int
goldilocks_verify (
const uint8_t signature[GOLDI_SIGNATURE_BYTES],
const uint8_t *message,
uint64_t message_len,
const struct goldilocks_public_key_t *pubkey
) {
if (!goldilocks_check_init()) {
return GOLDI_EUNINIT;
}
struct field_t pk;
word_t s[GOLDI_FIELD_WORDS];
mask_t succ = field_deserialize(&pk,pubkey->opaque);
if (!succ) return GOLDI_EINVAL;
succ = barrett_deserialize(s, &signature[GOLDI_FIELD_BYTES], &curve_prime_order);
if (!succ) return GOLDI_EINVAL;
word_t challenge[GOLDI_FIELD_WORDS];
goldilocks_derive_challenge(challenge, pubkey->opaque, signature, message, message_len);
struct field_t eph;
struct tw_extensible_t pk_text;
/* deserialize [nonce]G */
succ = field_deserialize(&eph, signature);
if (!succ) return GOLDI_EINVAL;
succ = deserialize_and_twist_approx(&pk_text, &sqrt_d_minus_1, &pk);
if (!succ) return GOLDI_EINVAL;
linear_combo_var_fixed_vt( &pk_text,
challenge, GOLDI_SCALAR_BITS,
s, GOLDI_SCALAR_BITS,
goldilocks_global.wnafs, WNAF_PRECMP_BITS );
untwist_and_double_and_serialize( &pk, &pk_text );
field_sub(&eph, &eph, &pk);
field_bias(&eph, 2);
succ = field_is_zero(&eph);
return succ ? 0 : GOLDI_EINVAL;
}
int
goldilocks_verify_precomputed (
const uint8_t signature[GOLDI_SIGNATURE_BYTES],
const uint8_t *message,
uint64_t message_len,
const struct goldilocks_precomputed_public_key_t *pubkey
) {
if (!goldilocks_check_init()) {
return GOLDI_EUNINIT;
}
word_t s[GOLDI_FIELD_WORDS];
mask_t succ = barrett_deserialize(s, &signature[GOLDI_FIELD_BYTES], &curve_prime_order);
if (!succ) return GOLDI_EINVAL;
word_t challenge[GOLDI_FIELD_WORDS];
goldilocks_derive_challenge(challenge, pubkey->pub.opaque, signature, message, message_len);
struct field_t eph, pk;
struct tw_extensible_t pk_text;
/* deserialize [nonce]G */
succ = field_deserialize(&eph, signature);
if (!succ) return GOLDI_EINVAL;
succ = linear_combo_combs_vt (
&pk_text,
challenge, GOLDI_SCALAR_BITS, &pubkey->table,
s, GOLDI_SCALAR_BITS, &goldilocks_global.fixed_base
);
if (!succ) return GOLDI_EINVAL;
untwist_and_double_and_serialize( &pk, &pk_text );
field_sub(&eph, &eph, &pk);
field_bias(&eph, 2);
succ = field_is_zero(&eph);
return succ ? 0 : GOLDI_EINVAL;
}
int
goldilocks_sign (
uint8_t signature_out[GOLDI_SIGNATURE_BYTES],
const uint8_t *message,
uint64_t message_len,
const struct goldilocks_private_key_t *privkey
) {
if (!goldilocks_check_init()) {
return GOLDI_EUNINIT;
}
/* challenge = H(pk, [nonceG], message). */
word_t skw[GOLDI_FIELD_WORDS];
mask_t succ = barrett_deserialize(skw,privkey->opaque,&curve_prime_order);
if (!succ) {
really_memset(skw,0,sizeof(skw));
return GOLDI_ECORRUPT;
}
/* Derive a nonce. TODO: use HMAC. FUTURE: factor. */
unsigned char sha_out[SHA512_OUTPUT_BYTES];
word_t tk[GOLDI_FIELD_WORDS];
struct sha512_ctx_t ctx;
sha512_init(&ctx);
sha512_update(&ctx, (const unsigned char *)"signonce", 8);
sha512_update(&ctx, &privkey->opaque[2*GOLDI_FIELD_BYTES], GOLDI_SYMKEY_BYTES);
sha512_update(&ctx, message, message_len);
sha512_update(&ctx, &privkey->opaque[2*GOLDI_FIELD_BYTES], GOLDI_SYMKEY_BYTES);
sha512_final(&ctx, sha_out);
barrett_deserialize_and_reduce(tk, sha_out, SHA512_OUTPUT_BYTES, &curve_prime_order);
/* 4[nonce]G */
uint8_t signature_tmp[GOLDI_FIELD_BYTES];
struct tw_extensible_t exta;
struct field_t gsk;
