proxmark3/common/mbedtls/ecdsa.c

/*
 *  Elliptic curve DSA
 *
 *  Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
 *  SPDX-License-Identifier: GPL-2.0
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License along
 *  with this program; if not, write to the Free Software Foundation, Inc.,
 *  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 *  This file is part of mbed TLS (https://tls.mbed.org)
 */

/*
 * References:
 *
 * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
 */

#if !defined(MBEDTLS_CONFIG_FILE)
#include "mbedtls/config.h"
#else
#include MBEDTLS_CONFIG_FILE
#endif

#if defined(MBEDTLS_ECDSA_C)

#include "mbedtls/ecdsa.h"
#include "mbedtls/asn1write.h"

#include <string.h>

#if defined(MBEDTLS_ECDSA_DETERMINISTIC)
#include "mbedtls/hmac_drbg.h"
#endif

/*
 * Derive a suitable integer for group grp from a buffer of length len
 * SEC1 4.1.3 step 5 aka SEC1 4.1.4 step 3
 */
static int derive_mpi(const mbedtls_ecp_group *grp, mbedtls_mpi *x,
                      const unsigned char *buf, size_t blen) {
    int ret;
    size_t n_size = (grp->nbits + 7) / 8;
    size_t use_size = blen > n_size ? n_size : blen;

    MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(x, buf, use_size));
    if (use_size * 8 > grp->nbits)
        MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(x, use_size * 8 - grp->nbits));

    /* While at it, reduce modulo N */
    if (mbedtls_mpi_cmp_mpi(x, &grp->N) >= 0)
        MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(x, x, &grp->N));

cleanup:
    return (ret);
}

#if !defined(MBEDTLS_ECDSA_SIGN_ALT)
/*
 * Compute ECDSA signature of a hashed message (SEC1 4.1.3)
 * Obviously, compared to SEC1 4.1.3, we skip step 4 (hash message)
 */
int mbedtls_ecdsa_sign(mbedtls_ecp_group *grp, mbedtls_mpi *r, mbedtls_mpi *s,
                       const mbedtls_mpi *d, const unsigned char *buf, size_t blen,
                       int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) {
    int ret, key_tries, sign_tries, blind_tries;
    mbedtls_ecp_point R;
    mbedtls_mpi k, e, t;

    /* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
    if (grp->N.p == NULL)
        return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA);

    /* Make sure d is in range 1..n-1 */
    if (mbedtls_mpi_cmp_int(d, 1) < 0 || mbedtls_mpi_cmp_mpi(d, &grp->N) >= 0)
        return (MBEDTLS_ERR_ECP_INVALID_KEY);

    mbedtls_ecp_point_init(&R);
    mbedtls_mpi_init(&k);
    mbedtls_mpi_init(&e);
    mbedtls_mpi_init(&t);

    sign_tries = 0;
    do {
        /*
         * Steps 1-3: generate a suitable ephemeral keypair
         * and set r = xR mod n
         */
        key_tries = 0;
        do {
            MBEDTLS_MPI_CHK(mbedtls_ecp_gen_keypair(grp, &k, &R, f_rng, p_rng));
            MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(r, &R.X, &grp->N));

            if (key_tries++ > 10) {
                ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
                goto cleanup;
            }
        } while (mbedtls_mpi_cmp_int(r, 0) == 0);

        /*
         * Step 5: derive MPI from hashed message
         */
        MBEDTLS_MPI_CHK(derive_mpi(grp, &e, buf, blen));

        /*
         * Generate a random value to blind inv_mod in next step,
         * avoiding a potential timing leak.
         */
        blind_tries = 0;
        do {
            size_t n_size = (grp->nbits + 7) / 8;
            MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(&t, n_size, f_rng, p_rng));
            MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&t, 8 * n_size - grp->nbits));

