decaf_error_t decaf_ed448_verify (
    const uint8_t signature[DECAF_EDDSA_448_SIGNATURE_BYTES],
    const uint8_t pubkey[DECAF_EDDSA_448_PUBLIC_BYTES],
    const uint8_t *message,
    size_t message_len,
    uint8_t prehashed,
    const uint8_t *context,
    uint8_t context_len
) {
    curve448_point_t pk_point, r_point;
    decaf_error_t error = curve448_point_decode_like_eddsa_and_mul_by_ratio(pk_point,pubkey);
    curve448_scalar_t challenge_scalar;
    curve448_scalar_t response_scalar;
    unsigned int c;
    if (DECAF_SUCCESS != error) { return error; }
    error = curve448_point_decode_like_eddsa_and_mul_by_ratio(r_point,signature);
    if (DECAF_SUCCESS != error) { return error; }
    {
        EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
        uint8_t challenge[2*DECAF_EDDSA_448_PRIVATE_BYTES];
        if (hashctx == NULL
                || !hash_init_with_dom(hashctx, prehashed, 0, context,
                                       context_len)
                || !EVP_DigestUpdate(hashctx, signature,
                                     DECAF_EDDSA_448_PUBLIC_BYTES)
                || !EVP_DigestUpdate(hashctx, pubkey,
                                     DECAF_EDDSA_448_PUBLIC_BYTES)
                || !EVP_DigestUpdate(hashctx, message, message_len)
                || !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge))) {
            EVP_MD_CTX_free(hashctx);
            return DECAF_FAILURE;
        }
        EVP_MD_CTX_free(hashctx);
        curve448_scalar_decode_long(challenge_scalar,challenge,sizeof(challenge));
        OPENSSL_cleanse(challenge,sizeof(challenge));
    }
    curve448_scalar_sub(challenge_scalar, curve448_scalar_zero, challenge_scalar);
    curve448_scalar_decode_long(
        response_scalar,
        &signature[DECAF_EDDSA_448_PUBLIC_BYTES],
        DECAF_EDDSA_448_PRIVATE_BYTES
    );
    for (c=1; c<DECAF_448_EDDSA_DECODE_RATIO; c<<=1) {
        curve448_scalar_add(response_scalar,response_scalar,response_scalar);
    }
    curve448_base_double_scalarmul_non_secret(
        pk_point,
        response_scalar,
        pk_point,
        challenge_scalar
    );
    return decaf_succeed_if(curve448_point_eq(pk_point,r_point));
}
['decaf_error_t decaf_ed448_verify (\n    const uint8_t signature[DECAF_EDDSA_448_SIGNATURE_BYTES],\n    const uint8_t pubkey[DECAF_EDDSA_448_PUBLIC_BYTES],\n    const uint8_t *message,\n    size_t message_len,\n    uint8_t prehashed,\n    const uint8_t *context,\n    uint8_t context_len\n) {\n    curve448_point_t pk_point, r_point;\n    decaf_error_t error = curve448_point_decode_like_eddsa_and_mul_by_ratio(pk_point,pubkey);\n    curve448_scalar_t challenge_scalar;\n    curve448_scalar_t response_scalar;\n    unsigned int c;\n    if (DECAF_SUCCESS != error) { return error; }\n    error = curve448_point_decode_like_eddsa_and_mul_by_ratio(r_point,signature);\n    if (DECAF_SUCCESS != error) { return error; }\n    {\n        EVP_MD_CTX *hashctx = EVP_MD_CTX_new();\n        uint8_t challenge[2*DECAF_EDDSA_448_PRIVATE_BYTES];\n        if (hashctx == NULL\n                || !hash_init_with_dom(hashctx, prehashed, 0, context,\n                                       context_len)\n                || !EVP_DigestUpdate(hashctx, signature,\n                                     DECAF_EDDSA_448_PUBLIC_BYTES)\n                || !EVP_DigestUpdate(hashctx, pubkey,\n                                     DECAF_EDDSA_448_PUBLIC_BYTES)\n                || !EVP_DigestUpdate(hashctx, message, message_len)\n                || !