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 = p
while q == p:
q = getprimeover(n_length // 2)
n = p * q
n_len = n.bit_length()
public_key = PaillierPublicKey(n)
private_key = PaillierPrivateKey(public_key, p, q)
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 = p
while q == p:
q = getprimeover(n_length // 2)
n = p * q
nsquare = n * n
n_len = n.bit_length()
random_alpha = random.randrange(34359738368) % nsquare
public_key = PaillierPublicKey(n,p,q, random_alpha)
private_key = PaillierPrivateKey(public_key, p, q, random_alpha)
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) #根据偶数返回一个随机的N位素数。
q = p
while q == p:
q = getprimeover(n_length // 2) #根据偶数返回一个随机的N位素数。
n = p * q
n_len = n.bit_length() #二进制长度
public_key = PaillierPublicKey(n) #生成N位公钥
private_key = PaillierPrivateKey(public_key, p, q) #根据公钥和P,Q生成私钥
if private_keyring is not None:
private_keyring.add(private_key)
return public_key, private_key
def testcPDSRandomNumberGenerator(self, n_length=DEFAULT_KEYSIZE):
p = q = n = None
n_len = 0
while n_len != n_length:
p = getprimeover(n_length // 2)
q = p
while q == p:
q = getprimeover(n_length // 2)
n = p * q
n_len = n.bit_length()
r = paillier.generate_random_value(n, 4)
self.assertEqual(sum(r), 0)
def generate_random_value(old_n, m):
n_length = 512
p = q = n = None
n_len = 0
while n_len != n_length:
p = getprimeover(n_length // 2)
q = p
while q == p:
q = getprimeover(n_length // 2)
n = p * q
n_len = n.bit_length()
r = [0] * m
for i in range(m - 1):
r[i] = random.SystemRandom().randrange(1, n)
r[-1] = sum(r) * -1
return r
def generate_paillier_keypair(private_keyring=None, n_length=DEFAULT_KEYSIZE):
p = q = n = None
n_len = 0
while n_len != n_length:
p = getprimeover(n_length // 2)
q = p
while q == p:
q = getprimeover(n_length // 2)
n = p * q
n_len = n.bit_length()
public_key = PaillierPublicKey(n)
private_key = PaillierPrivateKey(public_key, p, q)
if private_keyring is not None:
private_keyring.add(private_key)
return n, public_key, private_key
def generate_cPDS_keypair(m=4, 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 = p
while q == p:
q = getprimeover(n_length // 2)
n = p * q
n_len = n.bit_length()
# g in Z*n^2
#g = random.SystemRandom().randrange(1, n**2)
g = n + 1
mpk = PaillierPublicKey(n, g)
msk = PaillierPrivateKey(mpk, p, q)
r = generate_random_value(n, m)
public_key = [0] * m
private_key = [0] * m
for i in range(m):
public_key[i], private_key[i] = generate_key_pairs(n, g, p, q, r[i])
return mpk, msk, public_key, private_key
def keysDGK(n_length=DEFAULT_KEYSIZE,
l=DEFAULT_MSGSIZE,
t=DEFAULT_SECURITYSIZE):
u = 2**l
len_vp = t + 1
while len_vp > t:
vp = getprimeover(t)
len_vp = vp.bit_length()
len_vq = t + 1
while len_vq > t:
vq = getprimeover(t)
len_vq = vq.bit_length()
n_len = 0
prime = 0
# print(u,vp,vq)
while n_len != n_length:
fp = getprimeover((n_length // 2) - l - t)
p = u * vp * fp + 1
# print(p.bit_length())
while (not (gmpy2.is_prime(p))):
fp = getprimeover((n_length // 2) - l - t)
p = u * vp * fp + 1
fq = getprimeover((n_length // 2) - l - t + 1)
q = u * vq * fq + 1
# print(q.bit_length())
while (not (gmpy2.is_prime(q))):
fq = getprimeover((n_length // 2) - l - t + 1)
q = u * vq * fq + 1
n = p * q
n_len = n.bit_length()
# print(n_len)
n = p * q
g, h = find_gens(p, q, u, vp, vq, fp, fq, n, n_length, l, t)
return p, q, u, vp, vq, fp, fq, g, h
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 testPrimeOverN(self):
self.assertIn(util.getprimeover(3), {5, 7, 11, 13})
# Test we get at least a N-bit prime
for n in range(2, 50):
p = util.getprimeover(n)
self.assertGreaterEqual(p, 1 << (n-1))
def testPrimeOverN(self):
self.assertIn(util.getprimeover(3), {5, 7, 11, 13})
# Test we get at least a N-bit prime
for n in range(2, 50):
p = util.getprimeover(n)
self.assertGreaterEqual(p, 1 << (n - 1))
def find_gens(p,
q,
u,
vp,
vq,
fp,
fq,
n,
n_length=DEFAULT_KEYSIZE,
l=DEFAULT_MSGSIZE,
t=DEFAULT_SECURITYSIZE):
found = False
# compute g from CRT with g mod p = xp, g mod q = xq, g = g^(fp*fq) mod n
# xp is a prime element from Z^*_p, that does not have order a divisor of fp*u*vp
exp1 = mpz(fp * vp * u / 2)
exp2 = mpz(vp * u)
exp3 = mpz(fp * vp)
p_len = p.bit_length()
while not (found):
xp = getprimeover(p_len)
if (xp < p):
found = True
if (found):
order = gmpy2.powmod(xp, exp1, p)
if (order == 1):
found = False
else:
order = gmpy2.powmod(xp, exp2, p)
if (order == 1):
found = False
else:
order = gmpy2.powmod(xp, exp3, p)
if (order == 1):
found = False
# xq is a prime element from Z^*_q, that does not have order a divisor of fq*u*vq
found = False
exp1 = mpz(fq * vq * u / 2)
exp2 = mpz(vq * u)
exp3 = mpz(fq * vq)
q_len = q.bit_length()
while not (found):
xq = getprimeover(q_len)
if (xq < q):
found = True
if (found):
order = gmpy2.powmod(xq, exp1, q)
if (order == 1):
found = False
else:
order = gmpy2.powmod(xq, exp2, q)
if (order == 1):
found = False
else:
order = gmpy2.powmod(xq, exp3, q)
if (order == 1):
found = False
# CRT: g = xp*q*(q^{-1}mod p) + xq*p*(p^{-1}mod q) mod n, g = g^(fp*fq) mod n
inv_q = gmpy2.invert(q, p)
inv_p = gmpy2.invert(p, q)
tmp = xp * q * inv_q % n
tmp2 = xq * p * inv_p % n
g = (tmp + tmp2) % n
g = gmpy2.powmod(g, fp * fq, n)
# print(g)
# compute h as xh^(fp*fq*u) mod n
# xh is a prime element from Z^*_n
found = False
while not (found):
xh = getprimeover(n_length)
if (xh < n):
found = True
h = gmpy2.powmod(xh, fp * fq * u, n)
# print(h)
return g, h
