library/ecdsa.c

/*
 *  Elliptic curve DSA
 *
 *  Copyright The Mbed TLS Contributors
 *  SPDX-License-Identifier: Apache-2.0
 *
 *  Licensed under the Apache License, Version 2.0 (the "License"); you may
 *  not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *  http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
 *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 */

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

#include "common.h"

#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

#    if defined(MBEDTLS_PLATFORM_C)
#        include "mbedtls/platform.h"
#    else
#        include <stdlib.h>
#        define mbedtls_calloc calloc
#        define mbedtls_free   free
#    endif

#    include "mbedtls/platform_util.h"
#    include "mbedtls/error.h"

/* Parameter validation macros based on platform_util.h */
#    define ECDSA_VALIDATE_RET(cond) \
        MBEDTLS_INTERNAL_VALIDATE_RET(cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA)
#    define ECDSA_VALIDATE(cond) MBEDTLS_INTERNAL_VALIDATE(cond)

#    if defined(MBEDTLS_ECP_RESTARTABLE)

/*
 * Sub-context for ecdsa_verify()
 */
struct mbedtls_ecdsa_restart_ver {
    mbedtls_mpi u1, u2; /* intermediate values  */
    enum
    { /* what to do next?     */
        ecdsa_ver_init = 0, /* getting started      */
        ecdsa_ver_muladd, /* muladd step          */
    } state;
};

/*
 * Init verify restart sub-context
 */
static void ecdsa_restart_ver_init(mbedtls_ecdsa_restart_ver_ctx *ctx)
{
    mbedtls_mpi_init(&ctx->u1);
    mbedtls_mpi_init(&ctx->u2);
    ctx->state = ecdsa_ver_init;
}

/*
 * Free the components of a verify restart sub-context
 */
static void ecdsa_restart_ver_free(mbedtls_ecdsa_restart_ver_ctx *ctx)
{
    if (ctx == NULL)
        return;

    mbedtls_mpi_free(&ctx->u1);
    mbedtls_mpi_free(&ctx->u2);

    ecdsa_restart_ver_init(ctx);
}

/*
 * Sub-context for ecdsa_sign()
 */
struct mbedtls_ecdsa_restart_sig {
    int sign_tries;
    int key_tries;
    mbedtls_mpi k; /* per-signature random */
    mbedtls_mpi r; /* r value              */
    enum
    { /* what to do next?     */
        ecdsa_sig_init = 0, /* getting started      */
        ecdsa_sig_mul, /* doing ecp_mul()      */
        ecdsa_sig_modn, /* mod N computations   */
    } state;
};

/*
 * Init verify sign sub-context
 */
static void ecdsa_restart_sig_init(mbedtls_ecdsa_restart_sig_ctx *ctx)
{
    ctx->sign_tries = 0;
    ctx->key_tries = 0;
    mbedtls_mpi_init(&ctx->k);
    mbedtls_mpi_init(&ctx->r);
    ctx->state = ecdsa_sig_init;
}

/*
 * Free the components of a sign restart sub-context
 */
static void ecdsa_restart_sig_free(mbedtls_ecdsa_restart_sig_ctx *ctx)
{
    if (ctx == NULL)
        return;

    mbedtls_mpi_free(&ctx->k);
    mbedtls_mpi_free(&ctx->r);
}

#        if defined(MBEDTLS_ECDSA_DETERMINISTIC)
/*
 * Sub-context for ecdsa_sign_det()
 */
struct mbedtls_ecdsa_restart_det {
    mbedtls_hmac_drbg_context rng_ctx; /* DRBG state   */
    enum
    { /* what to do next?     */
        ecdsa_det_init = 0, /* getting started      */
        ecdsa_det_sign, /* make signature       */
    } state;
};

/*
 * Init verify sign_det sub-context
 */
static void ecdsa_restart_det_init(mbedtls_ecdsa_restart_det_ctx *ctx)
{
    mbedtls_hmac_drbg_init(&ctx->rng_ctx);
    ctx->state = ecdsa_det_init;
}

