/src/openssl111/crypto/ec/curve448/eddsa.c

Source (jump to first uncovered line)
/*
 * Copyright 2017-2020 The OpenSSL Project Authors. All Rights Reserved.
 * Copyright 2015-2016 Cryptography Research, Inc.
 *
 * Licensed under the OpenSSL license (the "License").  You may not use
 * this file except in compliance with the License.  You can obtain a copy
 * in the file LICENSE in the source distribution or at
 * https://www.openssl.org/source/license.html
 *
 * Originally written by Mike Hamburg
 */
#include <string.h>
#include <openssl/crypto.h>
#include <openssl/evp.h>
#include "curve448_local.h"
#include "word.h"
#include "ed448.h"
#include "internal/numbers.h"

#define COFACTOR 4

static c448_error_t oneshot_hash(uint8_t *out, size_t outlen,
                                 const uint8_t *in, size_t inlen)
{
    EVP_MD_CTX *hashctx = EVP_MD_CTX_new();

    if (hashctx == NULL)
        return C448_FAILURE;

    if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL)
            || !EVP_DigestUpdate(hashctx, in, inlen)
            || !EVP_DigestFinalXOF(hashctx, out, outlen)) {
        EVP_MD_CTX_free(hashctx);
        return C448_FAILURE;
    }

    EVP_MD_CTX_free(hashctx);
    return C448_SUCCESS;
}

static void clamp(uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES])
{
    secret_scalar_ser[0] &= -COFACTOR;
    secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 1] = 0;
    secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 2] |= 0x80;
}

static c448_error_t hash_init_with_dom(EVP_MD_CTX *hashctx, uint8_t prehashed,
                                       uint8_t for_prehash,
                                       const uint8_t *context,
                                       size_t context_len)
{
#ifdef CHARSET_EBCDIC
    const char dom_s[] = {0x53, 0x69, 0x67, 0x45,
                          0x64, 0x34, 0x34, 0x38, 0x00};
#else
    const char dom_s[] = "SigEd448";
#endif
    uint8_t dom[2];

    if (context_len > UINT8_MAX)
        return C448_FAILURE;

    dom[0] = (uint8_t)(2 - (prehashed == 0 ? 1 : 0)
                       - (for_prehash == 0 ? 1 : 0));
    dom[1] = (uint8_t)context_len;

    if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL)
            || !EVP_DigestUpdate(hashctx, dom_s, strlen(dom_s))
            || !EVP_DigestUpdate(hashctx, dom, sizeof(dom))
            || !EVP_DigestUpdate(hashctx, context, context_len))
        return C448_FAILURE;

    return C448_SUCCESS;
}

/* In this file because it uses the hash */
c448_error_t c448_ed448_convert_private_key_to_x448(
                            uint8_t x[X448_PRIVATE_BYTES],
                            const uint8_t ed [EDDSA_448_PRIVATE_BYTES])
{
    /* pass the private key through oneshot_hash function */
    /* and keep the first X448_PRIVATE_BYTES bytes */
    return oneshot_hash(x, X448_PRIVATE_BYTES, ed,
                        EDDSA_448_PRIVATE_BYTES);
}

c448_error_t c448_ed448_derive_public_key(
                        uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
                        const uint8_t privkey[EDDSA_448_PRIVATE_BYTES])
{
    /* only this much used for keygen */
    uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES];
    curve448_scalar_t secret_scalar;
    unsigned int c;
    curve448_point_t p;

    if (!oneshot_hash(secret_scalar_ser, sizeof(secret_scalar_ser), privkey,
                      EDDSA_448_PRIVATE_BYTES))
        return C448_FAILURE;

    clamp(secret_scalar_ser);

    curve448_scalar_decode_long(secret_scalar, secret_scalar_ser,
                                sizeof(secret_scalar_ser));

    /*
     * Since we are going to mul_by_cofactor during encoding, divide by it
     * here. However, the EdDSA base point is not the same as the decaf base
     * point if the sigma isogeny is in use: the EdDSA base point is on
     * Etwist_d/(1-d) and the decaf base point is on Etwist_d, and when
     * converted it effectively picks up a factor of 2 from the isogenies.  So
     * we might start at 2 instead of 1.
     */
    for (c = 1; c < C448_EDDSA_ENCODE_RATIO; c <<= 1)
        curve448_scalar_halve(secret_scalar, secret_scalar);

    curve448_precomputed_scalarmul(p, curve448_precomputed_base, secret_scalar);

    curve448_point_mul_by_ratio_and_encode_like_eddsa(pubkey, p);

