1 // SPDX-License-Identifier: BSD-2-Clause
2 /* LibTomCrypt, modular cryptographic library -- Tom St Denis
3 *
4 * LibTomCrypt is a library that provides various cryptographic
5 * algorithms in a highly modular and flexible manner.
6 *
7 * The library is free for all purposes without any express
8 * guarantee it works.
9 */
10
11 #include "tomcrypt_private.h"
12
13 #ifdef LTC_MECC
14
15 #ifdef LTC_ECC_SHAMIR
16
17 /**
18 @file ecc_recover_key.c
19 ECC Crypto, Russ Williams
20 */
21
22 /**
23 Recover ECC public key from signature and hash
24 @param sig The signature to verify
25 @param siglen The length of the signature (octets)
26 @param hash The hash (message digest) that was signed
27 @param hashlen The length of the hash (octets)
28 @param recid The recovery ID ("v"), can be -1 if signature contains it
29 @param sigformat The format of the signature (ecc_signature_type)
30 @param key The recovered public ECC key
31 @return CRYPT_OK if successful (even if the signature is not valid)
32 */
ecc_recover_key(const unsigned char * sig,unsigned long siglen,const unsigned char * hash,unsigned long hashlen,int recid,ecc_signature_type sigformat,ecc_key * key)33 int ecc_recover_key(const unsigned char *sig, unsigned long siglen,
34 const unsigned char *hash, unsigned long hashlen,
35 int recid, ecc_signature_type sigformat, ecc_key *key)
36 {
37 ecc_point *mG = NULL, *mQ = NULL, *mR = NULL;
38 void *p, *m, *a, *b;
39 void *r, *s, *v, *w, *t1, *t2, *u1, *u2, *v1, *v2, *e, *x, *y, *a_plus3;
40 void *mu = NULL, *ma = NULL;
41 void *mp = NULL;
42 int err;
43 unsigned long pbits, pbytes, i, shift_right;
44 unsigned char ch, buf[MAXBLOCKSIZE];
45
46 LTC_ARGCHK(sig != NULL);
47 LTC_ARGCHK(hash != NULL);
48 LTC_ARGCHK(key != NULL);
49
50 /* BEWARE: requires sqrtmod_prime */
51 if (ltc_mp.sqrtmod_prime == NULL) {
52 return CRYPT_ERROR;
53 }
54
55 /* allocate ints */
56 if ((err = mp_init_multi(&r, &s, &v, &w, &t1, &t2, &u1, &u2, &v1, &v2, &e, &x, &y, &a_plus3, NULL)) != CRYPT_OK) {
57 return err;
58 }
59
60 p = key->dp.order;
61 m = key->dp.prime;
62 a = key->dp.A;
63 b = key->dp.B;
64 if ((err = mp_add_d(a, 3, a_plus3)) != CRYPT_OK) {
65 goto error;
66 }
67
68 /* allocate points */
69 mG = ltc_ecc_new_point();
70 mQ = ltc_ecc_new_point();
71 mR = ltc_ecc_new_point();
72 if (mR == NULL || mQ == NULL || mG == NULL) {
73 err = CRYPT_MEM;
74 goto error;
75 }
76
77 if (sigformat == LTC_ECCSIG_ANSIX962) {
78 /* ANSI X9.62 format - ASN.1 encoded SEQUENCE{ INTEGER(r), INTEGER(s) } */
79 if ((err = der_decode_sequence_multi_ex(sig, siglen, LTC_DER_SEQ_SEQUENCE | LTC_DER_SEQ_STRICT,
80 LTC_ASN1_INTEGER, 1UL, r,
81 LTC_ASN1_INTEGER, 1UL, s,
82 LTC_ASN1_EOL, 0UL, NULL)) != CRYPT_OK) { goto error; }
83 }
84 else if (sigformat == LTC_ECCSIG_RFC7518) {
85 /* RFC7518 format - raw (r,s) */
86 i = mp_unsigned_bin_size(key->dp.order);
87 if (siglen != (2*i)) {
88 err = CRYPT_INVALID_PACKET;
89 goto error;
90 }
91 if ((err = mp_read_unsigned_bin(r, (unsigned char *)sig, i)) != CRYPT_OK) { goto error; }
92 if ((err = mp_read_unsigned_bin(s, (unsigned char *)sig+i, i)) != CRYPT_OK) { goto error; }
93 }
94 else if (sigformat == LTC_ECCSIG_ETH27) {
95 /* Ethereum (v,r,s) format */