/*
 * Free the components of a sign_det restart sub-context
 */
static void ecdsa_restart_det_free(mbedtls_ecdsa_restart_det_ctx *ctx)
{
    if (ctx == NULL)
        return;

    mbedtls_hmac_drbg_free(&ctx->rng_ctx);

    ecdsa_restart_det_init(ctx);
}
#        endif /* MBEDTLS_ECDSA_DETERMINISTIC */

#        define ECDSA_RS_ECP (rs_ctx == NULL ? NULL : &rs_ctx->ecp)

/* Utility macro for checking and updating ops budget */
#        define ECDSA_BUDGET(ops) \
            MBEDTLS_MPI_CHK(mbedtls_ecp_check_budget(grp, ECDSA_RS_ECP, ops));

/* Call this when entering a function that needs its own sub-context */
#        define ECDSA_RS_ENTER(SUB)                                        \
            do {                                                           \
                /* reset ops count for this call if top-level */           \
                if (rs_ctx != NULL && rs_ctx->ecp.depth++ == 0)            \
                    rs_ctx->ecp.ops_done = 0;                              \
                                                                           \
                /* set up our own sub-context if needed */                 \
                if (mbedtls_ecp_restart_is_enabled() && rs_ctx != NULL &&  \
                    rs_ctx->SUB == NULL) {                                 \
                    rs_ctx->SUB = mbedtls_calloc(1, sizeof(*rs_ctx->SUB)); \
                    if (rs_ctx->SUB == NULL)                               \
                        return MBEDTLS_ERR_ECP_ALLOC_FAILED;               \
                                                                           \
                    ecdsa_restart_##SUB##_init(rs_ctx->SUB);               \
                }                                                          \
            } while (0)

/* Call this when leaving a function that needs its own sub-context */
#        define ECDSA_RS_LEAVE(SUB)                                           \
            do {                                                              \
                /* clear our sub-context when not in progress (done or error) \
                 */                                                           \
                if (rs_ctx != NULL && rs_ctx->SUB != NULL &&                  \
                    ret != MBEDTLS_ERR_ECP_IN_PROGRESS) {                     \
                    ecdsa_restart_##SUB##_free(rs_ctx->SUB);                  \
                    mbedtls_free(rs_ctx->SUB);                                \
                    rs_ctx->SUB = NULL;                                       \
                }                                                             \
                                                                              \
                if (rs_ctx != NULL)                                           \
                    rs_ctx->ecp.depth--;                                      \
            } while (0)

#    else /* MBEDTLS_ECP_RESTARTABLE */

#        define ECDSA_RS_ECP NULL

#        define ECDSA_BUDGET(ops) /* no-op; for compatibility */

#        define ECDSA_RS_ENTER(SUB) (void)rs_ctx
#        define ECDSA_RS_LEAVE(SUB) (void)rs_ctx

#    endif /* MBEDTLS_ECP_RESTARTABLE */

#    if defined(MBEDTLS_ECDSA_DETERMINISTIC) || \
        !defined(MBEDTLS_ECDSA_SIGN_ALT) || !defined(MBEDTLS_ECDSA_VERIFY_ALT)
/*
 * 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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
    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;
}
#    endif /* ECDSA_DETERMINISTIC || !ECDSA_SIGN_ALT || !ECDSA_VERIFY_ALT */

#    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)
 */
static int
ecdsa_sign_restartable(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 (*f_rng_blind)(void *, unsigned char *, size_t),
                       void *p_rng_blind,
                       mbedtls_ecdsa_restart_ctx *rs_ctx)
{
    int ret, key_tries, sign_tries;
    int *p_sign_tries = &sign_tries, *p_key_tries = &key_tries;
    mbedtls_ecp_point R;
    mbedtls_mpi k, e, t;
    mbedtls_mpi *pk = &k, *pr = r;

    /* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
    if (!mbedtls_ecdsa_can_do(grp->id) || 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);

    ECDSA_RS_ENTER(sig);