    /* Cleanup */
    curve448_scalar_destroy(secret_scalar);
    curve448_point_destroy(p);
    OPENSSL_cleanse(secret_scalar_ser, sizeof(secret_scalar_ser));

    return C448_SUCCESS;
}

c448_error_t c448_ed448_sign(
                        uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
                        const uint8_t privkey[EDDSA_448_PRIVATE_BYTES],
                        const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
                        const uint8_t *message, size_t message_len,
                        uint8_t prehashed, const uint8_t *context,
                        size_t context_len)
{
    curve448_scalar_t secret_scalar;
    EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
    c448_error_t ret = C448_FAILURE;
    curve448_scalar_t nonce_scalar;
    uint8_t nonce_point[EDDSA_448_PUBLIC_BYTES] = { 0 };
    unsigned int c;
    curve448_scalar_t challenge_scalar;

    if (hashctx == NULL)
        return C448_FAILURE;

    {
        /*
         * Schedule the secret key, First EDDSA_448_PRIVATE_BYTES is serialised
         * secret scalar,next EDDSA_448_PRIVATE_BYTES bytes is the seed.
         */
        uint8_t expanded[EDDSA_448_PRIVATE_BYTES * 2];

        if (!oneshot_hash(expanded, sizeof(expanded), privkey,
                          EDDSA_448_PRIVATE_BYTES))
            goto err;
        clamp(expanded);
        curve448_scalar_decode_long(secret_scalar, expanded,
                                    EDDSA_448_PRIVATE_BYTES);

        /* Hash to create the nonce */
        if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len)
                || !EVP_DigestUpdate(hashctx,
                                     expanded + EDDSA_448_PRIVATE_BYTES,
                                     EDDSA_448_PRIVATE_BYTES)
                || !EVP_DigestUpdate(hashctx, message, message_len)) {
            OPENSSL_cleanse(expanded, sizeof(expanded));
            goto err;
        }
        OPENSSL_cleanse(expanded, sizeof(expanded));
    }

    /* Decode the nonce */
    {
        uint8_t nonce[2 * EDDSA_448_PRIVATE_BYTES];

        if (!EVP_DigestFinalXOF(hashctx, nonce, sizeof(nonce)))
            goto err;
        curve448_scalar_decode_long(nonce_scalar, nonce, sizeof(nonce));
        OPENSSL_cleanse(nonce, sizeof(nonce));
    }

    {
        /* Scalarmul to create the nonce-point */
        curve448_scalar_t nonce_scalar_2;
        curve448_point_t p;

        curve448_scalar_halve(nonce_scalar_2, nonce_scalar);
        for (c = 2; c < C448_EDDSA_ENCODE_RATIO; c <<= 1)
            curve448_scalar_halve(nonce_scalar_2, nonce_scalar_2);

        curve448_precomputed_scalarmul(p, curve448_precomputed_base,
                                       nonce_scalar_2);
        curve448_point_mul_by_ratio_and_encode_like_eddsa(nonce_point, p);
        curve448_point_destroy(p);
        curve448_scalar_destroy(nonce_scalar_2);
    }

    {
        uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];

        /* Compute the challenge */
        if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len)
                || !EVP_DigestUpdate(hashctx, nonce_point, sizeof(nonce_point))
                || !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES)
                || !EVP_DigestUpdate(hashctx, message, message_len)
                || !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge)))
            goto err;

        curve448_scalar_decode_long(challenge_scalar, challenge,
                                    sizeof(challenge));
        OPENSSL_cleanse(challenge, sizeof(challenge));
    }

    curve448_scalar_mul(challenge_scalar, challenge_scalar, secret_scalar);
    curve448_scalar_add(challenge_scalar, challenge_scalar, nonce_scalar);