            /* See mbedtls_ecp_gen_keypair() */
            if (++blind_tries > 30)
                return (MBEDTLS_ERR_ECP_RANDOM_FAILED);
        } while (mbedtls_mpi_cmp_int(&t, 1) < 0 ||
                 mbedtls_mpi_cmp_mpi(&t, &grp->N) >= 0);

        /*
         * Step 6: compute s = (e + r * d) / k = t (e + rd) / (kt) mod n
         */
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(s, r, d));
        MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&e, &e, s));
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(&e, &e, &t));
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(&k, &k, &t));
        MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(s, &k, &grp->N));
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(s, s, &e));
        MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(s, s, &grp->N));

        if (sign_tries++ > 10) {
            ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
            goto cleanup;
        }
    } while (mbedtls_mpi_cmp_int(s, 0) == 0);

cleanup:
    mbedtls_ecp_point_free(&R);
    mbedtls_mpi_free(&k);
    mbedtls_mpi_free(&e);
    mbedtls_mpi_free(&t);

    return (ret);
}
#endif /* MBEDTLS_ECDSA_SIGN_ALT */

#if defined(MBEDTLS_ECDSA_DETERMINISTIC)
/*
 * Deterministic signature wrapper
 */
int mbedtls_ecdsa_sign_det(mbedtls_ecp_group *grp, mbedtls_mpi *r, mbedtls_mpi *s,
                           const mbedtls_mpi *d, const unsigned char *buf, size_t blen,
                           mbedtls_md_type_t md_alg) {
    int ret;
    mbedtls_hmac_drbg_context rng_ctx;
    unsigned char data[2 * MBEDTLS_ECP_MAX_BYTES];
    size_t grp_len = (grp->nbits + 7) / 8;
    const mbedtls_md_info_t *md_info;
    mbedtls_mpi h;

    if ((md_info = mbedtls_md_info_from_type(md_alg)) == NULL)
        return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA);

    mbedtls_mpi_init(&h);
    mbedtls_hmac_drbg_init(&rng_ctx);

    /* Use private key and message hash (reduced) to initialize HMAC_DRBG */
    MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(d, data, grp_len));
    MBEDTLS_MPI_CHK(derive_mpi(grp, &h, buf, blen));
    MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&h, data + grp_len, grp_len));
    mbedtls_hmac_drbg_seed_buf(&rng_ctx, md_info, data, 2 * grp_len);

    ret = mbedtls_ecdsa_sign(grp, r, s, d, buf, blen,
                             mbedtls_hmac_drbg_random, &rng_ctx);

cleanup:
    mbedtls_hmac_drbg_free(&rng_ctx);
    mbedtls_mpi_free(&h);

    return (ret);
}
#endif /* MBEDTLS_ECDSA_DETERMINISTIC */

#if !defined(MBEDTLS_ECDSA_VERIFY_ALT)
/*
 * Verify ECDSA signature of hashed message (SEC1 4.1.4)
 * Obviously, compared to SEC1 4.1.3, we skip step 2 (hash message)
 */
int mbedtls_ecdsa_verify(mbedtls_ecp_group *grp,
                         const unsigned char *buf, size_t blen,
                         const mbedtls_ecp_point *Q, const mbedtls_mpi *r, const mbedtls_mpi *s) {
    int ret;
    mbedtls_mpi e, s_inv, u1, u2;
    mbedtls_ecp_point R;

    mbedtls_ecp_point_init(&R);
    mbedtls_mpi_init(&e);
    mbedtls_mpi_init(&s_inv);
    mbedtls_mpi_init(&u1);
    mbedtls_mpi_init(&u2);

    /* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
    if (grp->N.p == NULL)
        return (MBEDTLS_ERR_ECP_BAD_INPUT_DATA);

    /*
     * Step 1: make sure r and s are in range 1..n-1
     */
    if (mbedtls_mpi_cmp_int(r, 1) < 0 || mbedtls_mpi_cmp_mpi(r, &grp->N) >= 0 ||
            mbedtls_mpi_cmp_int(s, 1) < 0 || mbedtls_mpi_cmp_mpi(s, &grp->N) >= 0) {
        ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
        goto cleanup;
    }

