def raw_encrypt(self, plaintext, r_value=None):
"""Paillier encryption of a positive integer plaintext < :attr:`n`.
You probably should be using :meth:`encrypt` instead, because it
handles positive and negative ints and floats.
Args:
plaintext (int): a positive integer < :attr:`n` to be Paillier
encrypted. Typically this is an encoding of the actual
number you want to encrypt.
r_value (int): obfuscator for the ciphertext; by default (i.e.
r_value is None), a random value is used.
Returns:
int: Paillier encryption of plaintext.
Raises:
TypeError: if plaintext is not an int.
"""
if not isinstance(plaintext, int):
raise TypeError('Expected int type plaintext but got: %s' %
type(plaintext))
if self.n - self.max_int <= plaintext < self.n:
# Very large plaintext, take a sneaky shortcut using inverses
neg_plaintext = self.n - plaintext # = abs(plaintext - nsquare)
neg_ciphertext = powmod(self.g, neg_plaintext, self.nsquare)
nude_ciphertext = invert(neg_ciphertext, self.nsquare)
else:
nude_ciphertext = powmod(self.g, plaintext, self.nsquare)
r = r_value or self.get_random_lt_n()
obfuscator = powmod(r, self.n, self.nsquare)
return (nude_ciphertext * obfuscator) % self.nsquare
def my__mul__(self, other):
"""Multiply by an int, float, or EncodedNumber.
If `other` is a scalar, it is first encoded to fixed-point precision of `self`"""
if isinstance(other, paillier.EncryptedNumber):
raise NotImplementedError('Good luck with that...')
if isinstance(other, paillier.EncodedNumber):
encoding = other
else:
int_rep = int(other * pow(paillier.EncodedNumber.BASE, -self.exponent))
if abs(int_rep) > self.public_key.max_int:
raise ValueError('Integer needs to be within +/- %d but got %d' %
(self.public_key.max_int, int_rep))
# Wrap negative numbers by adding n
encoding = paillier.EncodedNumber(self.public_key,
int_rep % self.public_key.n,
self.exponent)
product = self._raw_mul(encoding.encoding)
exponent = self.exponent + encoding.exponent
unscaled_result = paillier.EncryptedNumber(self.public_key, product,
exponent)
# moving the decimal point to end up having the same number of digits to its right
scaling_multiplier = invert(paillier.EncodedNumber.BASE**(-self.exponent),
self.public_key.n)
scaled_product = unscaled_result._raw_mul(scaling_multiplier)
return paillier.EncryptedNumber(self.public_key, scaled_product,
self.exponent)
def raw_encrypt(self, plaintext, r_value=None):
"""Paillier encryption of a positive integer plaintext < :attr:`n`.
You probably should be using :meth:`encrypt` instead, because it
handles positive and negative ints and floats.
Args:
plaintext (int): a positive integer < :attr:`n` to be Paillier
encrypted. Typically this is an encoding of the actual
number you want to encrypt.
r_value (int): obfuscator for the ciphertext; by default (i.e.
r_value is None), a random value is used.
Returns:
int: Paillier encryption of plaintext.
Raises:
TypeError: if plaintext is not an int.
"""
if not isinstance(plaintext, int):
raise TypeError('Expected int type plaintext but got: %s' %
type(plaintext))
if self.n - self.max_int <= plaintext < self.n:
# Very large plaintext, take a sneaky shortcut using inverses
neg_plaintext = self.n - plaintext # = abs(plaintext - nsquare)
neg_ciphertext = powmod(self.g, neg_plaintext, self.nsquare)
nude_ciphertext = invert(neg_ciphertext, self.nsquare)
else:
nude_ciphertext = powmod(self.g, plaintext, self.nsquare)
r = r_value or self.get_random_lt_n()
obfuscator = powmod(r, self.n, self.nsquare)
return (nude_ciphertext * obfuscator) % self.nsquare
def _raw_mul(self, plaintext):
"""Returns the integer E(a * plaintext), where E(a) = ciphertext
Args:
plaintext (int): number by which to multiply the
`EncryptedNumber`. *plaintext* is typically an encoding.
0 <= *plaintext* < :attr:`~PaillierPublicKey.n`
Returns:
int: Encryption of the product of `self` and the scalar
encoded in *plaintext*.
Raises:
TypeError: if *plaintext* is not an int.
ValueError: if *plaintext* is not between 0 and
:attr:`PaillierPublicKey.n`.
