/* LibTomCrypt, modular cryptographic library -- Tom St Denis
*
* LibTomCrypt is a library that provides various cryptographic
* algorithms in a highly modular and flexible manner.
*
* The library is free for all purposes without any express
* guarantee it works.
*/
#include "tomcrypt_private.h"
#ifdef LTC_MECC
#ifdef LTC_ECC_SHAMIR
/**
@file ecc_recover_key.c
ECC Crypto, Russ Williams
*/
/**
Recover ECC public key from signature and hash
@param sig The signature to verify
@param siglen The length of the signature (octets)
@param hash The hash (message digest) that was signed
@param hashlen The length of the hash (octets)
@param recid The recovery ID ("v"), can be -1 if signature contains it
@param sigformat The format of the signature (ecc_signature_type)
@param key The recovered public ECC key
@return CRYPT_OK if successful (even if the signature is not valid)
*/
int 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)
{
ecc_point *mG = NULL, *mQ = NULL, *mR = NULL;
void *p, *m, *a, *b;
void *r, *s, *v, *w, *t1, *t2, *u1, *u2, *v1, *v2, *e, *x, *y, *a_plus3;
void *mu = NULL, *ma = NULL;
void *mp = NULL;
int err;
unsigned long pbits, pbytes, i, shift_right;
unsigned char ch, buf[MAXBLOCKSIZE];
LTC_ARGCHK(sig != NULL);
LTC_ARGCHK(hash != NULL);
LTC_ARGCHK(key != NULL);
/* BEWARE: requires sqrtmod_prime */
if (ltc_mp.sqrtmod_prime == NULL) {
return CRYPT_ERROR;
}
/* allocate ints */
if ((err = mp_init_multi(&r, &s, &v, &w, &t1, &t2, &u1, &u2, &v1, &v2, &e, &x, &y, &a_plus3, NULL)) != CRYPT_OK) {
return err;
}
p = key->dp.order;
m = key->dp.prime;
a = key->dp.A;
b = key->dp.B;
if ((err = mp_add_d(a, 3, a_plus3)) != CRYPT_OK) {
goto error;
}
/* allocate points */
mG = ltc_ecc_new_point();
mQ = ltc_ecc_new_point();
mR = ltc_ecc_new_point();
if (mR == NULL || mQ == NULL || mG == NULL) {
err = CRYPT_MEM;
goto error;
}
if (sigformat == LTC_ECCSIG_ANSIX962) {
/* ANSI X9.62 format - ASN.1 encoded SEQUENCE{ INTEGER(r), INTEGER(s) } */
if ((err = der_decode_sequence_multi_ex(sig, siglen, LTC_DER_SEQ_SEQUENCE | LTC_DER_SEQ_STRICT,
LTC_ASN1_INTEGER, 1UL, r,
LTC_ASN1_INTEGER, 1UL, s,
LTC_ASN1_EOL, 0UL, NULL)) != CRYPT_OK) { goto error; }
}
else if (sigformat == LTC_ECCSIG_RFC7518) {
/* RFC7518 format - raw (r,s) */
i = mp_unsigned_bin_size(key->dp.order);
if (siglen != (2*i)) {
err = CRYPT_INVALID_PACKET;
goto error;
}
if ((err = mp_read_unsigned_bin(r, (unsigned char *)sig, i)) != CRYPT_OK) { goto error; }
if ((err = mp_read_unsigned_bin(s, (unsigned char *)sig+i, i)) != CRYPT_OK) { goto error; }
}
else if (sigformat == LTC_ECCSIG_ETH27) {
/* Ethereum (v,r,s) format */
if (pk_oid_cmp_with_ulong("1.3.132.0.10", key->dp.oid, key->dp.oidlen) != CRYPT_OK) {
/* Only valid for secp256k1 - OID 1.3.132.0.10 */
err = CRYPT_ERROR; goto error;