    OPENSSL_cleanse(signature, EDDSA_448_SIGNATURE_BYTES);
    memcpy(signature, nonce_point, sizeof(nonce_point));
    curve448_scalar_encode(&signature[EDDSA_448_PUBLIC_BYTES],
                           challenge_scalar);

    curve448_scalar_destroy(secret_scalar);
    curve448_scalar_destroy(nonce_scalar);
    curve448_scalar_destroy(challenge_scalar);

    ret = C448_SUCCESS;
 err:
    EVP_MD_CTX_free(hashctx);
    return ret;
}

c448_error_t c448_ed448_sign_prehash(
                        uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
                        const uint8_t privkey[EDDSA_448_PRIVATE_BYTES],
                        const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
                        const uint8_t hash[64], const uint8_t *context,
                        size_t context_len)
{
    return c448_ed448_sign(signature, privkey, pubkey, hash, 64, 1, context,
                           context_len);
}

c448_error_t c448_ed448_verify(
                    const uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
                    const uint8_t pubkey[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;
    c448_error_t error;
    curve448_scalar_t challenge_scalar;
    curve448_scalar_t response_scalar;
    /* Order in little endian format */
    static const uint8_t order[] = {
        0xF3, 0x44, 0x58, 0xAB, 0x92, 0xC2, 0x78, 0x23, 0x55, 0x8F, 0xC5, 0x8D,
        0x72, 0xC2, 0x6C, 0x21, 0x90, 0x36, 0xD6, 0xAE, 0x49, 0xDB, 0x4E, 0xC4,
        0xE9, 0x23, 0xCA, 0x7C, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
        0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
        0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x3F, 0x00
    };
    int i;

    /*
     * Check that s (second 57 bytes of the sig) is less than the order. Both
     * s and the order are in little-endian format. This can be done in
     * variable time, since if this is not the case the signature if publicly
     * invalid.
     */
    for (i = EDDSA_448_PUBLIC_BYTES - 1; i >= 0; i--) {
        if (signature[i + EDDSA_448_PUBLIC_BYTES] > order[i])
            return C448_FAILURE;
        if (signature[i + EDDSA_448_PUBLIC_BYTES] < order[i])
            break;
    }
    if (i < 0)
        return C448_FAILURE;

    error =
        curve448_point_decode_like_eddsa_and_mul_by_ratio(pk_point, pubkey);

    if (C448_SUCCESS != error)
        return error;

    error =
        curve448_point_decode_like_eddsa_and_mul_by_ratio(r_point, signature);
    if (C448_SUCCESS != error)
        return error;

    {
        /* Compute the challenge */
        EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
        uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];

        if (hashctx == NULL
                || !hash_init_with_dom(hashctx, prehashed, 0, context,
                                       context_len)
                || !EVP_DigestUpdate(hashctx, signature, EDDSA_448_PUBLIC_BYTES)
                || !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES)
                || !EVP_DigestUpdate(hashctx, message, message_len)
                || !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge))) {
            EVP_MD_CTX_free(hashctx);
            return C448_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[EDDSA_448_PUBLIC_BYTES],
                                EDDSA_448_PRIVATE_BYTES);

    /* pk_point = -c(x(P)) + (cx + k)G = kG */
    curve448_base_double_scalarmul_non_secret(pk_point,
                                              response_scalar,
                                              pk_point, challenge_scalar);
    return c448_succeed_if(curve448_point_eq(pk_point, r_point));
}

c448_error_t c448_ed448_verify_prehash(
                    const uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
                    const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
                    const uint8_t hash[64], const uint8_t *context,
                    uint8_t context_len)
{
    return c448_ed448_verify(signature, pubkey, hash, 64, 1, context,
                             context_len);
}

int ED448_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
               const uint8_t public_key[57], const uint8_t private_key[57],
               const uint8_t *context, size_t context_len)
{
    return c448_ed448_sign(out_sig, private_key, public_key, message,
                           message_len, 0, context, context_len)
        == C448_SUCCESS;
}

int ED448_verify(const uint8_t *message, size_t message_len,
                 const uint8_t signature[114], const uint8_t public_key[57],
                 const uint8_t *context, size_t context_len)
{
    return c448_ed448_verify(signature, public_key, message, message_len, 0,
                             context, (uint8_t)context_len) == C448_SUCCESS;
}

int ED448ph_sign(uint8_t *out_sig, const uint8_t hash[64],
                 const uint8_t public_key[57], const uint8_t private_key[57],
                 const uint8_t *context, size_t context_len)
{
    return c448_ed448_sign_prehash(out_sig, private_key, public_key, hash,
                                   context, context_len) == C448_SUCCESS;

