| /* |
| * 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; |
| } |