#        if defined(MBEDTLS_ECP_RESTARTABLE)
    if (rs_ctx != NULL && rs_ctx->sig != NULL) {
        /* redirect to our context */
        p_sign_tries = &rs_ctx->sig->sign_tries;
        p_key_tries = &rs_ctx->sig->key_tries;
        pk = &rs_ctx->sig->k;
        pr = &rs_ctx->sig->r;

        /* jump to current step */
        if (rs_ctx->sig->state == ecdsa_sig_mul)
            goto mul;
        if (rs_ctx->sig->state == ecdsa_sig_modn)
            goto modn;
    }
#        endif /* MBEDTLS_ECP_RESTARTABLE */

    *p_sign_tries = 0;
    do {
        if ((*p_sign_tries)++ > 10) {
            ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
            goto cleanup;
        }

        /*
         * Steps 1-3: generate a suitable ephemeral keypair
         * and set r = xR mod n
         */
        *p_key_tries = 0;
        do {
            if ((*p_key_tries)++ > 10) {
                ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
                goto cleanup;
            }

            MBEDTLS_MPI_CHK(mbedtls_ecp_gen_privkey(grp, pk, f_rng, p_rng));

#        if defined(MBEDTLS_ECP_RESTARTABLE)
            if (rs_ctx != NULL && rs_ctx->sig != NULL)
                rs_ctx->sig->state = ecdsa_sig_mul;

mul:
#        endif
            MBEDTLS_MPI_CHK(mbedtls_ecp_mul_restartable(
                grp, &R, pk, &grp->G, f_rng_blind, p_rng_blind, ECDSA_RS_ECP));
            MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(pr, &R.X, &grp->N));
        } while (mbedtls_mpi_cmp_int(pr, 0) == 0);

#        if defined(MBEDTLS_ECP_RESTARTABLE)
        if (rs_ctx != NULL && rs_ctx->sig != NULL)
            rs_ctx->sig->state = ecdsa_sig_modn;

modn:
#        endif
        /*
         * Accounting for everything up to the end of the loop
         * (step 6, but checking now avoids saving e and t)
         */
        ECDSA_BUDGET(MBEDTLS_ECP_OPS_INV + 4);

        /*
         * 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.
         */
        MBEDTLS_MPI_CHK(
            mbedtls_ecp_gen_privkey(grp, &t, f_rng_blind, p_rng_blind));

        /*
         * Step 6: compute s = (e + r * d) / k = t (e + rd) / (kt) mod n
         */
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(s, pr, 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(pk, pk, &t));
        MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(pk, pk, &grp->N));
        MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(s, pk, &grp->N));
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(s, s, &e));
        MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(s, s, &grp->N));
    } while (mbedtls_mpi_cmp_int(s, 0) == 0);

#        if defined(MBEDTLS_ECP_RESTARTABLE)
    if (rs_ctx != NULL && rs_ctx->sig != NULL)
        mbedtls_mpi_copy(r, pr);
#        endif

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

    ECDSA_RS_LEAVE(sig);

    return ret;
}

int mbedtls_ecdsa_can_do(mbedtls_ecp_group_id gid)
{
    switch (gid) {
#        ifdef MBEDTLS_ECP_DP_CURVE25519_ENABLED
        case MBEDTLS_ECP_DP_CURVE25519:
            return 0;
#        endif
#        ifdef MBEDTLS_ECP_DP_CURVE448_ENABLED
        case MBEDTLS_ECP_DP_CURVE448:
            return 0;
#        endif
        default:
            return 1;
    }
}

/*
 * Compute ECDSA signature of a hashed 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)
{
    ECDSA_VALIDATE_RET(grp != NULL);
    ECDSA_VALIDATE_RET(r != NULL);
    ECDSA_VALIDATE_RET(s != NULL);
    ECDSA_VALIDATE_RET(d != NULL);
    ECDSA_VALIDATE_RET(f_rng != NULL);
    ECDSA_VALIDATE_RET(buf != NULL || blen == 0);

    /* Use the same RNG for both blinding and ephemeral key generation */
    return (ecdsa_sign_restartable(grp, r, s, d, buf, blen, f_rng, p_rng, f_rng,
                                   p_rng, NULL));
}
#    endif /* !MBEDTLS_ECDSA_SIGN_ALT */

#    if defined(MBEDTLS_ECDSA_DETERMINISTIC)
/*
 * Deterministic signature wrapper
 *
 * note:    The f_rng_blind parameter must not be NULL.
 *
 */
static int
ecdsa_sign_det_restartable(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 (*f_rng_blind)(void *, unsigned char *, size_t),
                           void *p_rng_blind,
                           mbedtls_ecdsa_restart_ctx *rs_ctx)
{
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
    mbedtls_hmac_drbg_context rng_ctx;
    mbedtls_hmac_drbg_context *p_rng = &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);

    ECDSA_RS_ENTER(det);

#        if defined(MBEDTLS_ECP_RESTARTABLE)
    if (rs_ctx != NULL && rs_ctx->det != NULL) {
        /* redirect to our context */
        p_rng = &rs_ctx->det->rng_ctx;

        /* jump to current step */
        if (rs_ctx->det->state == ecdsa_det_sign)
            goto sign;
    }
#        endif /* MBEDTLS_ECP_RESTARTABLE */

    /* 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(p_rng, md_info, data, 2 * grp_len);

#        if defined(MBEDTLS_ECP_RESTARTABLE)
    if (rs_ctx != NULL && rs_ctx->det != NULL)
        rs_ctx->det->state = ecdsa_det_sign;

sign:
#        endif
#        if defined(MBEDTLS_ECDSA_SIGN_ALT)
    (void)f_rng_blind;
    (void)p_rng_blind;
    ret = mbedtls_ecdsa_sign(grp, r, s, d, buf, blen, mbedtls_hmac_drbg_random,
                             p_rng);
#        else
    ret = ecdsa_sign_restartable(grp, r, s, d, buf, blen,
                                 mbedtls_hmac_drbg_random, p_rng, f_rng_blind,
                                 p_rng_blind, rs_ctx);
#        endif /* MBEDTLS_ECDSA_SIGN_ALT */

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

    ECDSA_RS_LEAVE(det);

    return ret;
}

/*
 * Deterministic signature wrapper
 */
int mbedtls_ecdsa_sign_det_ext(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 (*f_rng_blind)(void *,
                                                  unsigned char *,
                                                  size_t),
                               void *p_rng_blind)
{
    ECDSA_VALIDATE_RET(grp != NULL);
    ECDSA_VALIDATE_RET(r != NULL);
    ECDSA_VALIDATE_RET(s != NULL);
    ECDSA_VALIDATE_RET(d != NULL);
    ECDSA_VALIDATE_RET(buf != NULL || blen == 0);
    ECDSA_VALIDATE_RET(f_rng_blind != NULL);

    return (ecdsa_sign_det_restartable(grp, r, s, d, buf, blen, md_alg,
                                       f_rng_blind, p_rng_blind, NULL));
}
#    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)
 */
static int ecdsa_verify_restartable(mbedtls_ecp_group *grp,
                                    const unsigned char *buf,
                                    size_t blen,
                                    const mbedtls_ecp_point *Q,
                                    const mbedtls_mpi *r,
                                    const mbedtls_mpi *s,
                                    mbedtls_ecdsa_restart_ctx *rs_ctx)
{
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
    mbedtls_mpi e, s_inv, u1, u2;
    mbedtls_ecp_point R;
    mbedtls_mpi *pu1 = &u1, *pu2 = &u2;

    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 (!mbedtls_ecdsa_can_do(grp->id) || grp->N.p == NULL)
        return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;

    ECDSA_RS_ENTER(ver);

#        if defined(MBEDTLS_ECP_RESTARTABLE)
    if (rs_ctx != NULL && rs_ctx->ver != NULL) {
        /* redirect to our context */
        pu1 = &rs_ctx->ver->u1;
        pu2 = &rs_ctx->ver->u2;

        /* jump to current step */
        if (rs_ctx->ver->state == ecdsa_ver_muladd)
            goto muladd;
    }
#        endif /* MBEDTLS_ECP_RESTARTABLE */

    /*
     * 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;
    }

    /*
     * 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
     */
    ECDSA_BUDGET(MBEDTLS_ECP_OPS_CHK + MBEDTLS_ECP_OPS_INV + 2);

    MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&s_inv, s, &grp->N));

    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(pu1, &e, &s_inv));
    MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(pu1, pu1, &grp->N));

    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(pu2, r, &s_inv));
    MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(pu2, pu2, &grp->N));

#        if defined(MBEDTLS_ECP_RESTARTABLE)
    if (rs_ctx != NULL && rs_ctx->ver != NULL)
        rs_ctx->ver->state = ecdsa_ver_muladd;

muladd:
#        endif
    /*
     * Step 5: R = u1 G + u2 Q
     */
    MBEDTLS_MPI_CHK(mbedtls_ecp_muladd_restartable(grp, &R, pu1, &grp->G, pu2,
                                                   Q, ECDSA_RS_ECP));

    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);

    ECDSA_RS_LEAVE(ver);

    return ret;
}

/*
 * Verify ECDSA signature of hashed 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)
{
    ECDSA_VALIDATE_RET(grp != NULL);
    ECDSA_VALIDATE_RET(Q != NULL);
    ECDSA_VALIDATE_RET(r != NULL);
    ECDSA_VALIDATE_RET(s != NULL);
    ECDSA_VALIDATE_RET(buf != NULL || blen == 0);

    return ecdsa_verify_restartable(grp, buf, blen, Q, r, s, NULL);
}
#    endif /* !MBEDTLS_ECDSA_VERIFY_ALT */

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

    if (len > sig_size)
        return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;

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

    return 0;
}

/*
 * Compute and write signature
 */
int mbedtls_ecdsa_write_signature_restartable(mbedtls_ecdsa_context *ctx,
                                              mbedtls_md_type_t md_alg,
                                              const unsigned char *hash,
                                              size_t hlen,
                                              unsigned char *sig,
                                              size_t sig_size,
                                              size_t *slen,
                                              int (*f_rng)(void *,
                                                           unsigned char *,
                                                           size_t),
                                              void *p_rng,
                                              mbedtls_ecdsa_restart_ctx *rs_ctx)
{
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
    mbedtls_mpi r, s;
    ECDSA_VALIDATE_RET(ctx != NULL);
    ECDSA_VALIDATE_RET(hash != NULL);
    ECDSA_VALIDATE_RET(sig != NULL);
    ECDSA_VALIDATE_RET(slen != NULL);

    if (f_rng == NULL)
        return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;

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

#    if defined(MBEDTLS_ECDSA_DETERMINISTIC)
    MBEDTLS_MPI_CHK(ecdsa_sign_det_restartable(
        &ctx->grp, &r, &s, &ctx->d, hash, hlen, md_alg, f_rng, p_rng, rs_ctx));
#    else
    (void)md_alg;

#        if defined(MBEDTLS_ECDSA_SIGN_ALT)
    (void)rs_ctx;

    MBEDTLS_MPI_CHK(mbedtls_ecdsa_sign(&ctx->grp, &r, &s, &ctx->d, hash, hlen,
                                       f_rng, p_rng));
#        else
    /* Use the same RNG for both blinding and ephemeral key generation */
    MBEDTLS_MPI_CHK(ecdsa_sign_restartable(&ctx->grp, &r, &s, &ctx->d, hash,
                                           hlen, f_rng, p_rng, f_rng, p_rng,
                                           rs_ctx));
#        endif /* MBEDTLS_ECDSA_SIGN_ALT */
#    endif /* MBEDTLS_ECDSA_DETERMINISTIC */

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

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

    return ret;
}

/*
 * 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 sig_size,
                                  size_t *slen,
                                  int (*f_rng)(void *, unsigned char *, size_t),
                                  void *p_rng)
{
    ECDSA_VALIDATE_RET(ctx != NULL);
    ECDSA_VALIDATE_RET(hash != NULL);
    ECDSA_VALIDATE_RET(sig != NULL);
    ECDSA_VALIDATE_RET(slen != NULL);
    return (mbedtls_ecdsa_write_signature_restartable(
        ctx, md_alg, hash, hlen, sig, sig_size, slen, f_rng, p_rng, NULL));
}

