/* $OpenBSD: ecdsa.c,v 1.11 2023/07/07 13:54:45 beck Exp $ */ /* ==================================================================== * Copyright (c) 2000-2002 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * * 3. All advertising materials mentioning features or use of this * software must display the following acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * licensing@OpenSSL.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. * ==================================================================== * * This product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ #include #include #include #include #include #include #include #include #include #include #include #include "bn_local.h" #include "ec_local.h" #include "ecdsa_local.h" static const ASN1_TEMPLATE ECDSA_SIG_seq_tt[] = { { .flags = 0, .tag = 0, .offset = offsetof(ECDSA_SIG, r), .field_name = "r", .item = &BIGNUM_it, }, { .flags = 0, .tag = 0, .offset = offsetof(ECDSA_SIG, s), .field_name = "s", .item = &BIGNUM_it, }, }; const ASN1_ITEM ECDSA_SIG_it = { .itype = ASN1_ITYPE_SEQUENCE, .utype = V_ASN1_SEQUENCE, .templates = ECDSA_SIG_seq_tt, .tcount = sizeof(ECDSA_SIG_seq_tt) / sizeof(ASN1_TEMPLATE), .funcs = NULL, .size = sizeof(ECDSA_SIG), .sname = "ECDSA_SIG", }; ECDSA_SIG * d2i_ECDSA_SIG(ECDSA_SIG **a, const unsigned char **in, long len) { return (ECDSA_SIG *)ASN1_item_d2i((ASN1_VALUE **)a, in, len, &ECDSA_SIG_it); } LCRYPTO_ALIAS(d2i_ECDSA_SIG); int i2d_ECDSA_SIG(const ECDSA_SIG *a, unsigned char **out) { return ASN1_item_i2d((ASN1_VALUE *)a, out, &ECDSA_SIG_it); } LCRYPTO_ALIAS(i2d_ECDSA_SIG); ECDSA_SIG * ECDSA_SIG_new(void) { return (ECDSA_SIG *)ASN1_item_new(&ECDSA_SIG_it); } LCRYPTO_ALIAS(ECDSA_SIG_new); void ECDSA_SIG_free(ECDSA_SIG *a) { ASN1_item_free((ASN1_VALUE *)a, &ECDSA_SIG_it); } LCRYPTO_ALIAS(ECDSA_SIG_free); void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **pr, const BIGNUM **ps) { if (pr != NULL) *pr = sig->r; if (ps != NULL) *ps = sig->s; } LCRYPTO_ALIAS(ECDSA_SIG_get0); const BIGNUM * ECDSA_SIG_get0_r(const ECDSA_SIG *sig) { return sig->r; } LCRYPTO_ALIAS(ECDSA_SIG_get0_r); const BIGNUM * ECDSA_SIG_get0_s(const ECDSA_SIG *sig) { return sig->s; } LCRYPTO_ALIAS(ECDSA_SIG_get0_s); int ECDSA_SIG_set0(ECDSA_SIG *sig, BIGNUM *r, BIGNUM *s) { if (r == NULL || s == NULL) return 0; BN_free(sig->r); BN_free(sig->s); sig->r = r; sig->s = s; return 1; } LCRYPTO_ALIAS(ECDSA_SIG_set0); int ECDSA_size(const EC_KEY *r) { const EC_GROUP *group; const BIGNUM *order = NULL; ECDSA_SIG sig; int ret = 0; if (r == NULL) goto err; if ((group = EC_KEY_get0_group(r)) == NULL) goto err; if ((order = EC_GROUP_get0_order(group)) == NULL) goto err; sig.r = (BIGNUM *)order; sig.s = (BIGNUM *)order; if ((ret = i2d_ECDSA_SIG(&sig, NULL)) < 0) ret = 0; err: return ret; } LCRYPTO_ALIAS(ECDSA_size); /* * FIPS 186-5, section 6.4.1, step 2: convert hashed message into an integer. * Use the order_bits leftmost bits if it exceeds the group order. */ static int ecdsa_prepare_digest(const unsigned char *digest, int digest_len, const EC_KEY *key, BIGNUM *e) { const EC_GROUP *group; int digest_bits, order_bits; if (BN_bin2bn(digest, digest_len, e) == NULL) { ECerror(ERR_R_BN_LIB); return 0; } if ((group = EC_KEY_get0_group(key)) == NULL) return 