"""
if not isinstance(plaintext, int):
raise TypeError('Expected ciphertext to be int, not %s' %
type(plaintext))
if plaintext < 0 or plaintext >= self.public_key.n:
raise ValueError('Scalar out of bounds: %i' % plaintext)
if self.public_key.n - self.public_key.max_int <= plaintext:
# Very large plaintext, play a sneaky trick using inverses
neg_c = invert(self.ciphertext(False), self.public_key.nsquare)
neg_scalar = self.public_key.n - plaintext
return powmod(neg_c, neg_scalar, self.public_key.nsquare)
else:
return powmod(self.ciphertext(False), plaintext, self.public_key.nsquare)
def raw_decrypt(self, ciphertext):
"""Decrypt raw ciphertext and return raw plaintext.
Args:
ciphertext (int): (usually from :meth:`EncryptedNumber.ciphertext()`)
that is to be Paillier decrypted.
Returns:
int: Paillier decryption of ciphertext. This is a positive
integer < :attr:`public_key.n`.
Raises:
TypeError: if ciphertext is not an int.
"""
if not isinstance(ciphertext, dict):
raise TypeError('Expected ciphertext to be a dict, not: %s' %
type(ciphertext))
#decrypt_to_p = self.l_function(powmod(ciphertext, self.p-1, self.psquare), self.p) * self.hp % self.p
#decrypt_to_q = self.l_function(powmod(ciphertext, self.q-1, self.qsquare), self.q) * self.hq % self.q
#return self.crt(decrypt_to_p, decrypt_to_q)
t1=invert(ciphertext['A'],self.nsquare)
t2=powmod(t1,self.sk,self.nsquare)
t3=ciphertext['B']
t4=t3*t2
one=powmod(1,1,self.nsquare)
t5=t4 - one
t6=t5%self.nsquare
m = t6 // self.n
return m
def _raw_mul(self, plaintext):
"""Returns the integer E(a * plaintext), where E(a) = ciphertext
Args:
plaintext (int): number by which to multiply the
`EncryptedNumber`. *plaintext* is typically an encoding.
0 <= *plaintext* < :attr:`~PaillierPublicKey.n`
Returns:
int: Encryption of the product of `self` and the scalar
encoded in *plaintext*.
Raises:
TypeError: if *plaintext* is not an int.
ValueError: if *plaintext* is not between 0 and
:attr:`PaillierPublicKey.n`.
"""
a,b = self, plaintext
if not isinstance(plaintext, int):
raise TypeError('Expected ciphertext to be int, not %s' %
type(plaintext))
if plaintext < 0 or plaintext >= self.public_key.n:
raise ValueError('Scalar out of bounds: %i' % plaintext)
if self.public_key.n - self.public_key.max_int <= plaintext:
# Very large plaintext, play a sneaky trick using inverses
neg_c = invert(self.ciphertext, self.public_key.nsquare)
neg_scalar = self.public_key.n - plaintext
return powmod(neg_c, neg_scalar, self.public_key.nsquare)
else:
return a.exponentiate(plaintext)
def raw_decrypt(self, ciphertext):
if not isinstance(ciphertext, int):
raise TypeError('Expected ciphertext to be an int, not: %s' %
type(ciphertext))
n = self.n
t = self.t
SecretKeyShares = self.SecretKeyShares
theta = self.theta
nFac = math.factorial(n)
#c = Ciphertext.ciphertext()
