def _decapsulate_reencrypted(pub_key: Point, priv_key: BigNum, orig_pub_key: Point, capsule: Capsule, key_length=32, params: UmbralParameters = None) -> bytes: """Derive the same symmetric key""" params = params if params is not None else default_params() xcomp = capsule._point_noninteractive d = BigNum.hash_to_bn(xcomp, pub_key, priv_key * xcomp, params=params) e_prime = capsule._point_eph_e_prime v_prime = capsule._point_eph_v_prime shared_key = d * (e_prime + v_prime) key = kdf(shared_key, key_length) e = capsule._point_eph_e v = capsule._point_eph_v s = capsule._bn_sig h = BigNum.hash_to_bn(e, v, params=params) inv_d = ~d if not (s * inv_d) * orig_pub_key == (h * e_prime) + v_prime: raise GenericUmbralError() return key
def _check_challenge(capsule: Capsule, cfrag: CapsuleFrag, challenge_resp: ChallengeResponse, pub_a: Point, pub_b: Point, challenge_metadata: bytes = None, params: UmbralParameters = None) -> bool: params = params if params is not None else default_params() e = capsule._point_eph_e v = capsule._point_eph_v e1 = cfrag.point_eph_e1 v1 = cfrag.point_eph_v1 xcomp = cfrag.point_eph_ni kfrag_id = cfrag.bn_kfrag_id e2 = challenge_resp.point_eph_e2 v2 = challenge_resp.point_eph_v2 g = params.g u = params.u u1 = challenge_resp.point_kfrag_commitment u2 = challenge_resp.point_kfrag_pok z1 = challenge_resp.bn_kfrag_sig1 z2 = challenge_resp.bn_kfrag_sig2 z3 = challenge_resp.bn_sig g_y = (z2 * g) + (z1 * pub_a) hash_input = [e, e1, e2, v, v1, v2, u, u1, u2] if challenge_metadata is not None: hash_input.append(challenge_metadata) h = BigNum.hash_to_bn(*hash_input, params=params) check31 = z1 == BigNum.hash_to_bn(g_y, kfrag_id, pub_a, pub_b, u1, xcomp, params=params) check32 = z3 * e == e2 + (h * e1) check33 = z3 * u == u2 + (h * u1) check34 = z3 * v == v2 + (h * v1) return check31 & check32 & check33 & check34
def _reconstruct_shamirs_secret(self, pub_a: Union[UmbralPublicKey, Point], priv_b: Union[UmbralPrivateKey, BigNum], params: UmbralParameters = None) -> None: params = params if params is not None else default_params() if isinstance(priv_b, UmbralPrivateKey): priv_b = priv_b.bn_key if isinstance(pub_a, UmbralPublicKey): pub_a = pub_a.point_key g = params.g pub_b = priv_b * g g_ab = priv_b * pub_a blake2b = hashes.Hash(hashes.BLAKE2b(64), backend=backend) blake2b.update(pub_a.to_bytes()) blake2b.update(pub_b.to_bytes()) blake2b.update(g_ab.to_bytes()) hashed_dh_tuple = blake2b.finalize() id_cfrag_pairs = list(self._attached_cfrags.items()) id_0, cfrag_0 = id_cfrag_pairs[0] x_0 = BigNum.hash_to_bn(id_0, hashed_dh_tuple, params=params) if len(id_cfrag_pairs) > 1: xs = [ BigNum.hash_to_bn(_id, hashed_dh_tuple, params=params) for _id in self._attached_cfrags.keys() ] lambda_0 = lambda_coeff(x_0, xs) e = lambda_0 * cfrag_0.point_eph_e1 v = lambda_0 * cfrag_0.point_eph_v1 for id_i, cfrag in id_cfrag_pairs[1:]: x_i = BigNum.hash_to_bn(id_i, hashed_dh_tuple, params=params) lambda_i = lambda_coeff(x_i, xs) e = e + (lambda_i * cfrag.point_eph_e1) v = v + (lambda_i * cfrag.point_eph_v1) else: e = cfrag_0.point_eph_e1 v = cfrag_0.point_eph_v1 self._point_eph_e_prime = e self._point_eph_v_prime = v self._point_noninteractive = cfrag_0.point_eph_ni
def verify(self, params: UmbralParameters = None) -> bool: params = params if params is not None else default_params() e = self._point_eph_e v = self._point_eph_v s = self._bn_sig h = BigNum.hash_to_bn(e, v, params=params) return s * params.g == v + (h * e)