}

int ED448ph_verify(const uint8_t hash[64], const uint8_t signature[114],
                   const uint8_t public_key[57], const uint8_t *context,
                   size_t context_len)
{
    return c448_ed448_verify_prehash(signature, public_key, hash, context,
                                     (uint8_t)context_len) == C448_SUCCESS;
}

int ED448_public_from_private(uint8_t out_public_key[57],
                              const uint8_t private_key[57])
{
    return c448_ed448_derive_public_key(out_public_key, private_key)
        == C448_SUCCESS;
}

Coverage Report

Created: 2023-06-08 06:41

Line	Count	Source (jump to first uncovered line)
1		/*
2		* Copyright 2017-2020 The OpenSSL Project Authors. All Rights Reserved.
3		* Copyright 2015-2016 Cryptography Research, Inc.
4		*
5		* Licensed under the OpenSSL license (the "License"). You may not use
6		* this file except in compliance with the License. You can obtain a copy
7		* in the file LICENSE in the source distribution or at
8		* https://www.openssl.org/source/license.html
9		*
10		* Originally written by Mike Hamburg
11		*/
12		#include <string.h>
13		#include <openssl/crypto.h>
14		#include <openssl/evp.h>
15		#include "curve448_local.h"
16		#include "word.h"
17		#include "ed448.h"
18		#include "internal/numbers.h"
19
20	12	#define COFACTOR 4
21
22		static c448_error_t oneshot_hash(uint8_t *out, size_t outlen,
23		const uint8_t *in, size_t inlen)
24	12	{
25	12	EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
26
27	12	if (hashctx == NULL)
28	0	return C448_FAILURE;
29
30	12	if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL)
31	12	\|\| !EVP_DigestUpdate(hashctx, in, inlen)
32	12	\|\| !EVP_DigestFinalXOF(hashctx, out, outlen)) {
33	0	EVP_MD_CTX_free(hashctx);
34	0	return C448_FAILURE;
35	0	}
36
37	12	EVP_MD_CTX_free(hashctx);
38	12	return C448_SUCCESS;
39	12	}
40
41		static void clamp(uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES])
42	12	{
43	12	secret_scalar_ser[0] &= -COFACTOR;
44	12	secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 1] = 0;
45	12	secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 2] \|= 0x80;
46	12	}
47
48		static c448_error_t hash_init_with_dom(EVP_MD_CTX *hashctx, uint8_t prehashed,
49		uint8_t for_prehash,
50		const uint8_t *context,
51		size_t context_len)
52	0	{
53		#ifdef CHARSET_EBCDIC
54		const char dom_s[] = {0x53, 0x69, 0x67, 0x45,
55		0x64, 0x34, 0x34, 0x38, 0x00};
56		#else
57	0	const char dom_s[] = "SigEd448";
58	0	#endif
59	0	uint8_t dom[2];
60
61	0	if (context_len > UINT8_MAX)
62	0	return C448_FAILURE;
63
64	0	dom[0] = (uint8_t)(2 - (prehashed == 0 ? 1 : 0)
65	0	- (for_prehash == 0 ? 1 : 0));
66	0	dom[1] = (uint8_t)context_len;
67
68	0	if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL)
69	0	\|\| !EVP_DigestUpdate(hashctx, dom_s, strlen(dom_s))
70	0	\|\| !EVP_DigestUpdate(hashctx, dom, sizeof(dom))
71	0	\|\| !EVP_DigestUpdate(hashctx, context, context_len))
72	0	return C448_FAILURE;
73
74	0	return C448_SUCCESS;
75	0	}
76
77		/* In this file because it uses the hash */
78		c448_error_t c448_ed448_convert_private_key_to_x448(
79		uint8_t x[X448_PRIVATE_BYTES],
80		const uint8_t ed [EDDSA_448_PRIVATE_BYTES])
81	0	{
82		/* pass the private key through oneshot_hash function */
83		/* and keep the first X448_PRIVATE_BYTES bytes */
84	0	return oneshot_hash(x, X448_PRIVATE_BYTES, ed,
85	0	EDDSA_448_PRIVATE_BYTES);
86	0	}
87
88		c448_error_t c448_ed448_derive_public_key(
89		uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