c = ciphertext
N = self.public_key.n
NSquare = N**2
shares = SecretKeyShares.shares
degree = SecretKeyShares.degree
# NB: Here the reconstruction set is implicity defined, but any
# large enough subset of shares will do.
reconstruction_shares = {
key: shares[key]
for key in list(shares.keys())[:degree + 1]
}
lagrange_interpol_enum = {
i: mult_list([j for j in reconstruction_shares.keys() if i != j])
for i in reconstruction_shares.keys()
}
lagrange_interpol_denom = {
i: mult_list([(j - i) for j in reconstruction_shares.keys()
if i != j])
for i in reconstruction_shares.keys()
}
exponents = [
(nFac * lagrange_interpol_enum[i] * reconstruction_shares[i]) //
lagrange_interpol_denom[i] for i in reconstruction_shares.keys()
]
# Notice that the partial decryption is already raised to the power given
# by the Lagrange interpolation coefficient
partialDecryptions = [powmod(c, exp, NSquare) for exp in exponents]
combinedDecryption = mult_list(partialDecryptions) % NSquare
if (combinedDecryption - 1) % N != 0:
print("Error, combined decryption minus one not divisible by N")
message = ((combinedDecryption - 1) // N * invert(theta, N)) % N
return message
def raw_transform(self,encrypted_number):
ciphertext = encrypted_number.ciphertext
if not isinstance(ciphertext, dict):
raise TypeError('Expected ciphertext to be a dict, not: %s' % type(ciphertext))
A = ciphertext['A']
A1 = invert(ciphertext['A'],self.public_key.nsquare)
t2 = powmod(A1,self.sk,self.public_key.nsquare)
t3 = ciphertext['B']
t4=t3*t2
B=t4%self.public_key.nsquare
transformed_cipher = {"A":A,"B":B}
print('transformerssssss',transformed_cipher)
encrypted_number.ciphertext = transformed_cipher
return encrypted_number
def _raw_mul(self, plaintext):
if not isinstance(plaintext, int):
raise TypeError('Expected ciphertext to be int, not %s' %
type(plaintext))
if plaintext < 0 or plaintext >= self.public_key.n:
raise ValueError('Scalar out of bounds: %i' % plaintext)
if self.public_key.n - self.public_key.max_int <= plaintext:
# Very large plaintext, play a sneaky trick using inverses
neg_c = invert(self.ciphertext(False), self.public_key.nsquare)
neg_scalar = self.public_key.n - plaintext
return powmod(neg_c, neg_scalar, self.public_key.nsquare)
else:
return powmod(self.ciphertext(False), plaintext,
self.public_key.nsquare)
def secure_bit_decomposition_server(client, public_key, enc_x, bitlength_m):
l_inv2 = paillier.EncodedNumber.encode(public_key, invert(2, public_key.n))
T = enc_x + 0
x_decomp = []
send(client, bitlength_m)
for i in range(0, bitlength_m):
x_decomp.append(secure_lsb_server(client, public_key, T, i))
Z = T - x_decomp[i]
T = Z * l_inv2
if svr_server(client, public_key, enc_x, x_decomp) == 1:
return list(reversed(x_decomp))
else:
return secure_bit_decomposition_server(client, public_key, enc_x,
bitlength_m)
def __init__(self, public_key, p, q):
if not p*q == public_key.n:
raise ValueError('given public key does not match the given p and q.')
if p == q: #check that p and q are different, otherwise we can't compute p^-1 mod q
raise ValueError('p and q have to be different')
self.public_key = public_key
if q < p: #ensure that p < q.
self.p = q
self.q = p
else:
self.p = p
self.q = q
self.psquare = self.p * self.p
self.qsquare = self.q * self.q
self.p_inverse = invert(self.p, self.q)
self.hp = self.h_function(self.p, self.psquare);
self.hq = self.h_function(self.q, self.qsquare);
def __init__(self, public_key, p, q):
if not p*q == public_key.n:
raise ValueError('given public key does not match the given p and q.')
if p == q:
# check that p and q are different, otherwise we can't compute p^-1 mod q
raise ValueError('p and q have to be different')
self.public_key = public_key
if q < p: #ensure that p < q.
self.p = q
self.q = p
else:
self.p = p
self.q = q
self.psquare = self.p * self.p
self.qsquare = self.q * self.q
self.p_inverse = invert(self.p, self.q)
self.hp = self.h_function(self.p, self.psquare)
self.hq = self.h_function(self.q, self.qsquare)
def raw_encrypt(self, plaintext, r_value=None):
if not isinstance(plaintext, int):
raise TypeError('Expected int type plaintext but got: %s' %
type(plaintext))
if self.n - self.max_int <= plaintext < self.n:
# Very large plaintext, take a sneaky shortcut using inverses
neg_plaintext = self.n - plaintext # = abs(plaintext - nsquare)
neg_ciphertext = (self.n * neg_plaintext + 1) % self.nsquare
nude_ciphertext = invert(neg_ciphertext, self.nsquare)
else:
# we chose g = n + 1, so that we can exploit the fact that
# (n+1)^plaintext = n*plaintext + 1 mod n^2
nude_ciphertext = (self.n * plaintext + 1) % self.nsquare
r = r_value or self.get_random_lt_n()
obfuscator = powmod(r, self.n, self.nsquare)
return (nude_ciphertext * obfuscator) % self.nsquare
def raw_encrypt(self, plaintext, r_value=None):
"""Paillier encryption of a positive integer plaintext < :attr:`n`.
一个正整数的加密
You probably should be using :meth:`encrypt` instead, because it
handles positive and negative ints and floats.
应该使用方法encrypt加密，因为他处理正负的整数和浮点数
Args:
plaintext (int): a positive integer < :attr:`n` to be Paillier
encrypted. Typically this is an encoding of the actual
number you want to encrypt.
plaintext(int)为一个小于n的要加密的实际数字编码
r_value (int): obfuscator for the ciphertext; by default (i.e.
r_value is None), a random value is used.