def derive_privkey_by_label(self, label: bytes, salt: bytes = None, params: UmbralParameters = None): """ Derives an UmbralPrivateKey using a KDF from this instance of UmbralKeyingMaterial, a label, and an optional salt. """ params = params if params is not None else default_params() key_material = HKDF(algorithm=hashes.BLAKE2b(64), length=64, salt=salt, info=b"NuCypherKMS/KeyDerivation/" + label, backend=default_backend()).derive( self.keying_material) bn_key = BigNum.hash_to_bn(key_material, params=params) return UmbralPrivateKey(bn_key, params)
def _challenge(kfrag: KFrag, capsule: Capsule, cfrag: CapsuleFrag, challenge_metadata: bytes = None, params: UmbralParameters = None) -> ChallengeResponse: params = params if params is not None else default_params() e1 = cfrag.point_eph_e1 v1 = cfrag.point_eph_v1 e = capsule._point_eph_e v = capsule._point_eph_v u = params.u u1 = kfrag.point_commitment t = BigNum.gen_rand(params.curve) e2 = t * e v2 = t * v u2 = t * u hash_input = [e, e1, e2, v, v1, v2, u, u1, u2] if challenge_metadata is not None: hash_input.append(challenge_metadata) h = BigNum.hash_to_bn(*hash_input, params=params) z3 = t + h * kfrag.bn_key ch_resp = ChallengeResponse(e2=e2, v2=v2, u1=u1, u2=u2, z1=kfrag.bn_sig1, z2=kfrag.bn_sig2, z3=z3) # Check correctness of original ciphertext (check nº 2) at the end # to avoid timing oracles if not capsule.verify(params): raise capsule.NotValid("Capsule verification failed.") return ch_resp
def _encapsulate(alice_pub_key: Point, key_length=32, params: UmbralParameters = None) -> Tuple[bytes, Capsule]: """Generates a symmetric key and its associated KEM ciphertext""" params = params if params is not None else default_params() g = params.g priv_r = BigNum.gen_rand(params.curve) pub_r = priv_r * g priv_u = BigNum.gen_rand(params.curve) pub_u = priv_u * g h = BigNum.hash_to_bn(pub_r, pub_u, params=params) s = priv_u + (priv_r * h) shared_key = (priv_r + priv_u) * alice_pub_key # Key to be used for symmetric encryption key = kdf(shared_key, key_length) return key, Capsule(point_eph_e=pub_r, point_eph_v=pub_u, bn_sig=s)
def split_rekey(priv_a: Union[UmbralPrivateKey, BigNum], pub_b: Union[UmbralPublicKey, Point], threshold: int, N: int, params: UmbralParameters = None) -> List[KFrag]: """ Creates a re-encryption key from Alice to Bob and splits it in KFrags, using Shamir's Secret Sharing. Requires a threshold number of KFrags out of N to guarantee correctness of re-encryption. Returns a list of KFrags. """ params = params if params is not None else default_params() if isinstance(priv_a, UmbralPrivateKey): priv_a = priv_a.bn_key if isinstance(pub_b, UmbralPublicKey): pub_b = pub_b.point_key g = params.g pub_a = priv_a * g x = BigNum.gen_rand(params.curve) xcomp = x * g d = BigNum.hash_to_bn(xcomp, pub_b, pub_b * x, params=params) coeffs = [priv_a * (~d)] coeffs += [BigNum.gen_rand(params.curve) for _ in range(threshold - 1)] u = params.u g_ab = priv_a * pub_b blake2b = hashes.Hash(hashes.BLAKE2b(64), backend=backend) blake2b.update(pub_a.to_bytes()) blake2b.update(pub_b.to_bytes()) blake2b.update(g_ab.to_bytes()) hashed_dh_tuple = blake2b.finalize() kfrags = [] for _ in range(N): id_kfrag = BigNum.gen_rand(params.curve) share_x = BigNum.hash_to_bn(id_kfrag, hashed_dh_tuple, params=params) rk = poly_eval(coeffs, share_x) u1 = rk * u y = BigNum.gen_rand(params.curve) z1 = BigNum.hash_to_bn(y * g, id_kfrag, pub_a, pub_b, u1, xcomp, params=params) z2 = y - priv_a * z1 kfrag = KFrag(id_=id_kfrag, key=rk, x=xcomp, u1=u1, z1=z1, z2=z2) kfrags.append(kfrag) return kfrags