def _reconstruct_shamirs_secret(
self, priv_b: Union[UmbralPrivateKey, CurveBN]) -> None:
g = self._umbral_params.g
if isinstance(priv_b, UmbralPrivateKey):
pub_b = priv_b.get_pubkey()
priv_b = priv_b.bn_key
else:
pub_b = priv_b * g
cfrag_0 = self._attached_cfrags[0]
id_0 = cfrag_0._kfrag_id
ni = cfrag_0._point_noninteractive
xcoord = cfrag_0._point_xcoord
dh_xcoord = priv_b * xcoord
blake2b = hashes.Hash(hashes.BLAKE2b(64), backend=backend)
blake2b.update(xcoord.to_bytes())
blake2b.update(pub_b.to_bytes())
blake2b.update(dh_xcoord.to_bytes())
hashed_dh_tuple = blake2b.finalize()
if len(self._attached_cfrags) > 1:
xs = [
CurveBN.hash(cfrag._kfrag_id,
hashed_dh_tuple,
params=self._umbral_params)
for cfrag in self._attached_cfrags
]
x_0 = CurveBN.hash(id_0,
hashed_dh_tuple,
params=self._umbral_params)
lambda_0 = lambda_coeff(x_0, xs)
e = lambda_0 * cfrag_0._point_e1
v = lambda_0 * cfrag_0._point_v1
for cfrag in self._attached_cfrags[1:]:
if (ni, xcoord) != (cfrag._point_noninteractive,
cfrag._point_xcoord):
raise ValueError(
"Attached CFrags are not pairwise consistent")
x_i = CurveBN.hash(cfrag._kfrag_id,
hashed_dh_tuple,
params=self._umbral_params)
lambda_i = lambda_coeff(x_i, xs)
e = e + (lambda_i * cfrag._point_e1)
v = v + (lambda_i * cfrag._point_v1)
else:
e = cfrag_0._point_e1
v = cfrag_0._point_v1
self._point_e_prime = e
self._point_v_prime = v
self._point_noninteractive = ni
def _decapsulate_reencrypted(receiving_privkey: UmbralPrivateKey,
capsule: Capsule,
key_length: int = DEM_KEYSIZE) -> bytes:
"""Derive the same symmetric encapsulated_key"""
params = capsule.params
pub_key = receiving_privkey.get_pubkey().point_key
priv_key = receiving_privkey.bn_key
precursor = capsule._attached_cfrags[0]._point_precursor
dh_point = priv_key * precursor
from constant_sorrow import constants
# Combination of CFrags via Shamir's Secret Sharing reconstruction
if len(capsule._attached_cfrags) > 1:
xs = [
CurveBN.hash(precursor,
pub_key,
dh_point,
bytes(constants.X_COORDINATE),
cfrag._kfrag_id,
params=params) for cfrag in capsule._attached_cfrags
]
e_summands, v_summands = list(), list()
for cfrag, x in zip(capsule._attached_cfrags, xs):
if precursor != cfrag._point_precursor:
raise ValueError("Attached CFrags are not pairwise consistent")
lambda_i = lambda_coeff(x, xs)
e_summands.append(lambda_i * cfrag._point_e1)
v_summands.append(lambda_i * cfrag._point_v1)
e_prime = sum(e_summands[1:], e_summands[0])
v_prime = sum(v_summands[1:], v_summands[0])
else:
e_prime = capsule._attached_cfrags[0]._point_e1
v_prime = capsule._attached_cfrags[0]._point_v1
# Secret value 'd' allows to make Umbral non-interactive
d = CurveBN.hash(precursor,
pub_key,
dh_point,
bytes(constants.NON_INTERACTIVE),
params=params)
e, v, s = capsule.components()
h = CurveBN.hash(e, v, params=params)
orig_pub_key = capsule.get_correctness_keys(
)['delegating'].point_key # type: ignore
if not (s / d) * orig_pub_key == (h * e_prime) + v_prime:
raise GenericUmbralError()
shared_key = d * (e_prime + v_prime)
encapsulated_key = kdf(shared_key, key_length)
return encapsulated_key
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 recover_secret(shares):
points = [share[0] for share in shares]
summands = []
for point, value in shares:
lambda_i = utils.lambda_coeff(point, points)
summands.append(lambda_i * value)
return sum(summands[1:], summands[0])
def _reconstruct_shamirs_secret(self,
pub_a: Union[UmbralPublicKey, Point],
priv_b: Union[UmbralPrivateKey, CurveBN],
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()
cfrag_0 = self._attached_cfrags[0]
id_0 = cfrag_0._bn_kfrag_id
x_0 = CurveBN.hash(id_0, hashed_dh_tuple, params=params)
if len(self._attached_cfrags) > 1:
xs = [CurveBN.hash(cfrag._bn_kfrag_id, hashed_dh_tuple, params=params)
for cfrag in self._attached_cfrags]
lambda_0 = lambda_coeff(x_0, xs)
e = lambda_0 * cfrag_0._point_e1
v = lambda_0 * cfrag_0._point_v1
for cfrag in self._attached_cfrags[1:]:
x_i = CurveBN.hash(cfrag._bn_kfrag_id, hashed_dh_tuple, params=params)
lambda_i = lambda_coeff(x_i, xs)
e = e + (lambda_i * cfrag._point_e1)
v = v + (lambda_i * cfrag._point_v1)
else:
e = cfrag_0._point_e1
v = cfrag_0._point_v1
self._point_e_prime = e
self._point_v_prime = v
self._point_noninteractive = cfrag_0._point_noninteractive
def _reconstruct_shamirs_secret(self) -> None:
id_cfrag_pairs = list(self._attached_cfrags.items())
id_0, cfrag_0 = id_cfrag_pairs[0]
if len(id_cfrag_pairs) > 1:
ids = self._attached_cfrags.keys()
lambda_0 = lambda_coeff(id_0, ids)
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:]:
lambda_i = lambda_coeff(id_i, ids)
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