}
if (siglen != 65) { /* Only secp256k1 curves use this format, so must be 65 bytes long */
err = CRYPT_INVALID_PACKET;
goto error;
}
i = (unsigned long)sig[64];
if ((i>=27) && (i<31)) i -= 27; /* Ethereum adds 27 to recovery ID */
if (recid >= 0 && ((unsigned long)recid != i)) {
/* Recovery ID specified, but doesn't match signature */
err = CRYPT_INVALID_PACKET;
goto error;
}
recid = i;
if ((err = mp_read_unsigned_bin(r, (unsigned char *)sig, 32)) != CRYPT_OK) { goto error; }
if ((err = mp_read_unsigned_bin(s, (unsigned char *)sig+32, 32)) != CRYPT_OK) { goto error; }
}
#ifdef LTC_SSH
else if (sigformat == LTC_ECCSIG_RFC5656) {
char name[64], name2[64];
unsigned long namelen = sizeof(name2);
/* Decode as SSH data sequence, per RFC4251 */
if ((err = ssh_decode_sequence_multi(sig, siglen,
LTC_SSHDATA_STRING, name, 64,
LTC_SSHDATA_MPINT, r,
LTC_SSHDATA_MPINT, s,
LTC_SSHDATA_EOL, NULL)) != CRYPT_OK) { goto error; }
/* Check curve matches identifier string */
if ((err = ecc_ssh_ecdsa_encode_name(name2, &namelen, key)) != CRYPT_OK) { goto error; }
if (XSTRCMP(name,name2) != 0) {
err = CRYPT_INVALID_ARG;
goto error;
}
}
#endif
else {
/* Unknown signature format */
err = CRYPT_ERROR;
goto error;
}
if (recid < 0 || (unsigned long)recid >= 2*(key->dp.cofactor+1)) {
/* Recovery ID is out of range, reject it */
err = CRYPT_INVALID_ARG;
goto error;
}
/* check for zero */
if (mp_cmp_d(r, 0) != LTC_MP_GT || mp_cmp_d(s, 0) != LTC_MP_GT ||
mp_cmp(r, p) != LTC_MP_LT || mp_cmp(s, p) != LTC_MP_LT) {
err = CRYPT_INVALID_PACKET;
goto error;
}
/* read hash - truncate if needed */
pbits = mp_count_bits(p);
pbytes = (pbits+7) >> 3;
if (pbits > hashlen*8) {
if ((err = mp_read_unsigned_bin(e, (unsigned char *)hash, hashlen)) != CRYPT_OK) { goto error; }
}
else if (pbits % 8 == 0) {
if ((err = mp_read_unsigned_bin(e, (unsigned char *)hash, pbytes)) != CRYPT_OK) { goto error; }
}
else {
shift_right = 8 - pbits % 8;
for (i=0, ch=0; i<pbytes; i++) {
buf[i] = ch;
ch = (hash[i] << (8-shift_right));
buf[i] = buf[i] ^ (hash[i] >> shift_right);
}
if ((err = mp_read_unsigned_bin(e, (unsigned char *)buf, pbytes)) != CRYPT_OK) { goto error; }
}
/* decompress point from r=(x mod p) - BEWARE: requires sqrtmod_prime */
/* x = r + p*(recid/2) */
if ((err = mp_set(x, recid/2)) != CRYPT_OK) { goto error; }
if ((err = mp_mulmod(p, x, m, x)) != CRYPT_OK) { goto error; }
if ((err = mp_add(x, r, x)) != CRYPT_OK) { goto error; }
/* compute x^3 */
if ((err = mp_sqr(x, t1)) != CRYPT_OK) { goto error; }
if ((err = mp_mulmod(t1, x, m, t1)) != CRYPT_OK) { goto error; }
/* compute x^3 + a*x */
if ((err = mp_mulmod(a, x, m, t2)) != CRYPT_OK) { goto error; }
if ((err = mp_add(t1, t2, t1)) != CRYPT_OK) { goto error; }
/* compute x^3 + a*x + b */