scalarmul_fixed_base(&exta, tk, GOLDI_SCALAR_BITS, &goldilocks_global.fixed_base);
double_tw_extensible(&exta);
untwist_and_double_and_serialize(&gsk, &exta);
field_serialize(signature_tmp, &gsk);
word_t challenge[GOLDI_FIELD_WORDS];
goldilocks_derive_challenge (
challenge,
&privkey->opaque[GOLDI_FIELD_BYTES],
signature_tmp,
message,
message_len
);
/* reduce challenge and sub. */
barrett_negate(challenge,GOLDI_FIELD_WORDS,&curve_prime_order);
barrett_mac(
tk,GOLDI_FIELD_WORDS,
challenge,GOLDI_FIELD_WORDS,
skw,GOLDI_FIELD_WORDS,
&curve_prime_order
);
word_t carry = add_nr_ext_packed(tk,tk,GOLDI_FIELD_WORDS,tk,GOLDI_FIELD_WORDS,-1);
barrett_reduce(tk,GOLDI_FIELD_WORDS,carry,&curve_prime_order);
memcpy(signature_out, signature_tmp, GOLDI_FIELD_BYTES);
barrett_serialize(signature_out+GOLDI_FIELD_BYTES, tk, GOLDI_FIELD_BYTES);
really_memset((unsigned char *)tk,0,sizeof(tk));
really_memset((unsigned char *)skw,0,sizeof(skw));
really_memset((unsigned char *)challenge,0,sizeof(challenge));
/* response = 2(nonce_secret - sk*challenge)
* Nonce = 8[nonce_secret]*G
* PK = 2[sk]*G, except doubled (TODO)
* so [2] ( [response]G + 2[challenge]PK ) = Nonce
*/
return 0;
}
static int
goldilocks_shared_secret_core (
uint8_t shared[GOLDI_SHARED_SECRET_BYTES],
const struct goldilocks_private_key_t *my_privkey,
const struct goldilocks_public_key_t *your_pubkey,
const struct goldilocks_precomputed_public_key_t *pre
) {
/* This function doesn't actually need anything in goldilocks_global,
* so it doesn't check init.
*/
assert(GOLDI_SHARED_SECRET_BYTES == SHA512_OUTPUT_BYTES);
word_t sk[GOLDI_FIELD_WORDS];
struct field_t pk;
mask_t succ = field_deserialize(&pk,your_pubkey->opaque), msucc = -1;
#ifdef EXPERIMENT_ECDH_STIR_IN_PUBKEYS
struct field_t sum, prod;
msucc &= field_deserialize(&sum,&my_privkey->opaque[GOLDI_FIELD_BYTES]);
field_mul(&prod,&pk,&sum);
field_add(&sum,&pk,&sum);
#endif
msucc &= barrett_deserialize(sk,my_privkey->opaque,&curve_prime_order);
#if GOLDI_IMPLEMENT_PRECOMPUTED_KEYS
if (pre) {
struct tw_extensible_t tw;
succ &= scalarmul_fixed_base(&tw, sk, GOLDI_SCALAR_BITS, &pre->table);
untwist_and_double_and_serialize(&pk, &tw);
} else {
succ &= montgomery_ladder(&pk,&pk,sk,GOLDI_SCALAR_BITS,1);
}
#else
(void)pre;
succ &= montgomery_ladder(&pk,&pk,sk,GOLDI_SCALAR_BITS,1);
#endif
field_serialize(shared,&pk);
/* obliterate records of our failure by adjusting with obliteration key */
struct sha512_ctx_t ctx;
sha512_init(&ctx);
#ifdef EXPERIMENT_ECDH_OBLITERATE_CT
uint8_t oblit[GOLDI_DIVERSIFY_BYTES + GOLDI_SYMKEY_BYTES];
unsigned i;
for (i=0; i<GOLDI_DIVERSIFY_BYTES; i++) {
oblit[i] = "noshared"[i] & ~(succ&msucc);
}
for (i=0; i<GOLDI_SYMKEY_BYTES; i++) {
oblit[GOLDI_DIVERSIFY_BYTES+i] = my_privkey->opaque[2*GOLDI_FIELD_BYTES+i] & ~(succ&msucc);
}
sha512_update(&ctx, oblit, sizeof(oblit));
#endif
#ifdef EXPERIMENT_ECDH_STIR_IN_PUBKEYS
/* stir in the sum and product of the pubkeys. */
uint8_t a_pk[GOLDI_FIELD_BYTES];
field_serialize(a_pk, &sum);
sha512_update(&ctx, a_pk, GOLDI_FIELD_BYTES);
field_serialize(a_pk, &prod);
sha512_update(&ctx, a_pk, GOLDI_FIELD_BYTES);
#endif
/* stir in the shared key and finish */
sha512_update(&ctx, shared, GOLDI_FIELD_BYTES);
sha512_final(&ctx, shared);
return (GOLDI_ECORRUPT & ~msucc)
| (GOLDI_EINVAL & msucc &~ succ)
| (GOLDI_EOK & msucc & succ);
}