def from_totient(public_key, totient):
"""given the totient, one can factorize the modulus
The totient is defined as totient = (p - 1) * (q - 1),
and the modulus is defined as modulus = p * q
Args:
public_key (PaillierPublicKey): The corresponding public
key
totient (int): the totient of the modulus
Returns:
the :class:`PaillierPrivateKey` that corresponds to the inputs
Raises:
ValueError: if the given totient is not the totient of the modulus
of the given public key
"""
p_plus_q = public_key.n - totient + 1
p_minus_q = isqrt(p_plus_q * p_plus_q - public_key.n * 4)
q = (p_plus_q - p_minus_q) // 2
p = p_plus_q - q
if not p*q == public_key.n:
raise ValueError('given public key and totient do not match.')
return PaillierPrivateKey(public_key, p, q, random_alpha)
def from_totient(public_key, totient):
"""given the totient, one can factorize the modulus
The totient is defined as totient = (p - 1) * (q - 1),
and the modulus is defined as modulus = p * q
Args:
public_key (PaillierPublicKey): The corresponding public
key
totient (int): the totient of the modulus
Returns:
the :class:`PaillierPrivateKey` that corresponds to the inputs
Raises:
ValueError: if the given totient is not the totient of the modulus
of the given public key
"""
p_plus_q = public_key.n - totient + 1
p_minus_q = isqrt(p_plus_q * p_plus_q - public_key.n * 4)
q = (p_plus_q - p_minus_q) // 2
p = p_plus_q - q
if not p*q == public_key.n:
raise ValueError('given public key and totient do not match.')
return PaillierPrivateKey(public_key, p, q)
def from_totient(public_key, totient):
"""given the totient, one can factorize the modulus
The totient is defined as totient = (p - 1) * (q - 1),
and the modulus is defined as modulus = p * q
考虑到totient，可以分解模量。
totient被定义为totient = (p - 1) * (q - 1)，
模被定义为模= p * q。
Args:
public_key (PaillierPublicKey): The corresponding public
key
totient (int): the totient of the modulus
Returns:
the :class:`PaillierPrivateKey` that corresponds to the inputs
对应于输入的Paillier私钥。
Raises:
ValueError: if the given totient is not the totient of the modulus
of the given public key
如果给定的totient不是模量的totient给定的公钥。
"""
p_plus_q = public_key.n - totient + 1#加
p_minus_q = isqrt(p_plus_q * p_plus_q - public_key.n * 4)#乘
q = (p_plus_q - p_minus_q) // 2
p = p_plus_q - q
if not p*q == public_key.n:
raise ValueError('given public key and totient do not match.')
return PaillierPrivateKey(public_key, p, q)
def from_totient(public_key, totient):
p_plus_q = public_key.n - totient + 1
p_minus_q = isqrt(p_plus_q * p_plus_q - public_key.n * 4)
q = (p_plus_q - p_minus_q) // 2
p = p_plus_q - q
if not p * q == public_key.n:
raise ValueError('given public key and totient do not match.')
return PaillierPrivateKey(public_key, p, q)
def testIsqrt(self):
for _ in range(100):
n = random.randint(2, 10000000)
nsq = n*n
self.assertEqual(int(math.floor(math.sqrt(n))), util.isqrt(n))
self.assertEqual(util.isqrt(nsq), util.improved_i_sqrt(nsq))
def testIsqrt(self):
for _ in range(100):
n = random.randint(2, 10000000)
nsq = n * n
self.assertEqual(int(math.floor(math.sqrt(n))), util.isqrt(n))
self.assertEqual(util.isqrt(nsq), util.improved_i_sqrt(nsq))