96 if (pk_oid_cmp_with_ulong("1.3.132.0.10", key->dp.oid, key->dp.oidlen) != CRYPT_OK) {
97 /* Only valid for secp256k1 - OID 1.3.132.0.10 */
98 err = CRYPT_ERROR; goto error;
99 }
100 if (siglen != 65) { /* Only secp256k1 curves use this format, so must be 65 bytes long */
101 err = CRYPT_INVALID_PACKET;
102 goto error;
103 }
104 i = (unsigned long)sig[64];
105 if ((i>=27) && (i<31)) i -= 27; /* Ethereum adds 27 to recovery ID */
106 if (recid >= 0 && ((unsigned long)recid != i)) {
107 /* Recovery ID specified, but doesn't match signature */
108 err = CRYPT_INVALID_PACKET;
109 goto error;
110 }
111 recid = i;
112 if ((err = mp_read_unsigned_bin(r, (unsigned char *)sig, 32)) != CRYPT_OK) { goto error; }
113 if ((err = mp_read_unsigned_bin(s, (unsigned char *)sig+32, 32)) != CRYPT_OK) { goto error; }
114 }
115 #ifdef LTC_SSH
116 else if (sigformat == LTC_ECCSIG_RFC5656) {
117 char name[64], name2[64];
118 unsigned long namelen = sizeof(name2);
119
120 /* Decode as SSH data sequence, per RFC4251 */
121 if ((err = ssh_decode_sequence_multi(sig, siglen,
122 LTC_SSHDATA_STRING, name, 64,
123 LTC_SSHDATA_MPINT, r,
124 LTC_SSHDATA_MPINT, s,
125 LTC_SSHDATA_EOL, NULL)) != CRYPT_OK) { goto error; }
126
127
128 /* Check curve matches identifier string */
129 if ((err = ecc_ssh_ecdsa_encode_name(name2, &namelen, key)) != CRYPT_OK) { goto error; }
130 if (XSTRCMP(name,name2) != 0) {
131 err = CRYPT_INVALID_ARG;
132 goto error;
133 }
134 }
135 #endif
136 else {
137 /* Unknown signature format */
138 err = CRYPT_ERROR;
139 goto error;
140 }
141
142 if (recid < 0 || (unsigned long)recid >= 2*(key->dp.cofactor+1)) {
143 /* Recovery ID is out of range, reject it */
144 err = CRYPT_INVALID_ARG;
145 goto error;
146 }
147
148 /* check for zero */
149 if (mp_cmp_d(r, 0) != LTC_MP_GT || mp_cmp_d(s, 0) != LTC_MP_GT ||
150 mp_cmp(r, p) != LTC_MP_LT || mp_cmp(s, p) != LTC_MP_LT) {
151 err = CRYPT_INVALID_PACKET;
152 goto error;
153 }
154
155 /* read hash - truncate if needed */
156 pbits = mp_count_bits(p);
157 pbytes = (pbits+7) >> 3;
158 if (pbits > hashlen*8) {
159 if ((err = mp_read_unsigned_bin(e, (unsigned char *)hash, hashlen)) != CRYPT_OK) { goto error; }
160 }
161 else if (pbits % 8 == 0) {
162 if ((err = mp_read_unsigned_bin(e, (unsigned char *)hash, pbytes)) != CRYPT_OK) { goto error; }
163 }
164 else {
165 shift_right = 8 - pbits % 8;
166 for (i=0, ch=0; i<pbytes; i++) {
167 buf[i] = ch;
168 ch = (hash[i] << (8-shift_right));
169 buf[i] = buf[i] ^ (hash[i] >> shift_right);
170 }
171 if ((err = mp_read_unsigned_bin(e, (unsigned char *)buf, pbytes)) != CRYPT_OK) { goto error; }
172 }
173
174 /* decompress point from r=(x mod p) - BEWARE: requires sqrtmod_prime */
175 /* x = r + p*(recid/2) */
176 if ((err = mp_set(x, recid/2)) != CRYPT_OK) { goto error; }
177 if ((err = mp_mulmod(p, x, m, x)) != CRYPT_OK) { goto error; }
178 if ((err = mp_add(x, r, x)) != CRYPT_OK) { goto error; }
179 /* compute x^3 */
180 if ((err = mp_sqr(x, t1)) != CRYPT_OK) { goto error; }
181 if ((err = mp_mulmod(t1, x, m, t1)) != CRYPT_OK) { goto error; }
182 /* compute x^3 + a*x */
183 if ((err = mp_mulmod(a, x, m, t2)) != CRYPT_OK) { goto error; }