if ((err = mp_add(t1, b, t1)) != CRYPT_OK) { goto error; }
/* compute sqrt(x^3 + a*x + b) */
if ((err = mp_sqrtmod_prime(t1, m, t2)) != CRYPT_OK) { goto error; }
/* fill in mR */
if ((err = mp_copy(x, mR->x)) != CRYPT_OK) { goto error; }
if ((mp_isodd(t2) && (recid%2)) || (!mp_isodd(t2) && !(recid%2))) {
if ((err = mp_mod(t2, m, mR->y)) != CRYPT_OK) { goto error; }
}
else {
if ((err = mp_submod(m, t2, m, mR->y)) != CRYPT_OK) { goto error; }
}
if ((err = mp_set(mR->z, 1)) != CRYPT_OK) { goto error; }
/* w = r^-1 mod n */
if ((err = mp_invmod(r, p, w)) != CRYPT_OK) { goto error; }
/* v1 = sw */
if ((err = mp_mulmod(s, w, p, v1)) != CRYPT_OK) { goto error; }
/* v2 = -ew */
if ((err = mp_mulmod(e, w, p, v2)) != CRYPT_OK) { goto error; }
if ((err = mp_submod(p, v2, p, v2)) != CRYPT_OK) { goto error; }
/* w = s^-1 mod n */
if ((err = mp_invmod(s, p, w)) != CRYPT_OK) { goto error; }
/* u1 = ew */
if ((err = mp_mulmod(e, w, p, u1)) != CRYPT_OK) { goto error; }
/* u2 = rw */
if ((err = mp_mulmod(r, w, p, u2)) != CRYPT_OK) { goto error; }
/* find mG */
if ((err = ltc_ecc_copy_point(&key->dp.base, mG)) != CRYPT_OK) { goto error; }
/* find the montgomery mp */
if ((err = mp_montgomery_setup(m, &mp)) != CRYPT_OK) { goto error; }
/* for curves with a == -3 keep ma == NULL */
if (mp_cmp(a_plus3, m) != LTC_MP_EQ) {
if ((err = mp_init_multi(&mu, &ma, NULL)) != CRYPT_OK) { goto error; }
if ((err = mp_montgomery_normalization(mu, m)) != CRYPT_OK) { goto error; }
if ((err = mp_mulmod(a, mu, m, ma)) != CRYPT_OK) { goto error; }
}
/* recover mQ from mR */
/* compute v1*mR + v2*mG = mQ using Shamir's trick */
if ((err = ltc_mp.ecc_mul2add(mR, v1, mG, v2, mQ, ma, m)) != CRYPT_OK) { goto error; }
/* compute u1*mG + u2*mQ = mG using Shamir's trick */
if ((err = ltc_mp.ecc_mul2add(mG, u1, mQ, u2, mG, ma, m)) != CRYPT_OK) { goto error; }
/* v = X_x1 mod n */
if ((err = mp_mod(mG->x, p, v)) != CRYPT_OK) { goto error; }
/* does v == r */
if (mp_cmp(v, r) == LTC_MP_EQ) {
/* found public key which verifies signature */
if ((err = ltc_ecc_copy_point(mQ, &key->pubkey)) != CRYPT_OK) { goto error; }
/* point on the curve + other checks */
if ((err = ltc_ecc_verify_key(key)) != CRYPT_OK) { goto error; }
key->type = PK_PUBLIC;
err = CRYPT_OK;
}
else {
/* not found - recid is wrong or we're unable to calculate public key for some other reason */
err = CRYPT_INVALID_ARG;
}
error:
if (ma != NULL) mp_clear(ma);
if (mu != NULL) mp_clear(mu);
if (mp != NULL) mp_montgomery_free(mp);
if (mR != NULL) ltc_ecc_del_point(mR);
if (mQ != NULL) ltc_ecc_del_point(mQ);
if (mG != NULL) ltc_ecc_del_point(mG);
mp_clear_multi(a_plus3, y, x, e, v2, v1, u2, u1, t2, t1, w, v, s, r, NULL);
return err;
}
#endif
#endif
/* ref: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */