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 https://www.secg.org/sec1-v2.pdf
 */

#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

#include "mbedtls/platform.h"

#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)     || \
    !defined(MBEDTLS_ECDSA_VERIFY_ALT)

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;
    }
}

#endif /* !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_CHK(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;
}

/*
 * 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
 */
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_MPI_CHK(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
    if (f_rng_blind != NULL) {
        ret = ecdsa_sign_restartable(grp, r, s, d, buf, blen,
                                     mbedtls_hmac_drbg_random, p_rng,
                                     f_rng_blind, p_rng_blind, rs_ctx);
    } else {
        mbedtls_hmac_drbg_context *p_rng_blind_det;

#if !defined(MBEDTLS_ECP_RESTARTABLE)
        /*
         * To avoid reusing rng_ctx and risking incorrect behavior we seed a
         * second HMAC-DRBG with the same seed. We also apply a label to avoid
         * reusing the bits of the ephemeral key for blinding and eliminate the
         * risk that they leak this way.
         */
        const char *blind_label = "BLINDING CONTEXT";
        mbedtls_hmac_drbg_context rng_ctx_blind;

        mbedtls_hmac_drbg_init(&rng_ctx_blind);
        p_rng_blind_det = &rng_ctx_blind;
        mbedtls_hmac_drbg_seed_buf(p_rng_blind_det, md_info,
                                   data, 2 * grp_len);
        ret = mbedtls_hmac_drbg_update_ret(p_rng_blind_det,
                                           (const unsigned char *) blind_label,
                                           strlen(blind_label));
        if (ret != 0) {
            mbedtls_hmac_drbg_free(&rng_ctx_blind);
            goto cleanup;
        }
#else
        /*
         * In the case of restartable computations we would either need to store
         * the second RNG in the restart context too or set it up at every
         * restart. The first option would penalize the correct application of
         * the function and the second would defeat the purpose of the
         * restartable feature.
         *
         * Therefore in this case we reuse the original RNG. This comes with the
         * price that the resulting signature might not be a valid deterministic
         * ECDSA signature with a very low probability (same magnitude as
         * successfully guessing the private key). However even then it is still
         * a valid ECDSA signature.
         */
        p_rng_blind_det = p_rng;
#endif /* MBEDTLS_ECP_RESTARTABLE */

        /*
         * Since the output of the RNGs is always the same for the same key and
         * message, this limits the efficiency of blinding and leaks information
         * through side channels. After mbedtls_ecdsa_sign_det() is removed NULL
         * won't be a valid value for f_rng_blind anymore. Therefore it should
         * be checked by the caller and this branch and check can be removed.
         */
        ret = ecdsa_sign_restartable(grp, r, s, d, buf, blen,
                                     mbedtls_hmac_drbg_random, p_rng,
                                     mbedtls_hmac_drbg_random, p_rng_blind_det,
                                     rs_ctx);

#if !defined(MBEDTLS_ECP_RESTARTABLE)
        mbedtls_hmac_drbg_free(&rng_ctx_blind);
#endif
    }
#endif /* MBEDTLS_ECDSA_SIGN_ALT */

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

    ECDSA_RS_LEAVE(det);

    return ret;
}

/*
 * Deterministic signature wrappers
 */

#if !defined(MBEDTLS_DEPRECATED_REMOVED)
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)
{
    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);

    return ecdsa_sign_det_restartable(grp, r, s, d, buf, blen, md_alg,
                                      NULL, NULL, NULL);
}
#endif /* MBEDTLS_DEPRECATED_REMOVED */

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 *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));

    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 *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);

    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, 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 *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, slen, f_rng, p_rng, NULL);
}

#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)
{
    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(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)
{
    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 */