184 if ((err = mp_add(t1, t2, t1)) != CRYPT_OK) { goto error; }
185 /* compute x^3 + a*x + b */
186 if ((err = mp_add(t1, b, t1)) != CRYPT_OK) { goto error; }
187 /* compute sqrt(x^3 + a*x + b) */
188 if ((err = mp_sqrtmod_prime(t1, m, t2)) != CRYPT_OK) { goto error; }
189
190 /* fill in mR */
191 if ((err = mp_copy(x, mR->x)) != CRYPT_OK) { goto error; }
192 if ((mp_isodd(t2) && (recid%2)) || (!mp_isodd(t2) && !(recid%2))) {
193 if ((err = mp_mod(t2, m, mR->y)) != CRYPT_OK) { goto error; }
194 }
195 else {
196 if ((err = mp_submod(m, t2, m, mR->y)) != CRYPT_OK) { goto error; }
197 }
198 if ((err = mp_set(mR->z, 1)) != CRYPT_OK) { goto error; }
199
200 /* w = r^-1 mod n */
201 if ((err = mp_invmod(r, p, w)) != CRYPT_OK) { goto error; }
202 /* v1 = sw */
203 if ((err = mp_mulmod(s, w, p, v1)) != CRYPT_OK) { goto error; }
204 /* v2 = -ew */
205 if ((err = mp_mulmod(e, w, p, v2)) != CRYPT_OK) { goto error; }
206 if ((err = mp_submod(p, v2, p, v2)) != CRYPT_OK) { goto error; }
207
208 /* w = s^-1 mod n */
209 if ((err = mp_invmod(s, p, w)) != CRYPT_OK) { goto error; }
210 /* u1 = ew */
211 if ((err = mp_mulmod(e, w, p, u1)) != CRYPT_OK) { goto error; }
212 /* u2 = rw */
213 if ((err = mp_mulmod(r, w, p, u2)) != CRYPT_OK) { goto error; }
214
215 /* find mG */
216 if ((err = ltc_ecc_copy_point(&key->dp.base, mG)) != CRYPT_OK) { goto error; }
217
218 /* find the montgomery mp */
219 if ((err = mp_montgomery_setup(m, &mp)) != CRYPT_OK) { goto error; }
220
221 /* for curves with a == -3 keep ma == NULL */
222 if (mp_cmp(a_plus3, m) != LTC_MP_EQ) {
223 if ((err = mp_init_multi(&mu, &ma, NULL)) != CRYPT_OK) { goto error; }
224 if ((err = mp_montgomery_normalization(mu, m)) != CRYPT_OK) { goto error; }
225 if ((err = mp_mulmod(a, mu, m, ma)) != CRYPT_OK) { goto error; }
226 }
227
228 /* recover mQ from mR */
229 /* compute v1*mR + v2*mG = mQ using Shamir's trick */
230 if ((err = ltc_mp.ecc_mul2add(mR, v1, mG, v2, mQ, ma, m)) != CRYPT_OK) { goto error; }
231
232 /* compute u1*mG + u2*mQ = mG using Shamir's trick */
233 if ((err = ltc_mp.ecc_mul2add(mG, u1, mQ, u2, mG, ma, m)) != CRYPT_OK) { goto error; }
234
235 /* v = X_x1 mod n */
236 if ((err = mp_mod(mG->x, p, v)) != CRYPT_OK) { goto error; }
237
238 /* does v == r */
239 if (mp_cmp(v, r) == LTC_MP_EQ) {
240 /* found public key which verifies signature */
241 if ((err = ltc_ecc_copy_point(mQ, &key->pubkey)) != CRYPT_OK) { goto error; }
242 /* point on the curve + other checks */
243 if ((err = ltc_ecc_verify_key(key)) != CRYPT_OK) { goto error; }
244
245 key->type = PK_PUBLIC;
246
247 err = CRYPT_OK;
248 }
249 else {
250 /* not found - recid is wrong or we're unable to calculate public key for some other reason */
251 err = CRYPT_INVALID_ARG;
252 }
253
254 error:
255 if (ma != NULL) mp_clear(ma);
256 if (mu != NULL) mp_clear(mu);
257 if (mp != NULL) mp_montgomery_free(mp);
258 if (mR != NULL) ltc_ecc_del_point(mR);
259 if (mQ != NULL) ltc_ecc_del_point(mQ);
260 if (mG != NULL) ltc_ecc_del_point(mG);
261 mp_clear_multi(a_plus3, y, x, e, v2, v1, u2, u1, t2, t1, w, v, s, r, NULL);
262 return err;
263 }
264
265 #endif
266 #endif
267
268 /* ref: $Format:%D$ */
269 /* git commit: $Format:%H$ */
270 /* commit time: $Format:%ai$ */
271