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge))) {\n            EVP_MD_CTX_free(hashctx);\n            return DECAF_FAILURE;\n        }\n        EVP_MD_CTX_free(hashctx);\n        curve448_scalar_decode_long(challenge_scalar,challenge,sizeof(challenge));\n        OPENSSL_cleanse(challenge,sizeof(challenge));\n    }\n    curve448_scalar_sub(challenge_scalar, curve448_scalar_zero, challenge_scalar);\n    curve448_scalar_decode_long(\n        response_scalar,\n        &signature[DECAF_EDDSA_448_PUBLIC_BYTES],\n        DECAF_EDDSA_448_PRIVATE_BYTES\n    );\n    for (c=1; c<DECAF_448_EDDSA_DECODE_RATIO; c<<=1) {\n        curve448_scalar_add(response_scalar,response_scalar,response_scalar);\n    }\n    curve448_base_double_scalarmul_non_secret(\n        pk_point,\n        response_scalar,\n        pk_point,\n        challenge_scalar\n    );\n    return decaf_succeed_if(curve448_point_eq(pk_point,r_point));\n}', 'EVP_MD_CTX *EVP_MD_CTX_new(void)\n{\n    return OPENSSL_zalloc(sizeof(EVP_MD_CTX));\n}', 'void *CRYPTO_zalloc(size_t num, const char *file, int line)\n{\n    void *ret = CRYPTO_malloc(num, file, line);\n    FAILTEST();\n    if (ret != NULL)\n        memset(ret, 0, num);\n    return ret;\n}', 'void *CRYPTO_malloc(size_t num, const char *file, int line)\n{\n    void *ret = NULL;\n    INCREMENT(malloc_count);\n    if (malloc_impl != NULL && malloc_impl != CRYPTO_malloc)\n        return malloc_impl(num, file, line);\n    if (num == 0)\n        return NULL;\n    FAILTEST();\n    allow_customize = 0;\n#ifndef OPENSSL_NO_CRYPTO_MDEBUG\n    if (call_malloc_debug) {\n        CRYPTO_mem_debug_malloc(NULL, num, 0, file, line);\n        ret = malloc(num);\n        CRYPTO_mem_debug_malloc(ret, num, 1, file, line);\n    } else {\n        ret = malloc(num);\n    }\n#else\n    (void)(file); (void)(line);\n    ret = malloc(num);\n#endif\n    return ret;\n}', 'static decaf_error_t hash_init_with_dom(\n    EVP_MD_CTX *hashctx,\n    uint8_t prehashed,\n    uint8_t for_prehash,\n    const uint8_t *context,\n    size_t context_len\n) {\n    const char *dom_s = "SigEd448";\n    uint8_t dom[2];\n    dom[0] = 2 + word_is_zero(prehashed) + word_is_zero(for_prehash);\n    dom[1] = (uint8_t)context_len;\n    if (context_len > UINT8_MAX)\n        return DECAF_FAILURE;\n#if NO_CONTEXT\n    if (context_len == 0 && context == DECAF_ED448_NO_CONTEXT) {\n        (void)prehashed;\n        (void)for_prehash;\n        (void)context;\n        (void)context_len;\n        return DECAF_SUCCESS;\n    }\n#endif\n    if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL)\n            || !EVP_DigestUpdate(hashctx, dom_s, strlen(dom_s))\n            || !EVP_DigestUpdate(hashctx, dom, sizeof(dom))\n            || !EVP_DigestUpdate(hashctx, context, context_len))\n        return DECAF_FAILURE;\n    return DECAF_SUCCESS;\n}', 'static __inline__ __attribute((always_inline,unused))\nuint32_t word_is_zero(uint32_t a) {\n    return (((uint64_t)a)-1)>>32;\n}', 'void EVP_MD_CTX_free(EVP_MD_CTX *ctx)\n{\n    EVP_MD_CTX_reset(ctx);\n    OPENSSL_free(ctx);\n}', 'void CRYPTO_free(void *str, const char *file, int line)\n{\n    INCREMENT(free_count);\n    if (free_impl != NULL && free_impl != &CRYPTO_free) {\n        free_impl(str, file, line);\n        return;\n    }\n#ifndef OPENSSL_NO_CRYPTO_MDEBUG\n    if (call_malloc_debug) {\n        CRYPTO_mem_debug_free(str, 0, file, line);\n        free(str);\n        CRYPTO_mem_debug_free(str, 1, file, line);\n    } else {\n        free(str);\n    }\n#else\n    free(str);\n#endif\n}']