include <libecc/sig/sig_algs_internal.h>
24 #include <libecc/sig/ec_key.h>
25 #include <libecc/utils/utils.h>
26 #ifdef VERBOSE_INNER_VALUES
27 #define EC_SIG_ALG "ECDSA"
28 #endif
29 #include <libecc/utils/dbg_sig.h>
30 
31 
32 #if defined(WITH_SIG_DECDSA)
33 #include <libecc/hash/hmac.h>
34 
35 /*
36  * Deterministic nonce generation function for deterministic ECDSA, as
37  * described in RFC6979.
38  * NOTE: Deterministic nonce generation for ECDSA is useful against attackers
39  * in contexts where only poor RNG/entropy are available, or when nonce bits
40  * leaking can be possible through side-channel attacks.
41  * However, in contexts where fault attacks are easy to mount, deterministic
42  * ECDSA can bring more security risks than regular ECDSA.
43  *
44  * Depending on the context where you use the library, choose carefully if
45  * you want to use the deterministic version or not.
46  *
47  */
__ecdsa_rfc6979_nonce(nn_t k,nn_src_t q,bitcnt_t q_bit_len,nn_src_t x,const u8 * hash,u8 hsize,hash_alg_type hash_type)48 ATTRIBUTE_WARN_UNUSED_RET static int __ecdsa_rfc6979_nonce(nn_t k, nn_src_t q, bitcnt_t q_bit_len,
49 				 nn_src_t x, const u8 *hash, u8 hsize,
50 				 hash_alg_type hash_type)
51 {
52 	int ret, cmp;
53 	u8 V[MAX_DIGEST_SIZE];
54 	u8 K[MAX_DIGEST_SIZE];
55 	u8 T[BYTECEIL(CURVES_MAX_Q_BIT_LEN) + MAX_DIGEST_SIZE];
56 	u8 priv_key_buff[EC_PRIV_KEY_MAX_SIZE];
57 	hmac_context hmac_ctx;
58 	bitcnt_t t_bit_len;
59 	u8 q_len;
60 	u8 hmac_size;
61 	u8 tmp;
62 
63 	/* Sanity checks */
64 	MUST_HAVE((k != NULL), ret, err);
65 	MUST_HAVE((hash != NULL), ret, err);
66 	ret = nn_check_initialized(q); EG(ret, err);
67 	ret = nn_check_initialized(x); EG(ret, err);
68 
69 	q_len = (u8)BYTECEIL(q_bit_len);
70 
71 	MUST_HAVE((q_len <= EC_PRIV_KEY_MAX_SIZE) && (hsize <= MAX_BLOCK_SIZE), ret, err);
72 
73 	/* Steps b. and c.: set V = 0x01 ... 0x01 and K = 0x00 ... 0x00 */
74 	ret = local_memset(V, 0x01, hsize); EG(ret, err);
75 	ret = local_memset(K, 0x00, hsize); EG(ret, err);
76 	/* Export our private key in a buffer */
77 	ret = nn_export_to_buf(priv_key_buff, q_len, x); EG(ret, err);
78 	/* Step d.: set K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1))
79 	 * where x is the private key and h1 the message hash.
80 	 */
81 	ret = hmac_init(&hmac_ctx, K, hsize, hash_type); EG(ret, err);
82 	ret = hmac_update(&hmac_ctx, V, hsize); EG(ret, err);
83 
84 	tmp = 0x00;
85 	ret = hmac_update(&hmac_ctx, &tmp, 1); EG(ret, err);
86 	ret = hmac_update(&hmac_ctx, priv_key_buff, q_len); EG(ret, err);
87 
88 	/* We compute bits2octets(hash) here */
89 	ret = nn_init_from_buf(k, hash, hsize); EG(ret, err);
90 	if((8 * hsize) > q_bit_len){
91 		ret = nn_rshift(k, k, (bitcnt_t)((8 * hsize) - q_bit_len)); EG(ret, err);
92 	}
93 	ret = nn_mod(k, k, q); EG(ret, err);
94 	ret = nn_export_to_buf(T, q_len, k); EG(ret, err);
95 	ret = hmac_update(&hmac_ctx, T, q_len); EG(ret, err);
96 	hmac_size = sizeof(K);
97 	ret = hmac_finalize(&hmac_ctx, K, &hmac_size); EG(ret, err);
98 
99 	/* Step e.: set V = HMAC_K(V) */
100 	hmac_size = sizeof(V);
101 	ret = hmac(K, hsize, hash_type, V, hsize, V, &hmac_size); EG(ret, err);
102 	/*  Step f.: K = HMAC_K(V || 0x01 || int2octets(x) || bits2octets(h1)) */
103 	ret = hmac_init(&hmac_ctx, K, hsize, hash_type); EG(ret, err);
104 	ret = hmac_update(&hmac_ctx, V, hsize); EG(ret, err);
105 
106 	tmp = 0x01;
107 	ret = hmac_update(&hmac_ctx, &tmp, 1); EG(ret, err);
108 	ret = hmac_update(&hmac_ctx, priv_key_buff, q_len); EG(ret, err);
109 
110 	/* We compute bits2octets(hash) here */
111 	ret = hmac_update(&hmac_ctx, T, q_len); EG(ret, err);
112 	hmac_size = sizeof(K);
113 	ret = hmac_finalize(&hmac_ctx, K, &hmac_size); EG(ret, err);
114 	/* Step g.: set V = HMAC_K(V)*/
115 	hmac_size = sizeof(V);
116 	ret = hmac(K, hsize, hash_type, V, hsize, V, &hmac_size); EG(ret, err);
117 
118 	/* Step h. now apply the generation algorithm until we get
119 	 * a proper nonce value:
120 	 * 1.  Set T to the empty sequence.  The length of T (in bits) is
121 	 * denoted tlen; thus, at that point, tlen = 0.
122 	 * 2.  While tlen < qlen, do the following:
123 	 *    V = HMAC_K(V)
124 	 *    T = T || V
125 	 * 3.  Compute:
126 	 *    k = bits2int(T)
127 	 * If that value of k is within the [1,q-1] range, and is
128 	 * suitable for DSA or ECDSA (i.e., it results in an r value
129 	 * that is not 0; see Section 3.4), then the generation of k is
130 	 * finished.  The obtained value of k is used in DSA or ECDSA.
