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_encrypt(self, plaintext, r_value=None):
"""DGK encryption of a positive integer plaintext .
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 DGK
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 of 2t bits is used.
Returns:
int: DGK encryption of plaintext.
Raises:
TypeError: if plaintext is not an int or mpz.
"""
if not isinstance(plaintext, int) and not isinstance(
plaintext, type(mpz(1))):
raise TypeError('Expected int type plaintext but got: %s' %
type(plaintext))
nude_ciphertext = powmod(self.g, plaintext, self.n)
r = r_value or powmod(self.h, self.get_random_lt_2t(),
self.n) # Pass the precomputed obfuscator
obfuscator = r
return (nude_ciphertext * obfuscator) % self.n
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_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, int):
raise TypeError('Expected ciphertext to be an int, 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)
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_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 is_biprime_parametrized(N, pShares, qShares, testValue):
"""
Test whether N is the product of two primes.
If so, this test will succeed with probability 1.
If N is not the product of two primes, the test will fail with at least
probability 1/2.
"""
values = [
int(powmod(testValue, x // 4, N)) for x in [
sum(y) for y in zip(
list(pShares.values())[1:],
list(qShares.values())[1:])
]
]
values = [
int(powmod(testValue, (N - pShares[1] - qShares[1] + 1) // 4, N))
] + values
product = mult_list(values[1:])
if values[0] % N == product % N or values[0] % N == -product % N:
# Test succeeds, so N is "probably" the product of two primes.
return True
# Test fails, so N is definitely not the product of two primes.
return False
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):
if not isinstance(ciphertext, int):
raise TypeError('Expected ciphertext to be an int, 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)
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 __init__(self, n,p,q, random_alpha):
self.n = n
#self.g = n + 1
self.nsquare = n * n
self.random_alpha = random_alpha % self.nsquare
self.p = p
self.q = q
self.pp = self.p - 1 // 2
self.qq = self.q -1 // 2
self.g = random.randrange(1048576)
self.max_int = n // 3 - 1
one = powmod (1,1,self.nsquare)
ppqq=self.pp*self.qq
k = powmod(self.g,ppqq,self.n)
self.k = k - 1 // self.n
self.MK ={"pp":self.pp,"qq":self.qq}
self.h = powmod(self.g, self.random_alpha,self.nsquare)
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 = (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 = random.randrange(256) % self.nsquare
obfuscator_hr = powmod(self.h, r, self.nsquare)
obfuscator_gr = powmod(self.g, r, self.nsquare)
A = obfuscator_gr
B = (nude_ciphertext * obfuscator_hr) % self.nsquare
ciphertext = {"A":A,"B":B}
return ciphertext
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, int):
raise TypeError('Expected ciphertext to be an int, 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)
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_decrypt0(self, ciphertext):
"""Decrypt raw ciphertext and return raw plaintext.
Args:
ciphertext (int): (usually from :meth:`EncryptedNumber.ciphertext()`)
that is to be DGK decrypted.
Returns:
int: DGK decryption of ciphertext. 0 if the plaintext is 0 by
checking cyphertext^v mod p == 1, 1 otherwise
"""
c = powmod(ciphertext, self.v, self.p)
if c == 1:
return 0
else:
return 1
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 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, int):
raise TypeError('Expected ciphertext to be an int, not: %s' %
type(ciphertext))
u = powmod(ciphertext, self.Lambda, self.public_key.nsquare)
l_of_u = (u - 1) // self.public_key.n
return (l_of_u * self.mu) % self.public_key.n
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, int):
raise TypeError('Expected ciphertext to be an int, not: %s' %
type(ciphertext))
u = powmod(ciphertext, self.Lambda, self.public_key.nsquare)
l_of_u = (u - 1) // self.public_key.n
return (l_of_u * self.mu) % self.public_key.n
def obfuscate(self):
"""Disguise ciphertext by multiplying by r ** n with random r.
This operation must be performed for every `EncryptedNumber`
that is sent to an untrusted party, otherwise eavesdroppers
might deduce relationships between this and an antecedent
`EncryptedNumber`.