0; order_bits = EC_GROUP_order_bits(group); digest_bits = 8 * digest_len; if (digest_bits <= order_bits) return 1; return BN_rshift(e, e, digest_bits - order_bits); } int ecdsa_sign(int type, const unsigned char *digest, int digest_len, unsigned char *signature, unsigned int *signature_len, const BIGNUM *kinv, const BIGNUM *r, EC_KEY *key) { ECDSA_SIG *sig; int out_len = 0; int ret = 0; if ((sig = ECDSA_do_sign_ex(digest, digest_len, kinv, r, key)) == NULL) goto err; if ((out_len = i2d_ECDSA_SIG(sig, &signature)) < 0) { out_len = 0; goto err; } ret = 1; err: *signature_len = out_len; ECDSA_SIG_free(sig); return ret; } /* * FIPS 186-5, section 6.4.1, steps 3-8 and 11: Generate k, calculate r and * kinv. If r == 0, try again with a new random k. */ int ecdsa_sign_setup(EC_KEY *key, BN_CTX *in_ctx, BIGNUM **out_kinv, BIGNUM **out_r) { const EC_GROUP *group; EC_POINT *point = NULL; BN_CTX *ctx = NULL; BIGNUM *k = NULL, *r = NULL; const BIGNUM *order; BIGNUM *x; int order_bits; int ret = 0; BN_free(*out_kinv); *out_kinv = NULL; BN_free(*out_r); *out_r = NULL; if (key == NULL) { ECerror(ERR_R_PASSED_NULL_PARAMETER); goto err; } if ((group = EC_KEY_get0_group(key)) == NULL) { ECerror(ERR_R_PASSED_NULL_PARAMETER); goto err; } if ((k = BN_new()) == NULL) goto err; if ((r = BN_new()) == NULL) goto err; if ((ctx = in_ctx) == NULL) ctx = BN_CTX_new(); if (ctx == NULL) { ECerror(ERR_R_MALLOC_FAILURE); goto err; } BN_CTX_start(ctx); if ((x = BN_CTX_get(ctx)) == NULL) goto err; if ((point = EC_POINT_new(group)) == NULL) { ECerror(ERR_R_EC_LIB); goto err; } if ((order = EC_GROUP_get0_order(group)) == NULL) { ECerror(ERR_R_EC_LIB); goto err; } if (BN_cmp(order, BN_value_one()) <= 0) { ECerror(EC_R_INVALID_GROUP_ORDER); goto err; } /* Reject curves with an order that is smaller than 80 bits. */ if ((order_bits = BN_num_bits(order)) < 80) { ECerror(EC_R_INVALID_GROUP_ORDER); goto err; } /* Preallocate space. */ if (!BN_set_bit(k, order_bits) || !BN_set_bit(r, order_bits) || !BN_set_bit(x, order_bits)) goto err; /* Step 11: repeat until r != 0. */ do { /* Step 3: generate random k. */ if (!bn_rand_interval(k, BN_value_one(), order)) goto err; /* * We do not want timing information to leak the length of k, * so we compute G * k using an equivalent scalar of fixed * bit-length. * * We unconditionally perform both of these additions to prevent * a small timing information leakage. We then choose the sum * that is one bit longer than the order. This guarantees the * code path used in the constant time implementations * elsewhere. * * TODO: revisit the bn_copy aiming for a memory access agnostic * conditional copy. */ if (!BN_add(r, k, order) || !BN_add(x, r, order) || !bn_copy(k, BN_num_bits(r) > order_bits ? r : x)) goto err; BN_set_flags(k, BN_FLG_CONSTTIME); /* Step 5: P = k * G. */ if (!EC_POINT_mul(group, point, k, NULL, NULL, ctx)) { ECerror(ERR_R_EC_LIB); goto err; } /* Steps 6 (and 7): from P = (x, y) retain the x-coordinate. */ if (!EC_POINT_get_affine_coordinates(group, point, x, NULL, ctx)) { ECerror(ERR_R_EC_LIB); goto err; } /* Step 8: r = x (mod order). */ if (!BN_nnmod(r, x, order, ctx)) { ECerror(ERR_R_BN_LIB); goto err; } } while (BN_is_zero(r)); /* Step 4: calculate kinv. */ if (BN_mod_inverse_ct(k, k, order, ctx) == NULL) { ECerror(ERR_R_BN_LIB); goto err; } *out_kinv = k; k = NULL; *out_r = r; r = NULL; ret = 1; err: BN_CTX_end(ctx); if (ctx != in_ctx) BN_CTX_free(ctx); BN_free(k); BN_free(r); EC_POINT_free(point); return ret; } /* * FIPS 186-5, section 6.4.1, step 9: compute s = inv(k)(e + xr) mod order. * In order to reduce the possibility of a side-channel attack, the following * is calculated using a random blinding value b in [1, order): * s = inv(b)(be + bxr)inv(k) mod order. */ static int ecdsa_compute_s(BIGNUM **out_s, const BIGNUM *e, const BIGNUM *kinv, const BIGNUM *r, const EC_KEY *key, BN_CTX *ctx) { const EC_GROUP *group; const BIGNUM *order, *priv_key; BIGNUM *b, *binv, *be, *bxr; BIGNUM *s = NULL; int ret = 0; *out_s = NULL; BN_CTX_start(ctx); if ((group = EC_KEY_get0_group(key)) == NULL) { ECerror(ERR_R_PASSED_NULL_PARAMETER); goto err; } if ((order = EC_GROUP_get0_order(group)) == NULL) { ECerror(ERR_R_EC_LIB); goto err; } if ((priv_key = EC_KEY_get0_private_key(key)) == NULL) { ECerror(ERR_R_PASSED_NULL_PARAMETER); goto err; } if ((b = BN_CTX_get(ctx)) == NULL) goto err; if ((binv = BN_CTX_get(ctx)) == NULL) goto err; if ((be = BN_CTX_get(ctx)) == NULL) goto err; if ((bxr = BN_CTX_get(ctx)) == NULL) goto err; if ((s = BN_new()) == NULL) goto err; /* * In a valid ECDSA signature, r must be in [1, order). Since r can be * caller provided - either directly or by replacing sign_setup() - we * can't rely on this being the case. */ if (BN_cmp(r, BN_value_one()) < 0 || BN_cmp(r, order) >= 0) { ECerror(EC_R_BAD_SIGNATURE); goto err; } if (!bn_rand_interval(b, BN_value_one(), order)) { ECerror(ERR_R_BN_LIB); goto err; } if (BN_mod_inverse_ct(binv, b, order, ctx) == NULL) { ECerror(ERR_R_BN_LIB); goto err; } if (!BN_mod_mul(bxr, b, priv_key, order, ctx)) { ECerror(ERR_R_BN_LIB); goto err; } if (!BN_mod_mul(bxr, bxr, r, order, ctx)) { ECerror(ERR_R_BN_LIB); goto err; } if (!BN_mod_mul(be, b, e, order, ctx)) { ECerror(ERR_R_BN_LIB); goto err; } if (!BN_mod_add(s, be, bxr, order, ctx)) { ECerror(ERR_R_BN_LIB); goto err; } /* s = b(e + xr)k^-1 */ if (!BN_mod_mul(s, s, kinv, order, ctx)) { ECerror(ERR_R_BN_LIB); goto err; } /* s = (e + xr)k^-1 */ if (!BN_mod_mul(s, s, binv, order, ctx)) { ECerror(ERR_R_BN_LIB); goto err; } /* Step 11: if s == 0 start over. */ if (!BN_is_zero(s)) { *out_s = s; s = NULL; } ret = 1; err: BN_CTX_end(ctx); BN_free(s); return ret; } /* * It is too expensive to check curve parameters on every sign operation. * Instead, cap the number of retries. A single retry is very unlikely, so * allowing 32 retries is amply enough. */ #define ECDSA_MAX_SIGN_ITERATIONS 32 /* * FIPS 186-5: Section 6.4.1: ECDSA signature generation, steps 2-12. * The caller provides the hash of the message, thus performs step 1. * Step 10, zeroing k and kinv, is done by BN_free(). */ ECDSA_SIG * ecdsa_sign_sig(const unsigned char *digest, int digest_len, const BIGNUM *in_kinv, const BIGNUM *in_r, EC_KEY *key) { BN_CTX *ctx = NULL; BIGNUM *kinv = NULL, *r = NULL, *s = NULL; BIGNUM *e; int caller_supplied_values = 0; int attempts = 0; ECDSA_SIG *sig = NULL; if ((ctx = BN_CTX_new()) == NULL) { ECerror(ERR_R_MALLOC_FAILURE); goto err; } BN_CTX_start(ctx); if ((e = BN_CTX_get(ctx)) == NULL) goto