131 	 * Otherwise, compute:
132 	 *    K = HMAC_K(V || 0x00)
133 	 *    V = HMAC_K(V)
134 	 * and loop (try to generate a new T, and so on).
135 	 */
136 restart:
137 	t_bit_len = 0;
138 	while(t_bit_len < q_bit_len){
139 		/* V = HMAC_K(V) */
140 		hmac_size = sizeof(V);
141 		ret = hmac(K, hsize, hash_type, V, hsize, V, &hmac_size); EG(ret, err);
142 		ret = local_memcpy(&T[BYTECEIL(t_bit_len)], V, hmac_size); EG(ret, err);
143 		t_bit_len = (bitcnt_t)(t_bit_len + (8 * hmac_size));
144 	}
145 	ret = nn_init_from_buf(k, T, q_len); EG(ret, err);
146 	if((8 * q_len) > q_bit_len){
147 		ret = nn_rshift(k, k, (bitcnt_t)((8 * q_len) - q_bit_len)); EG(ret, err);
148 	}
149 	ret = nn_cmp(k, q, &cmp); EG(ret, err);
150 	if(cmp >= 0){
151 		/* K = HMAC_K(V || 0x00) */
152 		ret = hmac_init(&hmac_ctx, K, hsize, hash_type); EG(ret, err);
153 		ret = hmac_update(&hmac_ctx, V, hsize); EG(ret, err);
154 
155 		tmp = 0x00;
156 		ret = hmac_update(&hmac_ctx, &tmp, 1); EG(ret, err);
157 
158 		hmac_size = sizeof(K);
159 		ret = hmac_finalize(&hmac_ctx, K, &hmac_size); EG(ret, err);
160 		/* V = HMAC_K(V) */
161 		hmac_size = sizeof(V);
162 		ret = hmac(K, hsize, hash_type, V, hsize, V, &hmac_size); EG(ret, err);
163 
164 		goto restart;
165 	}
166 
167 err:
168 	return ret;
169 }
170 #endif
171 
__ecdsa_init_pub_key(ec_pub_key * out_pub,const ec_priv_key * in_priv,ec_alg_type key_type)172 int __ecdsa_init_pub_key(ec_pub_key *out_pub, const ec_priv_key *in_priv,
173 			 ec_alg_type key_type)
174 {
175 	prj_pt_src_t G;
176 	int ret, cmp;
177 	nn_src_t q;
178 
179 	MUST_HAVE((out_pub != NULL), ret, err);
180 
181 	/* Zero init public key to be generated */
182 	ret = local_memset(out_pub, 0, sizeof(ec_pub_key)); EG(ret, err);
183 
184 	ret = priv_key_check_initialized_and_type(in_priv, key_type); EG(ret, err);
185 	q = &(in_priv->params->ec_gen_order);
186 
187 	/* Sanity check on key compliance */
188 	MUST_HAVE((!nn_cmp(&(in_priv->x), q, &cmp)) && (cmp < 0), ret, err);
189 
190 	/* Y = xG */
191 	G = &(in_priv->params->ec_gen);
192 	/* Use blinding when computing point scalar multiplication */
193 	ret = prj_pt_mul_blind(&(out_pub->y), &(in_priv->x), G); EG(ret, err);
194 
195 	out_pub->key_type = key_type;
196 	out_pub->params = in_priv->params;
197 	out_pub->magic = PUB_KEY_MAGIC;
198 
199 err:
200 	return ret;
201 }
202 
__ecdsa_siglen(u16 p_bit_len,u16 q_bit_len,u8 hsize,u8 blocksize,u8 * siglen)203 int __ecdsa_siglen(u16 p_bit_len, u16 q_bit_len, u8 hsize, u8 blocksize, u8 *siglen)
204 {
205 	int ret;
206 
207 	MUST_HAVE(siglen != NULL, ret, err);
208 	MUST_HAVE((p_bit_len <= CURVES_MAX_P_BIT_LEN) &&
209 		  (q_bit_len <= CURVES_MAX_Q_BIT_LEN) &&
210 		  (hsize <= MAX_DIGEST_SIZE) && (blocksize <= MAX_BLOCK_SIZE), ret, err);
211 	(*siglen) = (u8)ECDSA_SIGLEN(q_bit_len);
212 	ret = 0;
213 
214 err:
215 	return ret;
216 }
217 
218 /*
219  * Generic *internal* ECDSA signature functions (init, update and finalize).
220  * Their purpose is to allow passing a specific hash function (along with
221  * its output size) and the random ephemeral key k, so that compliance
222  * tests against test vectors can be made without ugly hack in the code
223  * itself.
224  *
225  * Global EC-DSA signature process is as follows (I,U,F provides
226  * information in which function(s) (init(), update() or finalize())
227  * a specific step is performed):
228  *
229  *| IUF	 - ECDSA signature
230  *|
231  *|  UF	 1. Compute h = H(m)
232  *|   F	 2. If |h| > bitlen(q), set h to bitlen(q)
233  *|	    leftmost (most significant) bits of h
234  *|   F	 3. e = OS2I(h) mod q
235  *|   F	 4. Get a random value k in ]0,q[
236  *|   F	 5. Compute W = (W_x,W_y) = kG
237  *|   F	 6. Compute r = W_x mod q
238  *|   F	 7. If r is 0, restart the process at step 4.
239  *|   F	 8. If e == rx, restart the process at step 4.
240  *|   F	 9. Compute s = k^-1 * (xr + e) mod q
241  *|   F 10. If s is 0, restart the process at step 4.
242  *|   F 11. Return (r,s)
243  *
244  * Implementation notes:
245  *
246  * a) Usually (this is for instance the case in ISO 14888-3 and X9.62), the
247  *    process starts with steps 4 to 7 and is followed by steps 1 to 3.
248  *    The order is modified here w/o impact on the result and the security
249  *    in order to allow the algorithm to be compatible with an
250  *    init/update/finish API. More explicitly, the generation of k, which
251  *    may later result in a (unlikely) restart of the whole process is
252  *    postponed until the hash of the message has been computed.
253  * b) sig is built as the concatenation of r and s. Both r and s are
254  *    encoded on ceil(bitlen(q)/8) bytes.