90		const uint8_t privkey[EDDSA_448_PRIVATE_BYTES])
91	12	{
92		/* only this much used for keygen */
93	12	uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES];
94	12	curve448_scalar_t secret_scalar;
95	12	unsigned int c;
96	12	curve448_point_t p;
97
98	12	if (!oneshot_hash(secret_scalar_ser, sizeof(secret_scalar_ser), privkey,
99	12	EDDSA_448_PRIVATE_BYTES))
100	0	return C448_FAILURE;
101
102	12	clamp(secret_scalar_ser);
103
104	12	curve448_scalar_decode_long(secret_scalar, secret_scalar_ser,
105	12	sizeof(secret_scalar_ser));
106
107		/*
108		* Since we are going to mul_by_cofactor during encoding, divide by it
109		* here. However, the EdDSA base point is not the same as the decaf base
110		* point if the sigma isogeny is in use: the EdDSA base point is on
111		* Etwist_d/(1-d) and the decaf base point is on Etwist_d, and when
112		* converted it effectively picks up a factor of 2 from the isogenies. So
113		* we might start at 2 instead of 1.
114		*/
115	36	for (c = 1; c < C448_EDDSA_ENCODE_RATIO; c <<= 1)
116	24	curve448_scalar_halve(secret_scalar, secret_scalar);
117
118	12	curve448_precomputed_scalarmul(p, curve448_precomputed_base, secret_scalar);
119
120	12	curve448_point_mul_by_ratio_and_encode_like_eddsa(pubkey, p);
121
122		/* Cleanup */
123	12	curve448_scalar_destroy(secret_scalar);
124	12	curve448_point_destroy(p);
125	12	OPENSSL_cleanse(secret_scalar_ser, sizeof(secret_scalar_ser));
126
127	12	return C448_SUCCESS;
128	12	}
129
130		c448_error_t c448_ed448_sign(
131		uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
132		const uint8_t privkey[EDDSA_448_PRIVATE_BYTES],
133		const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
134		const uint8_t *message, size_t message_len,
135		uint8_t prehashed, const uint8_t *context,
136		size_t context_len)
137	0	{
138	0	curve448_scalar_t secret_scalar;
139	0	EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
140	0	c448_error_t ret = C448_FAILURE;
141	0	curve448_scalar_t nonce_scalar;
142	0	uint8_t nonce_point[EDDSA_448_PUBLIC_BYTES] = { 0 };
143	0	unsigned int c;
144	0	curve448_scalar_t challenge_scalar;
145
146	0	if (hashctx == NULL)
147	0	return C448_FAILURE;
148
149	0	{
150		/*
151		* Schedule the secret key, First EDDSA_448_PRIVATE_BYTES is serialised
152		* secret scalar,next EDDSA_448_PRIVATE_BYTES bytes is the seed.
153		*/
154	0	uint8_t expanded[EDDSA_448_PRIVATE_BYTES * 2];
155
156	0	if (!oneshot_hash(expanded, sizeof(expanded), privkey,
157	0	EDDSA_448_PRIVATE_BYTES))
158	0	goto err;
159	0	clamp(expanded);
160	0	curve448_scalar_decode_long(secret_scalar, expanded,
161	0	EDDSA_448_PRIVATE_BYTES);
162
163		/* Hash to create the nonce */
164	0	if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len)
165	0	\|\| !EVP_DigestUpdate(hashctx,
166	0	expanded + EDDSA_448_PRIVATE_BYTES,
167	0	EDDSA_448_PRIVATE_BYTES)
168	0	\|\| !EVP_DigestUpdate(hashctx, message, message_len)) {
169	0	OPENSSL_cleanse(expanded, sizeof(expanded));
170	0	goto err;
171	0	}
172	0	OPENSSL_cleanse(expanded, sizeof(expanded));
173	0	}
174
175		/* Decode the nonce */
176	0	{
177	0	uint8_t nonce[2 * EDDSA_448_PRIVATE_BYTES];
178
179	0	if (!EVP_DigestFinalXOF(hashctx, nonce, sizeof(nonce)))
180	0	goto err;
181	0	curve448_scalar_decode_long(nonce_scalar, nonce, sizeof(nonce));
182	0	OPENSSL_cleanse(nonce, sizeof(nonce));
183	0	}
184
185	0	{
186		/* Scalarmul to create the nonce-point */
187	0	curve448_scalar_t nonce_scalar_2;
188	0	curve448_point_t p;
189