err; /* Step 2: convert hash into an integer. */ if (!ecdsa_prepare_digest(digest, digest_len, key, e)) goto err; if (in_kinv != NULL && in_r != NULL) { /* * Use the caller's kinv and r. Don't call ECDSA_sign_setup(). * If we're unable to compute a valid signature, the caller * must provide new values. */ caller_supplied_values = 1; if ((kinv = BN_dup(in_kinv)) == NULL) { ECerror(ERR_R_MALLOC_FAILURE); goto err; } if ((r = BN_dup(in_r)) == NULL) { ECerror(ERR_R_MALLOC_FAILURE); goto err; } } do { /* Steps 3-8: calculate kinv and r. */ if (!caller_supplied_values) { if (!ECDSA_sign_setup(key, ctx, &kinv, &r)) { ECerror(ERR_R_EC_LIB); goto err; } } /* * Steps 9 and 11: if s is non-NULL, we have a valid signature. */ if (!ecdsa_compute_s(&s, e, kinv, r, key, ctx)) goto err; if (s != NULL) break; if (caller_supplied_values) { ECerror(EC_R_NEED_NEW_SETUP_VALUES); goto err; } if (++attempts > ECDSA_MAX_SIGN_ITERATIONS) { ECerror(EC_R_WRONG_CURVE_PARAMETERS); goto err; } } while (1); /* Step 12: output (r, s). */ if ((sig = ECDSA_SIG_new()) == NULL) { ECerror(ERR_R_MALLOC_FAILURE); goto err; } if (!ECDSA_SIG_set0(sig, r, s)) { ECDSA_SIG_free(sig); goto err; } r = NULL; s = NULL; err: BN_CTX_end(ctx); BN_CTX_free(ctx); BN_free(kinv); BN_free(r); BN_free(s); return sig; } int ecdsa_verify(int type, const unsigned char *digest, int digest_len, const unsigned char *sigbuf, int sig_len, EC_KEY *key) { ECDSA_SIG *s; unsigned char *der = NULL; const unsigned char *p; int der_len = 0; int ret = -1; if ((s = ECDSA_SIG_new()) == NULL) goto err; p = sigbuf; if (d2i_ECDSA_SIG(&s, &p, sig_len) == NULL) goto err; /* Ensure signature uses DER and doesn't have trailing garbage. */ if ((der_len = i2d_ECDSA_SIG(s, &der)) != sig_len) goto err; if (timingsafe_memcmp(sigbuf, der, der_len)) goto err; ret = ECDSA_do_verify(digest, digest_len, s, key); err: freezero(der, der_len); ECDSA_SIG_free(s); return ret; } /* * FIPS 186-5, section 6.4.2: ECDSA signature verification. * The caller provides us with the hash of the message, so has performed step 2. */ int ecdsa_verify_sig(const unsigned char *digest, int digest_len, const ECDSA_SIG *sig, EC_KEY *key) { const EC_GROUP *group; const EC_POINT *pub_key; EC_POINT *point = NULL; const BIGNUM *order; BN_CTX *ctx = NULL; BIGNUM *e, *sinv, *u, *v, *x; int ret = -1; if (key == NULL || sig == NULL) { ECerror(EC_R_MISSING_PARAMETERS); goto err; } if ((group = EC_KEY_get0_group(key)) == NULL) { ECerror(EC_R_MISSING_PARAMETERS); goto err; } if ((pub_key = EC_KEY_get0_public_key(key)) == NULL) { ECerror(EC_R_MISSING_PARAMETERS); goto err; } if ((ctx = BN_CTX_new()) == NULL) { ECerror(ERR_R_MALLOC_FAILURE); goto err; } BN_CTX_start(ctx); if ((e = BN_CTX_get(ctx)) == NULL) goto err; if ((sinv = BN_CTX_get(ctx)) == NULL) goto err; if ((u = BN_CTX_get(ctx)) == NULL) goto err; if ((v = BN_CTX_get(ctx)) == NULL) goto err; if ((x = BN_CTX_get(ctx)) == NULL) goto err; if ((order = EC_GROUP_get0_order(group)) == NULL) { ECerror(ERR_R_EC_LIB); goto err; } /* Step 1: verify that r and s are in the range [1, order). */ if (BN_cmp(sig->r, BN_value_one()) < 0 || BN_cmp(sig->r, order) >= 0) { ECerror(EC_R_BAD_SIGNATURE); ret = 0; goto err; } if (BN_cmp(sig->s, BN_value_one()) < 0 || BN_cmp(sig->s, order) >= 