255  * c) in EC-DSA, the public part of the key is not needed per se during the
256  *    signature but - as it is needed in other signature algs implemented
257  *    in the library - the whole key pair is passed instead of just the
258  *    private key.
259  */
260 
261 #define ECDSA_SIGN_MAGIC ((word_t)(0x80299a2bf630945bULL))
262 #define ECDSA_SIGN_CHECK_INITIALIZED(A, ret, err) \
263 	MUST_HAVE((((void *)(A)) != NULL) && ((A)->magic == ECDSA_SIGN_MAGIC), ret, err)
264 
__ecdsa_sign_init(struct ec_sign_context * ctx,ec_alg_type key_type)265 int __ecdsa_sign_init(struct ec_sign_context *ctx, ec_alg_type key_type)
266 {
267 	int ret;
268 
269 	/* First, verify context has been initialized */
270 	ret = sig_sign_check_initialized(ctx); EG(ret, err);
271 
272 	/* Additional sanity checks on input params from context */
273 	ret = key_pair_check_initialized_and_type(ctx->key_pair, key_type); EG(ret, err);
274 
275 	MUST_HAVE((ctx->h != NULL) && (ctx->h->digest_size <= MAX_DIGEST_SIZE) &&
276 		  (ctx->h->block_size <= MAX_BLOCK_SIZE), ret, err);
277 
278 	/*
279 	 * Initialize hash context stored in our private part of context
280 	 * and record data init has been done
281 	 */
282 	/* Since we call a callback, sanity check our mapping */
283 	ret = hash_mapping_callbacks_sanity_check(ctx->h); EG(ret, err);
284 	ret = ctx->h->hfunc_init(&(ctx->sign_data.ecdsa.h_ctx)); EG(ret, err);
285 
286 	ctx->sign_data.ecdsa.magic = ECDSA_SIGN_MAGIC;
287 
288 err:
289 	return ret;
290 }
291 
__ecdsa_sign_update(struct ec_sign_context * ctx,const u8 * chunk,u32 chunklen,ec_alg_type key_type)292 int __ecdsa_sign_update(struct ec_sign_context *ctx,
293 		       const u8 *chunk, u32 chunklen, ec_alg_type key_type)
294 {
295 	int ret;
296 
297 	/*
298 	 * First, verify context has been initialized and private
299 	 * part too. This guarantees the context is an ECDSA
300 	 * signature one and we do not update() or finalize()
301 	 * before init().
302 	 */
303 	ret = sig_sign_check_initialized(ctx); EG(ret, err);
304 	ECDSA_SIGN_CHECK_INITIALIZED(&(ctx->sign_data.ecdsa), ret, err);
305 
306 	/* Additional sanity checks on input params from context */
307 	ret = key_pair_check_initialized_and_type(ctx->key_pair, key_type); EG(ret, err);
308 
309 	/* 1. Compute h = H(m) */
310 	/* Since we call a callback, sanity check our mapping */
311 	ret = hash_mapping_callbacks_sanity_check(ctx->h); EG(ret, err);
312 	ret = ctx->h->hfunc_update(&(ctx->sign_data.ecdsa.h_ctx), chunk, chunklen);
313 
314 err:
315 	return ret;
316 }
317 
__ecdsa_sign_finalize(struct ec_sign_context * ctx,u8 * sig,u8 siglen,ec_alg_type key_type)318 int __ecdsa_sign_finalize(struct ec_sign_context *ctx, u8 *sig, u8 siglen,
319 			  ec_alg_type key_type)
320 {
321 	int ret, iszero, cmp;
322 	const ec_priv_key *priv_key;
323 	prj_pt_src_t G;
324 	u8 hash[MAX_DIGEST_SIZE];
325 	bitcnt_t rshift, q_bit_len;
326 	prj_pt kG;
327 	nn_src_t q, x;
328 	u8 hsize, q_len;
329 	nn k, r, e, tmp, s, kinv;
330 #ifdef USE_SIG_BLINDING
331 	/* b is the blinding mask */
332 	nn b;
333 	b.magic = WORD(0);
334 #endif
335 
336 	k.magic = r.magic = e.magic = WORD(0);
337 	tmp.magic = s.magic = kinv.magic = WORD(0);
338 	kG.magic = WORD(0);
339 
340 	/*
341 	 * First, verify context has been initialized and private
342 	 * part too. This guarantees the context is an ECDSA
343 	 * signature one and we do not finalize() before init().
344 	 */
345 	ret = sig_sign_check_initialized(ctx); EG(ret, err);
346 	ECDSA_SIGN_CHECK_INITIALIZED(&(ctx->sign_data.ecdsa), ret, err);
347 	MUST_HAVE((sig != NULL), ret, err);
348 
349 	/* Additional sanity checks on input params from context */
350 	ret = key_pair_check_initialized_and_type(ctx->key_pair, key_type); EG(ret, err);
351 
352 	/* Zero init out point */
353 	ret = local_memset(&kG, 0, sizeof(prj_pt)); EG(ret, err);
354 
355 	/* Make things more readable */
356 	priv_key = &(ctx->key_pair->priv_key);
357 	q = &(priv_key->params->ec_gen_order);
358 	q_bit_len = priv_key->params->ec_gen_order_bitlen;
359 	G = &(priv_key->params->ec_gen);
360 	q_len = (u8)BYTECEIL(q_bit_len);
361 	x = &(priv_key->x);
362 	hsize = ctx->h->digest_size;
363 
364 	MUST_HAVE((priv_key->key_type == key_type), ret, err);
365 
366 	/* Sanity check */
367 	ret = nn_cmp(x, q, &cmp); EG(ret, err);
368 	/* This should not happen and means that our
369 	 * private key is not compliant!
370 	 */
371 	MUST_HAVE((cmp < 0), ret, err);
372 
373 	dbg_nn_print("p", &(priv_key->params->ec_fp.p));
374 	dbg_nn_print("q", &(priv_key->params->ec_gen_order));
375 	dbg_priv_key_print("x", priv_key);
376 	dbg_ec_point_print("G", &(priv_key->params->ec_gen));
377 	dbg_pub_key_print("Y", &(ctx->key_pair->pub_key));
378 
379 	/* Check given signature buffer length has the expected size */
380 	MUST_HAVE((siglen == ECDSA_SIGLEN(q_bit_len)), ret, err);
381 
382 	/* 1. Compute h = H(m) */
383 	ret = local_memset(hash, 0, hsize); EG(ret, err);
384 	/* Since we call a callback, sanity check our mapping */
385 	ret = hash_mapping_callbacks_sanity_check(ctx->h); EG(ret, err);
386 	ret = ctx->h->hfunc_finalize(&(ctx->sign_data.ecdsa.h_ctx), hash); EG(ret, err);
387 	dbg_buf_print("h", hash, hsize);
388 
389 	/*
390 	 * 2. If |h| > bitlen(q), set h to bitlen(q)
391 	 *    leftmost bits of h.
392 	 *
393 	 * Note that it's easier to check if the truncation has
394 	 * to be done here but only implement it using a logical
395 	 * shift at the beginning of step 3. below once the hash
396 	 * has been converted to an integer.
397 	 */
398 	rshift = 0;
399 	if ((hsize * 8) > q_bit_len) {
400 		rshift = (bitcnt_t)((hsize * 8) - q_bit_len);
401 	}
402 
403 	/*
404 	 * 3. Compute e = OS2I(h) mod q, i.e. by converting h to an
405 	 *    integer and reducing it mod q
406 	 */
407 	ret = nn_init_from_buf(&e, hash, hsize); EG(ret, err);
408 	dbg_nn_print("h initial import as nn", &e);
409 	if (rshift) {
410 		ret = nn_rshift_fixedlen(&e, &e, rshift); EG(ret, err);
411 	}
412 	dbg_nn_print("h	  final import as nn", &e);
413 	ret = nn_mod(&e, &e, q); EG(ret, err);
414 	dbg_nn_print("e", &e);
415 
416  restart:
417 	/* 4. get a random value k in ]0,q[ */
418 #ifdef NO_KNOWN_VECTORS
419 	/* NOTE: when we do not need self tests for known vectors,
420 	 * we can be strict about random function handler!
421 	 * This allows us to avoid the corruption of such a pointer.
422 	 */
423 	/* Sanity check on the handler before calling it */
424 	if(ctx->rand != nn_get_random_mod){
425 #ifdef WITH_SIG_DECDSA
426 		/* In deterministic ECDSA, nevermind! */
427 		if(key_type != DECDSA)
428 #endif
429 		{
430 			ret = -1;
431 			goto err;
432 		}
433 	}
434 #endif
435 	if(ctx->rand != NULL){
436 		/* Non-deterministic generation, or deterministic with
437 		 * test vectors.
438 		 */
439 		ret = ctx->rand(&k, q);
440 	}
441 	else
442 #if defined(WITH_SIG_DECDSA)
443 	{
444 		/* Only applies for DETERMINISTIC ECDSA */
445 		if(key_type != DECDSA){
446 			ret = -1;
447 			goto err;
448 		}
449 		/* Deterministically generate k as RFC6979 mandates */
450 		ret = __ecdsa_rfc6979_nonce(&k, q, q_bit_len, &(priv_key->x),
451 					    hash, hsize, ctx->h->type);
452 	}
453 #else
454 	{
455 		/* NULL rand function is not accepted for regular ECDSA */
456 		ret = -1;
457 		goto err;
458 	}
459 #endif
460 	if (ret) {
461 		ret = -1;
462 		goto err;
463 	}
464 	dbg_nn_print("k", &k);
465 
466 #ifdef USE_SIG_BLINDING
467 	/* Note: if we use blinding, r and e are multiplied by
468 	 * a random value b in ]0,q[ */
469 	ret = nn_get_random_mod(&b, q); EG(ret, err);
470 
471 	dbg_nn_print("b", &b);
472 #endif /* USE_SIG_BLINDING */
473 
474 
475 	/* 5. Compute W = (W_x,W_y) = kG */
476 #ifdef USE_SIG_BLINDING
477 	ret = prj_pt_mul_blind(&kG, &k, G); EG(ret, err);
478 #else
479 	ret = prj_pt_mul(&kG, &k, G); EG(ret, err);
480 #endif /* USE_SIG_BLINDING */
481 	ret = prj_pt_unique(&kG, &kG); EG(ret, err);
482 
483 	dbg_nn_print("W_x", &(kG.X.fp_val));
484 	dbg_nn_print("W_y", &(kG.Y.fp_val));
485 
486 	/* 6. Compute r = W_x mod q */
487 	ret = nn_mod(&r, &(kG.X.fp_val), q); EG(ret, err);
488 	dbg_nn_print("r", &r);
489 
490 	/* 7. If r is 0, restart the process at step 4. */
491 	ret = nn_iszero(&r, &iszero); EG(ret, err);
492 	if (iszero) {
493 		goto restart;
494 	}
495 
496 	/* Clean hash buffer as we do not need it anymore */
497 	ret = local_memset(hash, 0, hsize); EG(ret, err);
498 
499 	/* Export r */
500 	ret = nn_export_to_buf(sig, q_len, &r); EG(ret, err);
501 
502 #ifdef USE_SIG_BLINDING
503 	/* Blind r with b */
504 	ret = nn_mod_mul(&r, &r, &b, q); EG(ret, err);
505 
506 	/* Blind the message e */
507 	ret = nn_mod_mul(&e, &e, &b, q); EG(ret, err);
508 #endif /* USE_SIG_BLINDING */
509 
510 	/* tmp = xr mod q */
511 	ret = nn_mod_mul(&tmp, x, &r, q); EG(ret, err);
512 	dbg_nn_print("x*r mod q", &tmp);
513 
514 	/* 8. If e == rx, restart the process at step 4. */
515 	ret = nn_cmp(&e, &tmp, &cmp); EG(ret, err);
516 	if (!cmp) {
517 		goto restart;
518 	}
519 
520 	/* 9. Compute s = k^-1 * (xr + e) mod q */
521 
522 	/* tmp = (e + xr) mod q */
523 	ret = nn_mod_add(&tmp, &tmp, &e, q); EG(ret, err);
524 	dbg_nn_print("(xr + e) mod q", &tmp);
525 
526 #ifdef USE_SIG_BLINDING
527 	/*
528 	 * In case of blinding, we compute (b*k)^-1, and b^-1 will
529 	 * automatically unblind (r*x) in the following.