    /*
     * Additional precaution: make sure Q is valid
     */
    MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, Q));

    /*
     * Step 3: derive MPI from hashed message
     */
    MBEDTLS_MPI_CHK(derive_mpi(grp, &e, buf, blen));

    /*
     * Step 4: u1 = e / s mod n, u2 = r / s mod n
     */
    MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&s_inv, s, &grp->N));

    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(&u1, &e, &s_inv));
    MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&u1, &u1, &grp->N));

    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(&u2, r, &s_inv));
    MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&u2, &u2, &grp->N));

    /*
     * Step 5: R = u1 G + u2 Q
     *
     * Since we're not using any secret data, no need to pass a RNG to
     * mbedtls_ecp_mul() for countermesures.
     */
    MBEDTLS_MPI_CHK(mbedtls_ecp_muladd(grp, &R, &u1, &grp->G, &u2, Q));

    if (mbedtls_ecp_is_zero(&R)) {
        ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
        goto cleanup;
    }

    /*
     * Step 6: convert xR to an integer (no-op)
     * Step 7: reduce xR mod n (gives v)
     */
    MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&R.X, &R.X, &grp->N));

    /*
     * Step 8: check if v (that is, R.X) is equal to r
     */
    if (mbedtls_mpi_cmp_mpi(&R.X, r) != 0) {
        ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
        goto cleanup;
    }

cleanup:
    mbedtls_ecp_point_free(&R);
    mbedtls_mpi_free(&e);
    mbedtls_mpi_free(&s_inv);
    mbedtls_mpi_free(&u1);
    mbedtls_mpi_free(&u2);

    return (ret);
}
#endif /* MBEDTLS_ECDSA_VERIFY_ALT */

/*
 * Convert a signature (given by context) to ASN.1
 */
int ecdsa_signature_to_asn1(const mbedtls_mpi *r, const mbedtls_mpi *s,
                            unsigned char *sig, size_t *slen) {
    int ret;
    unsigned char buf[MBEDTLS_ECDSA_MAX_LEN];
    unsigned char *p = buf + sizeof(buf);
    size_t len = 0;

    MBEDTLS_ASN1_CHK_ADD(len, mbedtls_asn1_write_mpi(&p, buf, s));
    MBEDTLS_ASN1_CHK_ADD(len, mbedtls_asn1_write_mpi(&p, buf, r));

    MBEDTLS_ASN1_CHK_ADD(len, mbedtls_asn1_write_len(&p, buf, len));
    MBEDTLS_ASN1_CHK_ADD(len, mbedtls_asn1_write_tag(&p, buf,
                                                     MBEDTLS_ASN1_CONSTRUCTED | MBEDTLS_ASN1_SEQUENCE));

    memcpy(sig, p, len);
    *slen = len;

    return (0);
}

/*
 * Compute and write signature
 */
int mbedtls_ecdsa_write_signature(mbedtls_ecdsa_context *ctx, mbedtls_md_type_t md_alg,
                                  const unsigned char *hash, size_t hlen,
                                  unsigned char *sig, size_t *slen,
                                  int (*f_rng)(void *, unsigned char *, size_t),
                                  void *p_rng) {
    int ret;
    mbedtls_mpi r, s;

    mbedtls_mpi_init(&r);
    mbedtls_mpi_init(&s);

#if defined(MBEDTLS_ECDSA_DETERMINISTIC)
    (void) f_rng;
    (void) p_rng;

    MBEDTLS_MPI_CHK(mbedtls_ecdsa_sign_det(&ctx->grp, &r, &s, &ctx->d,
                                           hash, hlen, md_alg));
#else
    (void) md_alg;

    MBEDTLS_MPI_CHK(mbedtls_ecdsa_sign(&ctx->grp, &r, &s, &ctx->d,
                                       hash, hlen, f_rng, p_rng));
#endif