For example::
enc = public_key.encrypt(1337)
send_to_nsa(enc) # NSA can't decrypt (we hope!)
product = enc * 3.14
send_to_nsa(product) # NSA can deduce 3.14 by bruteforce attack
product2 = enc * 2.718
product2.obfuscate()
send_to_nsa(product) # NSA can't deduce 2.718 by bruteforce attack
"""
r = self.public_key.get_random_lt_n()
r_pow_n = powmod(r, self.public_key.n, self.public_key.nsquare)
self.__ciphertext = self.__ciphertext * r_pow_n % self.public_key.nsquare
self.__is_obfuscated = True
def obfuscate(self):
"""Disguise ciphertext by multiplying by r ** n with random r.
This operation must be performed for every `EncryptedNumber`
that is sent to an untrusted party, otherwise eavesdroppers
might deduce relationships between this and an antecedent
`EncryptedNumber`.
For example::
enc = public_key.encrypt(1337)
send_to_nsa(enc) # NSA can't decrypt (we hope!)
product = enc * 3.14
send_to_nsa(product) # NSA can deduce 3.14 by bruteforce attack
product2 = enc * 2.718
product2.obfuscate()
send_to_nsa(product) # NSA can't deduce 2.718 by bruteforce attack
"""
r = self.public_key.get_random_lt_n()
r_pow_n = powmod(r, self.public_key.n, self.public_key.nsquare)
self.__ciphertext['A'] = self.__ciphertext['A'] * r_pow_n % self.public_key.nsquare
self.__is_obfuscated = True
def obfuscate(self):
r = self.public_key.get_random_lt_n()
r_pow_n = powmod(r, self.public_key.n, self.public_key.nsquare)
self.__ciphertext = self.__ciphertext * r_pow_n % self.public_key.nsquare
self.__is_obfuscated = True
def testPowMod(self):
self.assertEqual(util.powmod(5, 3, 3), 2)
self.assertEqual(util.powmod(2, 10, 1000), 24)
def testPowMod(self):
self.assertEqual(util.powmod(5, 3, 3), 2)
self.assertEqual(util.powmod(2, 10, 1000), 24)
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 exponentiate(self,m):
ciphertext=self.ciphertext
text ={}
text['A'] = powmod(ciphertext['A'],m, self.public_key.nsquare)
text['B'] = powmod(ciphertext['B'],m,self.public_key.nsquare)
return text
def handle_client(conn):
#Sending message to connected client
#conn.send('Welcome to the server. Type something and hit enter\n'.encode('ASCII')) #send only takes string
#infinite loop so that function do not terminate and thread do not end.
while True:
#Receiving blinded message from client
data = conn.recv(1024)
print(sys.getsizeof(data), data)
if not data:
break
#determine if ZKP was sent or blind signature
print("Data: ", data)
try:
print("Data decoded: ", data.decode('ascii'))
if data.decode('ascii') == "ZKP START":
print("here...")
#start ZKP
for i in range(1, 5):
successful = False #used to control if the multiplicative inverse of x^e does not exist, then repeat the round
while not successful:
#wait for u
c = conn.recv(2049)
print("C data: ", c)
c = int(c.decode('ascii'))
print("Received c: ", c)
u = conn.recv(2048)
u = int(u.decode('ascii'))
print("Received u: ", u)
A = random.randint(3, 20)
e = random.randint(0, A)
print("e: ", e)
conn.send(bytes(str(e), 'ascii'))
wn = conn.recv(2048)
wn = wn.decode('ascii')
if wn != "restart":
wn = int(wn)
print("wn: ", wn)
v = conn.recv(2048)
v = int(v.decode('ascii'))
print("v: ", v)
gv = powmod(public_key.g, v, public_key.nsquare)
ce = powmod(c, e, public_key.nsquare)
check = (gv * ce * wn) % public_key.nsquare
print("N2: ", public_key.nsquare)
print("Check: ", check)
print("u: ", u)
if check == u:
conn.send(bytes("PASS ROUND", 'ascii'))
successful = True
elif check == "Invalid":
conn.send(bytes("REPEAT ROUND", 'ascii'))
else:
conn.send(bytes("FAILED ROUND", 'ascii'))
successful = True
else:
print(
"Retrying with new s and e... no inverse to w."
)
except UnicodeDecodeError:
print("there...")
#print(type(data),data.decode('ascii'),data)
#calculate signature
msg_blinded_signature = RSA_private_key.sign(data, 0)
print(msg_blinded_signature[0])
print(type(msg_blinded_signature[0]))
#send the signature, second element is always None
conn.send(bytes(str(msg_blinded_signature[0]), 'ascii'))
except ValueError:
pass