530 	 */
531 	ret = nn_mod_mul(&k, &k, &b, q); EG(ret, err);
532 #endif
533 	/* Compute k^-1 mod q */
534 	/* NOTE: we use Fermat's little theorem inversion for
535 	 * constant time here. This is possible since q is prime.
536 	 */
537 	ret = nn_modinv_fermat(&kinv, &k, q); EG(ret, err);
538 
539 	dbg_nn_print("k^-1 mod q", &kinv);
540 
541 	/* s = k^-1 * tmp2 mod q */
542 	ret = nn_mod_mul(&s, &tmp, &kinv, q); EG(ret, err);
543 
544 	dbg_nn_print("s", &s);
545 
546 	/* 10. If s is 0, restart the process at step 4. */
547 	ret = nn_iszero(&s, &iszero); EG(ret, err);
548 	if (iszero) {
549 		goto restart;
550 	}
551 
552 	/* 11. return (r,s) */
553 	ret = nn_export_to_buf(sig + q_len, q_len, &s);
554 
555 err:
556 	nn_uninit(&k);
557 	nn_uninit(&r);
558 	nn_uninit(&e);
559 	nn_uninit(&tmp);
560 	nn_uninit(&s);
561 	nn_uninit(&kinv);
562 	prj_pt_uninit(&kG);
563 #ifdef USE_SIG_BLINDING
564 	nn_uninit(&b);
565 #endif
566 
567 	/*
568 	 * We can now clear data part of the context. This will clear
569 	 * magic and avoid further reuse of the whole context.
570 	 */
571 	if(ctx != NULL){
572 		IGNORE_RET_VAL(local_memset(&(ctx->sign_data.ecdsa), 0, sizeof(ecdsa_sign_data)));
573 	}
574 
575 	/* Clean what remains on the stack */
576 	PTR_NULLIFY(priv_key);
577 	PTR_NULLIFY(G);
578 	PTR_NULLIFY(q);
579 	PTR_NULLIFY(x);
580 	VAR_ZEROIFY(q_len);
581 	VAR_ZEROIFY(q_bit_len);
582 	VAR_ZEROIFY(rshift);
583 	VAR_ZEROIFY(hsize);
584 
585 	return ret;
586 }
587 
588 /*
589  * Generic *internal* ECDSA verification functions (init, update and finalize).
590  * Their purpose is to allow passing a specific hash function (along with
591  * its output size) and the random ephemeral key k, so that compliance
592  * tests against test vectors can be made without ugly hack in the code
593  * itself.
594  *
595  * Global ECDSA verification process is as follows (I,U,F provides
596  * information in which function(s) (init(), update() or finalize())
597  * a specific step is performed):
598  *
599  *| IUF	 - ECDSA verification
600  *|
601  *| I	 1. Reject the signature if r or s is 0.
602  *|  UF	 2. Compute h = H(m)
603  *|   F	 3. If |h| > bitlen(q), set h to bitlen(q)
604  *|	    leftmost (most significant) bits of h
605  *|   F	 4. Compute e = OS2I(h) mod q
606  *|   F	 5. Compute u = (s^-1)e mod q
607  *|   F	 6. Compute v = (s^-1)r mod q
608  *|   F	 7. Compute W' = uG + vY
609  *|   F	 8. If W' is the point at infinity, reject the signature.
610  *|   F	 9. Compute r' = W'_x mod q
611  *|   F 10. Accept the signature if and only if r equals r'
612  *
613  */
614 
615 #define ECDSA_VERIFY_MAGIC ((word_t)(0x5155fe73e7fd51beULL))
616 #define ECDSA_VERIFY_CHECK_INITIALIZED(A, ret, err) \
617 	MUST_HAVE((((void *)(A)) != NULL) && ((A)->magic == ECDSA_VERIFY_MAGIC), ret, err)
618 
__ecdsa_verify_init(struct ec_verify_context * ctx,const u8 * sig,u8 siglen,ec_alg_type key_type)619 int __ecdsa_verify_init(struct ec_verify_context *ctx, const u8 *sig, u8 siglen,
620 			ec_alg_type key_type)
621 {
622 	bitcnt_t q_bit_len;
623 	u8 q_len;
624 	nn_src_t q;
625 	nn *r, *s;
626 	int ret, cmp1, cmp2, iszero1, iszero2;
627 
628 	/* First, verify context has been initialized */
629 	ret = sig_verify_check_initialized(ctx); EG(ret, err);
630 
631 	/* Do some sanity checks on input params */
632 	ret = pub_key_check_initialized_and_type(ctx->pub_key, key_type); EG(ret, err);
633 	MUST_HAVE((ctx->h != NULL) && (ctx->h->digest_size <= MAX_DIGEST_SIZE) &&
634 		(ctx->h->block_size <= MAX_BLOCK_SIZE), ret, err);
635 	MUST_HAVE((sig != NULL), ret, err);
636 
637 	/* Make things more readable */
638 	q = &(ctx->pub_key->params->ec_gen_order);
639 	q_bit_len = ctx->pub_key->params->ec_gen_order_bitlen;
640 	q_len = (u8)BYTECEIL(q_bit_len);
641 	r = &(ctx->verify_data.ecdsa.r);
642 	s = &(ctx->verify_data.ecdsa.s);
643 
644 	/* Check given signature length is the expected one */
645 	MUST_HAVE((siglen == ECDSA_SIGLEN(q_bit_len)), ret, err);
646 
647 	/* Import r and s values from signature buffer */
648 	ret = nn_init_from_buf(r, sig, q_len); EG(ret, err);
649 	ret = nn_init_from_buf(s, sig + q_len, q_len); EG(ret, err);
650 	dbg_nn_print("r", r);
651 	dbg_nn_print("s", s);
652 
653 	/* 1. Reject the signature if r or s is 0. */
654 	ret = nn_iszero(r, &iszero1); EG(ret, err);
655 	ret = nn_iszero(s, &iszero2); EG(ret, err);
656 	ret = nn_cmp(r, q, &cmp1); EG(ret, err);
657 	ret = nn_cmp(s, q, &cmp2); EG(ret, err);
658 	MUST_HAVE(((!iszero1) && (cmp1 < 0) && !iszero2 && (cmp2 < 0)), ret, err);
659 
660 	/* Initialize the remaining of verify context. */
661 	/* Since we call a callback, sanity check our mapping */
662 	ret = hash_mapping_callbacks_sanity_check(ctx->h); EG(ret, err);
663 	ret = ctx->h->hfunc_init(&(ctx->verify_data.ecdsa.h_ctx)); EG(ret, err);
664 
665 	ctx->verify_data.ecdsa.magic = ECDSA_VERIFY_MAGIC;
666 
667  err:
668 	VAR_ZEROIFY(q_len);
669 	VAR_ZEROIFY(q_bit_len);
670 	PTR_NULLIFY(q);
671 	PTR_NULLIFY(r);
672 	PTR_NULLIFY(s);
673 
674 	return ret;
675 }
676 
__ecdsa_verify_update(struct ec_verify_context * ctx,const u8 * chunk,u32 chunklen,ec_alg_type key_type)677 int __ecdsa_verify_update(struct ec_verify_context *ctx,
678 			 const u8 *chunk, u32 chunklen, ec_alg_type key_type)
679 {
680 	int ret;
681 
682 	/*
683 	 * First, verify context has been initialized and public
684 	 * part too. This guarantees the context is an ECDSA
685 	 * verification one and we do not update() or finalize()
686 	 * before init().