/*
 * 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)
{
    ECDSA_VALIDATE_RET(ctx != NULL);
    ECDSA_VALIDATE_RET(hash != NULL);
    ECDSA_VALIDATE_RET(sig != NULL);
    return (mbedtls_ecdsa_read_signature_restartable(ctx, hash, hlen, sig, slen,
                                                     NULL));
}

/*
 * Restartable read and check signature
 */
int mbedtls_ecdsa_read_signature_restartable(mbedtls_ecdsa_context *ctx,
                                             const unsigned char *hash,
                                             size_t hlen,
                                             const unsigned char *sig,
                                             size_t slen,
                                             mbedtls_ecdsa_restart_ctx *rs_ctx)
{
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
    unsigned char *p = (unsigned char *)sig;
    const unsigned char *end = sig + slen;
    size_t len;
    mbedtls_mpi r, s;
    ECDSA_VALIDATE_RET(ctx != NULL);
    ECDSA_VALIDATE_RET(hash != NULL);
    ECDSA_VALIDATE_RET(sig != NULL);

    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_ERROR_ADD(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 defined(MBEDTLS_ECDSA_VERIFY_ALT)
    (void)rs_ctx;

    if ((ret = mbedtls_ecdsa_verify(&ctx->grp, hash, hlen, &ctx->Q, &r, &s)) !=
        0)
        goto cleanup;
#    else
    if ((ret = ecdsa_verify_restartable(&ctx->grp, hash, hlen, &ctx->Q, &r, &s,
                                        rs_ctx)) != 0)
        goto cleanup;
#    endif /* MBEDTLS_ECDSA_VERIFY_ALT */

    /* 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)
{
    int ret = 0;
    ECDSA_VALIDATE_RET(ctx != NULL);
    ECDSA_VALIDATE_RET(f_rng != NULL);

    ret = mbedtls_ecp_group_load(&ctx->grp, gid);
    if (ret != 0)
        return ret;

    return (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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
    ECDSA_VALIDATE_RET(ctx != NULL);
    ECDSA_VALIDATE_RET(key != NULL);

    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)
{
    ECDSA_VALIDATE(ctx != NULL);

    mbedtls_ecp_keypair_init(ctx);
}

/*
 * Free context
 */
void mbedtls_ecdsa_free(mbedtls_ecdsa_context *ctx)
{
    if (ctx == NULL)
        return;

    mbedtls_ecp_keypair_free(ctx);
}

#    if defined(MBEDTLS_ECP_RESTARTABLE)
/*
 * Initialize a restart context
 */
void mbedtls_ecdsa_restart_init(mbedtls_ecdsa_restart_ctx *ctx)
{
    ECDSA_VALIDATE(ctx != NULL);

    mbedtls_ecp_restart_init(&ctx->ecp);

    ctx->ver = NULL;
    ctx->sig = NULL;
#        if defined(MBEDTLS_ECDSA_DETERMINISTIC)
    ctx->det = NULL;
#        endif
}

/*
 * Free the components of a restart context
 */
void mbedtls_ecdsa_restart_free(mbedtls_ecdsa_restart_ctx *ctx)
{
    if (ctx == NULL)
        return;

    mbedtls_ecp_restart_free(&ctx->ecp);

    ecdsa_restart_ver_free(ctx->ver);
    mbedtls_free(ctx->ver);
    ctx->ver = NULL;

    ecdsa_restart_sig_free(ctx->sig);
    mbedtls_free(ctx->sig);
    ctx->sig = NULL;

#        if defined(MBEDTLS_ECDSA_DETERMINISTIC)
    ecdsa_restart_det_free(ctx->det);
    mbedtls_free(ctx->det);
    ctx->det = NULL;
#        endif
}
#    endif /* MBEDTLS_ECP_RESTARTABLE */

#endif /* MBEDTLS_ECDSA_C */