0) { ECerror(EC_R_BAD_SIGNATURE); ret = 0; goto err; } /* Step 3: convert the hash into an integer. */ if (!ecdsa_prepare_digest(digest, digest_len, key, e)) goto err; /* Step 4: compute the inverse of s modulo order. */ if (BN_mod_inverse_ct(sinv, sig->s, order, ctx) == NULL) { ECerror(ERR_R_BN_LIB); goto err; } /* Step 5: compute u = s^-1 * e and v = s^-1 * r (modulo order). */ if (!BN_mod_mul(u, e, sinv, order, ctx)) { ECerror(ERR_R_BN_LIB); goto err; } if (!BN_mod_mul(v, sig->r, sinv, order, ctx)) { ECerror(ERR_R_BN_LIB); goto err; } /* * Steps 6 and 7: compute R = G * u + pub_key * v = (x, y). Reject if * it's the point at infinity - getting affine coordinates fails. Keep * the x coordinate. */ if ((point = EC_POINT_new(group)) == NULL) { ECerror(ERR_R_MALLOC_FAILURE); goto err; } if (!EC_POINT_mul(group, point, u, pub_key, v, ctx)) { ECerror(ERR_R_EC_LIB); goto err; } if (!EC_POINT_get_affine_coordinates(group, point, x, NULL, ctx)) { ECerror(ERR_R_EC_LIB); goto err; } /* Step 8: convert x to a number in [0, order). */ if (!BN_nnmod(x, x, order, ctx)) { ECerror(ERR_R_BN_LIB); goto err; } /* Step 9: the signature is valid iff the x-coordinate is equal to r. */ ret = (BN_cmp(x, sig->r) == 0); err: BN_CTX_end(ctx); BN_CTX_free(ctx); EC_POINT_free(point); return ret; } ECDSA_SIG * ECDSA_do_sign(const unsigned char *digest, int digest_len, EC_KEY *key) { return ECDSA_do_sign_ex(digest, digest_len, NULL, NULL, key); } LCRYPTO_ALIAS(ECDSA_do_sign); ECDSA_SIG * ECDSA_do_sign_ex(const unsigned char *digest, int digest_len, const BIGNUM *kinv, const BIGNUM *out_r, EC_KEY *key) { if (key->meth->sign_sig == NULL) { ECerror(EC_R_NOT_IMPLEMENTED); return 0; } return key->meth->sign_sig(digest, digest_len, kinv, out_r, key); } LCRYPTO_ALIAS(ECDSA_do_sign_ex); int ECDSA_sign(int type, const unsigned char *digest, int digest_len, unsigned char *signature, unsigned int *signature_len, EC_KEY *key) { return ECDSA_sign_ex(type, digest, digest_len, signature, signature_len, NULL, NULL, key); } LCRYPTO_ALIAS(ECDSA_sign); int ECDSA_sign_ex(int type, const unsigned char *digest, int digest_len, unsigned char *signature, unsigned int *signature_len, const BIGNUM *kinv, const BIGNUM *r, EC_KEY *key) { if (key->meth->sign == NULL) { ECerror(EC_R_NOT_IMPLEMENTED); return 0; } return key->meth->sign(type, digest, digest_len, signature, signature_len, kinv, r, key); } LCRYPTO_ALIAS(ECDSA_sign_ex); int ECDSA_sign_setup(EC_KEY *key, BN_CTX *in_ctx, BIGNUM **out_kinv, BIGNUM **out_r) { if (key->meth->sign_setup == NULL) { ECerror(EC_R_NOT_IMPLEMENTED); return 0; } return key->meth->sign_setup(key, in_ctx, out_kinv, out_r); } LCRYPTO_ALIAS(ECDSA_sign_setup); int ECDSA_do_verify(const unsigned char *digest, int digest_len, const ECDSA_SIG *sig, EC_KEY *key) { if (key->meth->verify_sig == NULL) { ECerror(EC_R_NOT_IMPLEMENTED); return 0; } return key->meth->verify_sig(digest, digest_len, sig, key); } LCRYPTO_ALIAS(ECDSA_do_verify); int ECDSA_verify(int type, const unsigned char *digest, int digest_len, const unsigned char *sigbuf, int sig_len, EC_KEY *key) { if (key->meth->verify == NULL) { ECerror(EC_R_NOT_IMPLEMENTED); return 0; } return key->meth->verify(type, digest, digest_len, sigbuf, sig_len, key); } LCRYPTO_ALIAS(ECDSA_verify);