687 	 */
688 	ret = sig_verify_check_initialized(ctx); EG(ret, err);
689 	ECDSA_VERIFY_CHECK_INITIALIZED(&(ctx->verify_data.ecdsa), ret, err);
690 	/* Do some sanity checks on input params */
691 	ret = pub_key_check_initialized_and_type(ctx->pub_key, key_type); EG(ret, err);
692 
693 	/* 2. Compute h = H(m) */
694 	/* Since we call a callback, sanity check our mapping */
695 	ret = hash_mapping_callbacks_sanity_check(ctx->h); EG(ret, err);
696 	ret = ctx->h->hfunc_update(&(ctx->verify_data.ecdsa.h_ctx), chunk, chunklen);
697 
698 err:
699 	return ret;
700 }
701 
__ecdsa_verify_finalize(struct ec_verify_context * ctx,ec_alg_type key_type)702 int __ecdsa_verify_finalize(struct ec_verify_context *ctx,
703 			    ec_alg_type key_type)
704 {
705 	prj_pt uG, vY;
706 	prj_pt_t W_prime;
707 	nn e, sinv, uv, r_prime;
708 	prj_pt_src_t G, Y;
709 	u8 hash[MAX_DIGEST_SIZE];
710 	bitcnt_t rshift, q_bit_len;
711 	nn_src_t q;
712 	nn *s, *r;
713 	u8 hsize;
714 	int ret, iszero, cmp;
715 
716 	uG.magic = vY.magic = WORD(0);
717 	e.magic = sinv.magic = uv.magic = r_prime.magic = WORD(0);
718 
719 	/* NOTE: we reuse uG for W_prime to optimize local variables */
720 	W_prime = &uG;
721 
722 	/*
723 	 * First, verify context has been initialized and public
724 	 * part too. This guarantees the context is an ECDSA
725 	 * verification one and we do not finalize() before init().
726 	 */
727 	ret = sig_verify_check_initialized(ctx); EG(ret, err);
728 	ECDSA_VERIFY_CHECK_INITIALIZED(&(ctx->verify_data.ecdsa), ret, err);
729 	/* Do some sanity checks on input params */
730 	ret = pub_key_check_initialized_and_type(ctx->pub_key, key_type); EG(ret, err);
731 
732 	/* Zero init points */
733 	ret = local_memset(&uG, 0, sizeof(prj_pt)); EG(ret, err);
734 	ret = local_memset(&vY, 0, sizeof(prj_pt)); EG(ret, err);
735 
736 	/* Make things more readable */
737 	G = &(ctx->pub_key->params->ec_gen);
738 	Y = &(ctx->pub_key->y);
739 	q = &(ctx->pub_key->params->ec_gen_order);
740 	q_bit_len = ctx->pub_key->params->ec_gen_order_bitlen;
741 	hsize = ctx->h->digest_size;
742 	r = &(ctx->verify_data.ecdsa.r);
743 	s = &(ctx->verify_data.ecdsa.s);
744 
745 	/* 2. Compute h = H(m) */
746 	/* Since we call a callback, sanity check our mapping */
747 	ret = hash_mapping_callbacks_sanity_check(ctx->h); EG(ret, err);
748 	ret = ctx->h->hfunc_finalize(&(ctx->verify_data.ecdsa.h_ctx), hash); EG(ret, err);
749 	dbg_buf_print("h = H(m)", hash, hsize);
750 
751 	/*
752 	 * 3. If |h| > bitlen(q), set h to bitlen(q)
753 	 *    leftmost bits of h.
754 	 *
755 	 * Note that it's easier to check here if the truncation
756 	 * needs to be done but implement it using a logical
757 	 * shift at the beginning of step 3. below once the hash
758 	 * has been converted to an integer.
759 	 */
760 	rshift = 0;
761 	if ((hsize * 8) > q_bit_len) {
762 		rshift = (bitcnt_t)((hsize * 8) - q_bit_len);
763 	}
764 
765 	/*
766 	 * 4. Compute e = OS2I(h) mod q, by converting h to an integer
767 	 * and reducing it mod q
768 	 */
769 	ret = nn_init_from_buf(&e, hash, hsize); EG(ret, err);
770 	ret = local_memset(hash, 0, hsize); EG(ret, err);
771 	dbg_nn_print("h initial import as nn", &e);
772 	if (rshift) {
773 		ret = nn_rshift_fixedlen(&e, &e, rshift); EG(ret, err);
774 	}
775 	dbg_nn_print("h	  final import as nn", &e);
776 
777 	ret = nn_mod(&e, &e, q); EG(ret, err);
778 	dbg_nn_print("e", &e);
779 
780 	/* Compute s^-1 mod q */
781 	ret = nn_modinv(&sinv, s, q); EG(ret, err);
782 	dbg_nn_print("s", s);
783 	dbg_nn_print("sinv", &sinv);
784 
785 	/* 5. Compute u = (s^-1)e mod q */
786 	ret = nn_mod_mul(&uv, &e, &sinv, q); EG(ret, err);
787 	dbg_nn_print("u = (s^-1)e mod q", &uv);
788 	ret = prj_pt_mul(&uG, &uv, G); EG(ret, err);
789 
790 	/* 6. Compute v = (s^-1)r mod q */
791 	ret = nn_mod_mul(&uv, r, &sinv, q); EG(ret, err);
792 	dbg_nn_print("v = (s^-1)r mod q", &uv);
793 	ret = prj_pt_mul(&vY, &uv, Y); EG(ret, err);
794 
795 	/* 7. Compute W' = uG + vY */
796 	ret = prj_pt_add(W_prime, &uG, &vY); EG(ret, err);
797 
798 	/* 8. If W' is the point at infinity, reject the signature. */
799 	ret = prj_pt_iszero(W_prime, &iszero); EG(ret, err);
800 	MUST_HAVE(!iszero, ret, err);
801 
802 	/* 9. Compute r' = W'_x mod q */
803 	ret = prj_pt_unique(W_prime, W_prime); EG(ret, err);
804 	dbg_nn_print("W'_x", &(W_prime->X.fp_val));
805 	dbg_nn_print("W'_y", &(W_prime->Y.fp_val));
806 	ret = nn_mod(&r_prime, &(W_prime->X.fp_val), q); EG(ret, err);
807 
808 	/* 10. Accept the signature if and only if r equals r' */
809 	ret = nn_cmp(&r_prime, r, &cmp); EG(ret, err);
810 	ret = (cmp != 0) ? -1 : 0;
811 
812  err:
813 	prj_pt_uninit(&uG);
814 	prj_pt_uninit(&vY);
815 	nn_uninit(&e);
816 	nn_uninit(&sinv);
817 	nn_uninit(&uv);
818 	nn_uninit(&r_prime);
819 
820 	/*
821 	 * We can now clear data part of the context. This will clear
822 	 * magic and avoid further reuse of the whole context.
823 	 */
824 	if(ctx != NULL){
825 		IGNORE_RET_VAL(local_memset(&(ctx->verify_data.ecdsa), 0, sizeof(ecdsa_verify_data)));
826 	}
827 
828 	/* Clean what remains on the stack */
829 	PTR_NULLIFY(W_prime);
830 	PTR_NULLIFY(G);
831 	PTR_NULLIFY(Y);
832 	VAR_ZEROIFY(rshift);
833 	VAR_ZEROIFY(q_bit_len);
834 	PTR_NULLIFY(q);
835 	PTR_NULLIFY(s);
836 	PTR_NULLIFY(r);
837 	VAR_ZEROIFY(hsize);
838 
839 	return ret;
840 }
841 
842 /* Public key recovery from a signature.
843  * For ECDSA, it is possible to recover two possible public keys from
844  * a signature and a digest.
845  *
846  * Please note that this recovery is not perfect as some information is
847  * lost when reducing Rx modulo the order q during the signature. Hence,
848  * a few possible R points can provide the same r. The following algorithm
849  * assumes that Rx == r, i.e. Rx is < q and already reduced. This should
850  * happen with a probability q / p, and "bad" cases with probability
851  * (p - q) / p. Actually, some small multiples of r are also tested,
852  * but we give up after 10 tries as this can be very time consuming.
853  *
854  * With usual curve parameters, this last probability is negligible if
855  * everything is random (which should be the case for a "regular" signature
856  * algorithm) for curves with cofactor = 1. However, an adversary could
857  * willingly choose a Rx > q and the following algorithm will most certainly
858  * fail.
859  *
860  * For curves with cofactor > 1, q is usually some orders of magnitudes
861  * smaller than p and this function will certainly fail.
862  *
863  * Please use the resulting public keys with care and with all these
864  * warnings in mind!
865  *
866  */
__ecdsa_public_key_from_sig(ec_pub_key * out_pub1,ec_pub_key * out_pub2,const ec_params * params,const u8 * sig,u8 siglen,const u8 * hash,u8 hsize,ec_alg_type key_type)867 int __ecdsa_public_key_from_sig(ec_pub_key *out_pub1, ec_pub_key *out_pub2, const ec_params *params,
868 				const u8 *sig, u8 siglen, const u8 *hash, u8 hsize,
869 	                        ec_alg_type key_type)
870 {
871 	int ret, iszero1, iszero2, cmp1, cmp2;
872 	prj_pt uG;
873 	prj_pt_t Y1, Y2;
874 	prj_pt_src_t G;
875 	nn u, v, e, r, s;
876 	nn_src_t q, p;
877 	bitcnt_t rshift, q_bit_len;
878 	u8 q_len;
879 	word_t order_multiplier = WORD(1);
880 
881 	uG.magic = WORD(0);
882 	u.magic = v.magic = e.magic = r.magic = s.magic = WORD(0);
883 
884 	/* Zero init points */
885 	ret = local_memset(&uG, 0, sizeof(prj_pt)); EG(ret, err);
886 
887 	/* Sanity checks */
888 	MUST_HAVE((params != NULL) && (sig != NULL) && (hash != NULL) && (out_pub1 != NULL) && (out_pub2 != NULL), ret, err);
889 
890 	/* Import our params */
891 	G = &(params->ec_gen);
892 	p = &(params->ec_fp.p);
893 	q = &(params->ec_gen_order);
894 	q_bit_len = params->ec_gen_order_bitlen;
895 	q_len = (u8)BYTECEIL(q_bit_len);
896 	Y1 = &(out_pub1->y);
897 	Y2 = &(out_pub2->y);
898 
899 	/* Check given signature length is the expected one */
900 	MUST_HAVE((siglen == ECDSA_SIGLEN(q_bit_len)), ret, err);
901 
902 restart:
903 	/* Import r and s values from signature buffer */
904 	ret = nn_init_from_buf(&r, sig, q_len); EG(ret, err);
905 	ret = nn_init_from_buf(&s, sig + q_len, q_len); EG(ret, err);
906 
907 	/* Reject the signature if r or s is 0. */
908 	ret = nn_iszero(&r, &iszero1); EG(ret, err);
909 	ret = nn_iszero(&s, &iszero2); EG(ret, err);
910 	ret = nn_cmp(&r, q, &cmp1); EG(ret, err);
911 	ret = nn_cmp(&s, q, &cmp2); EG(ret, err);
912 	MUST_HAVE(((!iszero1) && (cmp1 < 0) && !iszero2 && (cmp2 < 0)), ret, err);
913 
914 	/* Add a multiple of the order to r using our current order multiplier */
915 	if(order_multiplier > 1){
916 		int cmp;
917 		ret = nn_init(&u, 0);
918 		ret = nn_mul_word(&u, q, order_multiplier); EG(ret, err);
919 		ret = nn_add(&r, &r, &u); EG(ret, err);
920 		/* If we have reached > p, leave with an error */
921 		ret = nn_cmp(&r, p, &cmp); EG(ret, err);
922 		/* NOTE: we do not use a MUST_HAVE macro here since
923 		 * this condition can nominally happen, and we do not want
924 		 * a MUST_HAVE in debug mode (i.e. with an assert) to break
925 		 * the execution flow.
926 		 */
927 		if(cmp < 0){
928 			ret = -1;
929 			goto err;
930 		}
931 	}
932 
933 	/*
934 	 * Compute e.
935 	 * If |h| > bitlen(q), set h to bitlen(q)
936 	 * leftmost bits of h.
937 	 *
938 	 * Note that it's easier to check here if the truncation
939 	 * needs to be done but implement it using a logical
940 	 * shift.
941 	 */
942 	rshift = 0;
943 	if ((hsize * 8) > q_bit_len) {
944 		rshift = (bitcnt_t)((hsize * 8) - q_bit_len);
945 	}
946 	ret = nn_init_from_buf(&e, hash, hsize); EG(ret, err);
947 	if (rshift) {
948 		ret = nn_rshift_fixedlen(&e, &e, rshift); EG(ret, err);
949 	}
950 	ret = nn_mod(&e, &e, q); EG(ret, err);
951 
952 	/* Now to find the y coordinate by solving the curve equation.
953 	 * NOTE: we use uG as temporary storage.
954 	 */
955 	ret = fp_init(&(uG.X), &(params->ec_fp)); EG(ret, err);
956 	ret = fp_init(&(uG.Y), &(params->ec_fp)); EG(ret, err);
957 	ret = fp_init(&(uG.Z), &(params->ec_fp)); EG(ret, err);
958 	ret = fp_set_nn(&(uG.Z), &r); EG(ret, err);
959 	ret = aff_pt_y_from_x(&(uG.X), &(uG.Y), &(uG.Z), &(params->ec_curve));
960 	if(ret){
961 		/* If we have failed here, this means that our r has certainly been
962 		 * reduced. Increment our multiplier and restart the process.
963 		 */
964 		order_multiplier = (word_t)(order_multiplier + 1);
965 		if(order_multiplier > 10){
966 			/* Too much tries, leave ... */
967 			ret = -1;
968 			goto err;
969 		}
970 		goto restart;
971 	}
972 
973 	/* Initialize Y1 and Y2 */
974 	ret = fp_init(&(Y2->Z), &(params->ec_fp)); EG(ret, err);
975 	ret = fp_one(&(Y2->Z)); EG(ret, err);
976 	/* Y1 */
977 	ret = prj_pt_init_from_coords(Y1, &(params->ec_curve), &(uG.Z), &(uG.X), &(Y2->Z)); EG(ret, err);
978 	/* Y2 */
979 	ret = prj_pt_init_from_coords(Y2, &(params->ec_curve), &(uG.Z), &(uG.Y), &(Y1->Z)); EG(ret, err);
980 
981 	/* Now compute u = (-e r^-1) mod q, and v = (s r^-1) mod q */
982 	ret = nn_init(&u, 0); EG(ret, err);
983 	ret = nn_init(&v, 0); EG(ret, err);
984 	ret = nn_modinv(&r, &r, q); EG(ret, err);
985 	/* u */
986 	ret = nn_mod_mul(&u, &e, &r, q); EG(ret, err);
987 	/* NOTE: -x mod q is (q - x) mod q, i.e. (q - x) when x is reduced, except for 0 */
988 	ret = nn_mod_neg(&u, &u, q); EG(ret, err);
989 	/* v */
990 	ret = nn_mod_mul(&v, &s, &r, q); EG(ret, err);
991 
992 	/* Compute uG */
993 	ret = prj_pt_mul(&uG, &u, G); EG(ret, err);
994 	/* Compute vR1 and possible Y1 */
995 	ret = prj_pt_mul(Y1, &v, Y1); EG(ret, err);
996 	ret = prj_pt_add(Y1, Y1, &uG); EG(ret, err);
997 	/* Compute vR2 and possible Y2 */
998 	ret = prj_pt_mul(Y2, &v, Y2); EG(ret, err);
999 	ret = prj_pt_add(Y2, Y2, &uG); EG(ret, err);
1000 
1001 	/* Now initialize our two public keys */
1002 	/* out_pub1 */
1003 	out_pub1->key_type = key_type;
1004 	out_pub1->params = params;
1005 	out_pub1->magic = PUB_KEY_MAGIC;
1006 	/* out_pub2 */
1007 	out_pub2->key_type = key_type;
1008 	out_pub2->params = params;
1009 	out_pub2->magic = PUB_KEY_MAGIC;
1010 
1011 	ret = 0;
1012 
1013 err:
1014 	prj_pt_uninit(&uG);
1015 	nn_uninit(&r);
1016 	nn_uninit(&s);
1017 	nn_uninit(&u);
1018 	nn_uninit(&v);
1019 	nn_uninit(&e);
1020 
1021 	/* Clean what remains on the stack */
1022 	PTR_NULLIFY(G);
1023 	PTR_NULLIFY(Y1);
1024 	PTR_NULLIFY(Y2);
1025 	VAR_ZEROIFY(rshift);
1026 	VAR_ZEROIFY(q_bit_len);
1027 	PTR_NULLIFY(q);
1028 	PTR_NULLIFY(p);
1029 
1030 	return ret;
1031 }
1032 
1033 #else /* defined(WITH_SIG_ECDSA) || defined(WITH_SIG_DECDSA) */
1034 
1035 /*
1036  * Dummy definition to avoid the empty translation unit ISO C warning
1037  */
1038 typedef int dummy;
1039 #endif /* WITH_SIG_ECDSA */
1040