    MBEDTLS_MPI_CHK(ecdsa_signature_to_asn1(&r, &s, sig, slen));

cleanup:
    mbedtls_mpi_free(&r);
    mbedtls_mpi_free(&s);

    return (ret);
}

#if ! defined(MBEDTLS_DEPRECATED_REMOVED) && \
    defined(MBEDTLS_ECDSA_DETERMINISTIC)
int mbedtls_ecdsa_write_signature_det(mbedtls_ecdsa_context *ctx,
                                      const unsigned char *hash, size_t hlen,
                                      unsigned char *sig, size_t *slen,
                                      mbedtls_md_type_t md_alg) {
    return (mbedtls_ecdsa_write_signature(ctx, md_alg, hash, hlen, sig, slen,
                                          NULL, NULL));
}
#endif

/*
 * Read and check signature
 */
int mbedtls_ecdsa_read_signature(mbedtls_ecdsa_context *ctx,
                                 const unsigned char *hash, size_t hlen,
                                 const unsigned char *sig, size_t slen) {
    int ret;
    unsigned char *p = (unsigned char *) sig;
    const unsigned char *end = sig + slen;
    size_t len;
    mbedtls_mpi r, s;

    mbedtls_mpi_init(&r);
    mbedtls_mpi_init(&s);

    if ((ret = mbedtls_asn1_get_tag(&p, end, &len,
                                    MBEDTLS_ASN1_CONSTRUCTED | MBEDTLS_ASN1_SEQUENCE)) != 0) {
        ret += MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
        goto cleanup;
    }

    if (p + len != end) {
        ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA +
              MBEDTLS_ERR_ASN1_LENGTH_MISMATCH;
        goto cleanup;
    }

    if ((ret = mbedtls_asn1_get_mpi(&p, end, &r)) != 0 ||
            (ret = mbedtls_asn1_get_mpi(&p, end, &s)) != 0) {
        ret += MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
        goto cleanup;
    }

    if ((ret = mbedtls_ecdsa_verify(&ctx->grp, hash, hlen,
                                    &ctx->Q, &r, &s)) != 0)
        goto cleanup;

    /* At this point we know that the buffer starts with a valid signature.
     * Return 0 if the buffer just contains the signature, and a specific
     * error code if the valid signature is followed by more data. */
    if (p != end)
        ret = MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH;

cleanup:
    mbedtls_mpi_free(&r);
    mbedtls_mpi_free(&s);

    return (ret);
}

#if !defined(MBEDTLS_ECDSA_GENKEY_ALT)
/*
 * Generate key pair
 */
int mbedtls_ecdsa_genkey(mbedtls_ecdsa_context *ctx, mbedtls_ecp_group_id gid,
                         int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) {
    return (mbedtls_ecp_group_load(&ctx->grp, gid) ||
            mbedtls_ecp_gen_keypair(&ctx->grp, &ctx->d, &ctx->Q, f_rng, p_rng));
}
#endif /* MBEDTLS_ECDSA_GENKEY_ALT */

/*
 * Set context from an mbedtls_ecp_keypair
 */
int mbedtls_ecdsa_from_keypair(mbedtls_ecdsa_context *ctx, const mbedtls_ecp_keypair *key) {
    int ret;

    if ((ret = mbedtls_ecp_group_copy(&ctx->grp, &key->grp)) != 0 ||
            (ret = mbedtls_mpi_copy(&ctx->d, &key->d)) != 0 ||
            (ret = mbedtls_ecp_copy(&ctx->Q, &key->Q)) != 0) {
        mbedtls_ecdsa_free(ctx);
    }

    return (ret);
}

/*
 * Initialize context
 */
void mbedtls_ecdsa_init(mbedtls_ecdsa_context *ctx) {
    mbedtls_ecp_keypair_init(ctx);
}

/*
 * Free context
 */
void mbedtls_ecdsa_free(mbedtls_ecdsa_context *ctx) {
    mbedtls_ecp_keypair_free(ctx);
}

#endif /* MBEDTLS_ECDSA_C */