190	0	curve448_scalar_halve(nonce_scalar_2, nonce_scalar);
191	0	for (c = 2; c < C448_EDDSA_ENCODE_RATIO; c <<= 1)
192	0	curve448_scalar_halve(nonce_scalar_2, nonce_scalar_2);
193
194	0	curve448_precomputed_scalarmul(p, curve448_precomputed_base,
195	0	nonce_scalar_2);
196	0	curve448_point_mul_by_ratio_and_encode_like_eddsa(nonce_point, p);
197	0	curve448_point_destroy(p);
198	0	curve448_scalar_destroy(nonce_scalar_2);
199	0	}
200
201	0	{
202	0	uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];
203
204		/* Compute the challenge */
205	0	if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len)
206	0	\|\| !EVP_DigestUpdate(hashctx, nonce_point, sizeof(nonce_point))
207	0	\|\| !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES)
208	0	\|\| !EVP_DigestUpdate(hashctx, message, message_len)
209	0	\|\| !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge)))
210	0	goto err;
211
212	0	curve448_scalar_decode_long(challenge_scalar, challenge,
213	0	sizeof(challenge));
214	0	OPENSSL_cleanse(challenge, sizeof(challenge));
215	0	}
216
217	0	curve448_scalar_mul(challenge_scalar, challenge_scalar, secret_scalar);
218	0	curve448_scalar_add(challenge_scalar, challenge_scalar, nonce_scalar);
219
220	0	OPENSSL_cleanse(signature, EDDSA_448_SIGNATURE_BYTES);
221	0	memcpy(signature, nonce_point, sizeof(nonce_point));
222	0	curve448_scalar_encode(&signature[EDDSA_448_PUBLIC_BYTES],
223	0	challenge_scalar);
224
225	0	curve448_scalar_destroy(secret_scalar);
226	0	curve448_scalar_destroy(nonce_scalar);
227	0	curve448_scalar_destroy(challenge_scalar);
228
229	0	ret = C448_SUCCESS;
230	0	err:
231	0	EVP_MD_CTX_free(hashctx);
232	0	return ret;
233	0	}
234
235		c448_error_t c448_ed448_sign_prehash(
236		uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
237		const uint8_t privkey[EDDSA_448_PRIVATE_BYTES],
238		const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
239		const uint8_t hash[64], const uint8_t *context,
240		size_t context_len)
241	0	{
242	0	return c448_ed448_sign(signature, privkey, pubkey, hash, 64, 1, context,
243	0	context_len);
244	0	}
245
246		c448_error_t c448_ed448_verify(
247		const uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
248		const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
249		const uint8_t *message, size_t message_len,
250		uint8_t prehashed, const uint8_t *context,
251		uint8_t context_len)
252	0	{
253	0	curve448_point_t pk_point, r_point;
254	0	c448_error_t error;
255	0	curve448_scalar_t challenge_scalar;
256	0	curve448_scalar_t response_scalar;
257		/* Order in little endian format */
258	0	static const uint8_t order[] = {
259	0	0xF3, 0x44, 0x58, 0xAB, 0x92, 0xC2, 0x78, 0x23, 0x55, 0x8F, 0xC5, 0x8D,
260	0	0x72, 0xC2, 0x6C, 0x21, 0x90, 0x36, 0xD6, 0xAE, 0x49, 0xDB, 0x4E, 0xC4,
261	0	0xE9, 0x23, 0xCA, 0x7C, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
262	0	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
263	0	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x3F, 0x00
264	0	};
265	0	int i;
266
267		/*
268		* Check that s (second 57 bytes of the sig) is less than the order. Both
269		* s and the order are in little-endian format. This can be done in
270		* variable time, since if this is not the case the signature if publicly
271		* invalid.
272		*/
273	0	for (i = EDDSA_448_PUBLIC_BYTES - 1; i >= 0; i--) {
274	0	if (signature[i + EDDSA_448_PUBLIC_BYTES] > order[i])
275	0	return C448_FAILURE;
276	0	if (signature[i + EDDSA_448_PUBLIC_BYTES] < order[i])
277	0	break;
278	0	}
279	0	if (i < 0)