密文模糊处理;默认情况下时(即r_value为None)使用随机值。
Returns:
int: Paillier encryption of plaintext.
plaintext的Paillier加密
Raises:
TypeError: if plaintext is not an int.
异常：plaintext不是整数
"""
#异常判断
if not isinstance(plaintext, int):
raise TypeError('Expected int type plaintext but got: %s' %
type(plaintext))
#加密plaintext
if self.n - self.max_int <= plaintext < self.n:
# Very large plaintext, take a sneaky shortcut using inverses
neg_plaintext = self.n - plaintext # = abs(plaintext - nsquare)
neg_ciphertext = (self.n * neg_plaintext + 1) % self.nsquare
nude_ciphertext = invert(neg_ciphertext, self.nsquare)
else:
# we chose g = n + 1, so that we can exploit the fact that
# (n+1)^plaintext = n*plaintext + 1 mod n^2
nude_ciphertext = (self.n * plaintext + 1) % self.nsquare
r = r_value or self.get_random_lt_n()
obfuscator = powmod(r, self.n, self.nsquare)#使用gmp
return (nude_ciphertext * obfuscator) % self.nsquare
def generate_paillier_keypair(private_keyring=None, n_length=DEFAULT_KEYSIZE):
"""Return a new :class:`PaillierPublicKey` and :class:`PaillierPrivateKey`.
Add the private key to *private_keyring* if given.
Args:
private_keyring (PaillierPrivateKeyring): a
:class:`PaillierPrivateKeyring` on which to store the private
key.
n_length: key size in bits.
Returns:
tuple: The generated :class:`PaillierPublicKey` and
:class:`PaillierPrivateKey`
"""
p = q = n = None
n_len = 0
while n_len != n_length:
p = getprimeover(n_length // 2)
q = getprimeover(n_length // 2)
n = p * q
n_len = n.bit_length()
# Simpler Paillier variant with g=n+1 results in lambda equal to phi
# and mu is phi inverse mod n.
g = n + 1
public_key = PaillierPublicKey(g, n)
phi_n = (p - 1) * (q - 1)
Lambda = phi_n
mu = invert(phi_n, n)
private_key = PaillierPrivateKey(public_key, Lambda, mu)
if private_keyring is not None:
private_keyring.add(private_key)
return public_key, private_key
def generate_paillier_keypair(private_keyring=None, n_length=DEFAULT_KEYSIZE):
"""Return a new :class:`PaillierPublicKey` and :class:`PaillierPrivateKey`.
Add the private key to *private_keyring* if given.
Args:
private_keyring (PaillierPrivateKeyring): a
:class:`PaillierPrivateKeyring` on which to store the private
key.
n_length: key size in bits.
Returns:
tuple: The generated :class:`PaillierPublicKey` and
:class:`PaillierPrivateKey`
"""
p = q = n = None
n_len = 0
while n_len != n_length:
p = getprimeover(n_length // 2)
q = getprimeover(n_length // 2)
n = p * q
n_len = n.bit_length()
# Simpler Paillier variant with g=n+1 results in lambda equal to phi
# and mu is phi inverse mod n.
g = n + 1
public_key = PaillierPublicKey(g, n)
phi_n = (p - 1) * (q - 1)
Lambda = phi_n
mu = invert(phi_n, n)
private_key = PaillierPrivateKey(public_key, Lambda, mu)
if private_keyring is not None:
private_keyring.add(private_key)
return public_key, private_key
def h_function(self, x, xsquare):
"""Computes the h-function as defined in Paillier's paper page 12,
'Decryption using Chinese-remaindering'.
"""
return invert(self.l_function(powmod(self.public_key.g, x - 1, xsquare),x), x)
def h_function(self, x, xsquare):
"""Computes the h-function as defined in Paillier's paper page 12,
'Decryption using Chinese-remaindering'.
"""
return invert(self.l_function(powmod(self.public_key.g, x - 1, xsquare),x), x)
def testInvertNonPrime(self):
a = 3
p = 4
self.assertEqual(a * util.invert(a, p) % p, 1)
def testInvert(self):
p = 101
for i in range(1, p):
iinv = util.invert(i, p)
self.assertEqual((iinv * i) % p, 1)
def testInvert(self):
p = 101
for i in range(1, p):
iinv = util.invert(i, p)
self.assertEqual((iinv * i) % p, 1)
def testInvertNonPrime(self):
a = 3
p = 4
self.assertEqual(a * util.invert(a, p) % p, 1)