def encrypt(self, v):
"""Encrypt a given number v.
The ciphertext of v is defined:
.. math::
Enc(v) = g^{v} r^{m} \\mod m^{2}
Args:
v: scalar or vector to be encrypted.
Returns:
vector of ciphertexts; even if the input is a scalar, one dimension
vector is returned.
"""
if not isinstance(v, np.ndarray):
if not isinstance(v, (tuple, list)):
v = np.array([v])
else:
v = np.array(v)
r = [random_m(self.m) for _ in range(len(v))]
m2 = self.m2
return np.array([
(powmod(self.g, int(vi), m2) * powmod(ri, self.m, m2)) % m2
for vi, ri in zip(v, r)
])
def generate_keypair(m_length=2048):
"""Generate a key pair.
"""
p = q = m = None
while not m or gcd(m, (p - 1) * (q - 1)) != 1:
m_len = 0
while m_len < m_length:
p = getprimeover(m_length // 2)
q = getprimeover(m_length // 2)
if p == q:
continue
m = p * q
m_len = m.bit_length()
beta = random_m(m)
Lambda = beta * lcm(p - 1, q - 1)
a = random_m(m)
b = random_m(m)
m2 = m**2
g = (powmod(1 + m, a, m2) * powmod(b, m, m2)) % m2
pk = PublicKey(m, g, powmod(g, Lambda, m2))
sk = PrivateKey(pk, Lambda)
return sk, pk
def share(c):
"""Compute the description share associated with this encryption.
"""
return np.array([
powmod(int(ci), self.Lambda_u, self.m2) * powmod(
self.pk.glambda, -int(ri), self.m2)
for ci, ri in zip(c, r)
])
def share(c):
"""Compute a decryption share.
"""
return np.array([
powmod(int(ci), self.Lambda_u, self.m2) *
powmod(self.pk.glambda, -int(ri), self.m2)
for ci, ri in zip(c, r)
])
def decrypt(self, v):
"""Decrypt a given ciphertext v with given key pair.
The plain text is defined:
.. math::
Dec(v) = \\frac{L(v^{\\lambda})}{L(g^{\\lambda})} \\mod m
Args:
v: scalar or vector of ciphertext.
Returns:
vector of plain texts; even if the input is a scalar, one dimension
vector is returned.
"""
if not isinstance(v, (tuple, list, np.ndarray)):
v = [v]
X = [
(powmod(int(vi), self.Lambda, self.m2) - 1) % self.m2 // self.pk.m
for vi in v
]
Y = (self.pk.glambda - 1) % self.m2 // self.pk.m
return np.array([(Xi * invert(Y, self.pk.m)) % self.pk.m for Xi in X])
def share(c):
"""Compute the description share associated with this encryption.
"""
return (np.array([
powmod(int(ci), int(yi) - self.a + self.b, self.m2)
for ci, yi in zip(c, y)
]) * self.pk.encrypt(r)) % self.m2
def test_g(self):
"""Test :math:`g^{\\lambda}`.
"""
self.assertEqual(
powmod(self.pk.g, self.sk.Lambda, self.pk.m**2), self.pk.glambda)
def test_glambda(self):
"""Test :math:`(g^{\\lambda})^{m} \\equiv 1 \\mod m^{2}`.
"""
self.assertEqual(powmod(self.pk.glambda, self.pk.m, self.pk.m**2), 1)
def test_propertyof_m_and_lambda(self):
"""Test :math:`b^{m\\lambda} \\equiv 1 \\mod m^{2}`.
"""
b = random_m(self.pk.m)
self.assertEqual(
powmod(b, self.pk.m * self.sk.Lambda, self.pk.m**2), 1)