280	0	return C448_FAILURE;
281
282	0	error =
283	0	curve448_point_decode_like_eddsa_and_mul_by_ratio(pk_point, pubkey);
284
285	0	if (C448_SUCCESS != error)
286	0	return error;
287
288	0	error =
289	0	curve448_point_decode_like_eddsa_and_mul_by_ratio(r_point, signature);
290	0	if (C448_SUCCESS != error)
291	0	return error;
292
293	0	{
294		/* Compute the challenge */
295	0	EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
296	0	uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];
297
298	0	if (hashctx == NULL
299	0	\|\| !hash_init_with_dom(hashctx, prehashed, 0, context,
300	0	context_len)
301	0	\|\| !EVP_DigestUpdate(hashctx, signature, EDDSA_448_PUBLIC_BYTES)
302	0	\|\| !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES)
303	0	\|\| !EVP_DigestUpdate(hashctx, message, message_len)
304	0	\|\| !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge))) {
305	0	EVP_MD_CTX_free(hashctx);
306	0	return C448_FAILURE;
307	0	}
308
309	0	EVP_MD_CTX_free(hashctx);
310	0	curve448_scalar_decode_long(challenge_scalar, challenge,
311	0	sizeof(challenge));
312	0	OPENSSL_cleanse(challenge, sizeof(challenge));
313	0	}
314	0	curve448_scalar_sub(challenge_scalar, curve448_scalar_zero,
315	0	challenge_scalar);
316
317	0	curve448_scalar_decode_long(response_scalar,
318	0	&signature[EDDSA_448_PUBLIC_BYTES],
319	0	EDDSA_448_PRIVATE_BYTES);
320
321		/* pk_point = -c(x(P)) + (cx + k)G = kG */
322	0	curve448_base_double_scalarmul_non_secret(pk_point,
323	0	response_scalar,
324	0	pk_point, challenge_scalar);
325	0	return c448_succeed_if(curve448_point_eq(pk_point, r_point));
326	0	}
327
328		c448_error_t c448_ed448_verify_prehash(
329		const uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
330		const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
331		const uint8_t hash[64], const uint8_t *context,
332		uint8_t context_len)
333	0	{
334	0	return c448_ed448_verify(signature, pubkey, hash, 64, 1, context,
335	0	context_len);
336	0	}
337
338		int ED448_sign(uint8_t out_sig, const uint8_t message, size_t message_len,
339		const uint8_t public_key[57], const uint8_t private_key[57],
340		const uint8_t *context, size_t context_len)
341	0	{
342	0	return c448_ed448_sign(out_sig, private_key, public_key, message,
343	0	message_len, 0, context, context_len)
344	0	== C448_SUCCESS;
345	0	}
346
347		int ED448_verify(const uint8_t *message, size_t message_len,
348		const uint8_t signature[114], const uint8_t public_key[57],
349		const uint8_t *context, size_t context_len)
350	0	{
351	0	return c448_ed448_verify(signature, public_key, message, message_len, 0,
352	0	context, (uint8_t)context_len) == C448_SUCCESS;
353	0	}
354
355		int ED448ph_sign(uint8_t *out_sig, const uint8_t hash[64],
356		const uint8_t public_key[57], const uint8_t private_key[57],
357		const uint8_t *context, size_t context_len)
358	0	{
359	0	return c448_ed448_sign_prehash(out_sig, private_key, public_key, hash,
360	0	context, context_len) == C448_SUCCESS;
361
362	0	}
363
364		int ED448ph_verify(const uint8_t hash[64], const uint8_t signature[114],
365		const uint8_t public_key[57], const uint8_t *context,
366		size_t context_len)
367	0	{
368	0	return c448_ed448_verify_prehash(signature, public_key, hash, context,
369	0	(uint8_t)context_len) == C448_SUCCESS;
370	0	}
371
372		int ED448_public_from_private(uint8_t out_public_key[57],
373		const uint8_t private_key[57])
374	12	{
375	12	return c448_ed448_derive_public_key(out_public_key, private_key)
376	12	== C448_SUCCESS;
377	12	}