def dict2RSA(**kw):
""" Create Crypto.PublicKey.RSA from dict
Required RSA priv. key params (as long)
n, e - modulus and public exponent (public key only)
n, d, e - modulus, private and public exponent
or
p, q, e - primes p, q, and public exponent e
If also dp, dq, qinv present, they are checked to be consistent.
Default value for e is 0x10001
Return Crypto.PublicKey.RSA object
dp = d mod (p-1), dq = d mod (q-1), q*qinv mod p = 1
"""
for par in ('n', 'd', 'p', 'q', 'dp', 'dq', 'qinv'):
if par in kw:
assert isinstance(long(kw[par]), long), \
"RSA parameter %s must be long" % par
e = long(kw.get('e', 0x10001L))
if all([par not in kw for par in ('d', 'p', 'q', 'dp', 'dq', 'qinv')]):
assert 'n' in kw, "At least modulus must be in dict"
return RSA.construct((kw['n'], e))
if 'n' in kw and 'd' in kw:
return RSA.construct((kw['n'], e, kw['d']))
assert 'p' in kw and 'q' in kw, "Either n, d or p, q must be in dict"
p = kw['p']
q = kw['q']
n = p*q
d = number.inverse(e, (p-1)*(q-1))
if 'd' in kw:
assert d == kw['d'], "Inconsinstent private exponent"
if 'dp' in kw:
assert d % (p-1) == kw['dp'], "Inconsistent d mod (p-1)"
if 'dq' in kw:
assert d % (q-1) == kw['dq'], "Inconsistent d mod (q-1)"
u = number.inverse(q, p)
if 'qinv' in kw:
assert u == kw['qinv'], "Inconsistent q inv"
return RSA.construct((n, e, d, q, p, u))
python类inverse()的实例源码
def chinese_remainder(n, a):
''' Compute a number from its moduluses.
From Rosetta Code. '''
sum = 0
prod = reduce(lambda a, b: a*b, n)
for n_i, a_i in zip(n, a):
p = prod / n_i
sum += a_i * number.inverse(p, n_i) * p
return sum % prod
def setUp(self):
global RSA, Random, bytes_to_long
from Crypto.PublicKey import RSA
from Crypto import Random
from Crypto.Util.number import bytes_to_long, inverse
self.n = bytes_to_long(a2b_hex(self.modulus))
self.p = bytes_to_long(a2b_hex(self.prime_factor))
# Compute q, d, and u from n, e, and p
self.q = divmod(self.n, self.p)[0]
self.d = inverse(self.e, (self.p-1)*(self.q-1))
self.u = inverse(self.p, self.q) # u = e**-1 (mod q)
self.rsa = RSA
def _exercise_primitive(self, rsaObj):
# Since we're using a randomly-generated key, we can't check the test
# vector, but we can make sure encryption and decryption are inverse
# operations.
ciphertext = a2b_hex(self.ciphertext)
# Test decryption
plaintext = rsaObj.decrypt((ciphertext,))
# Test encryption (2 arguments)
(new_ciphertext2,) = rsaObj.encrypt(plaintext, b(""))
self.assertEqual(b2a_hex(ciphertext), b2a_hex(new_ciphertext2))
# Test blinded decryption
blinding_factor = Random.new().read(len(ciphertext)-1)
blinded_ctext = rsaObj.blind(ciphertext, blinding_factor)
blinded_ptext = rsaObj.decrypt((blinded_ctext,))
unblinded_plaintext = rsaObj.unblind(blinded_ptext, blinding_factor)
self.assertEqual(b2a_hex(plaintext), b2a_hex(unblinded_plaintext))
# Test signing (2 arguments)
signature2 = rsaObj.sign(ciphertext, b(""))
self.assertEqual((bytes_to_long(plaintext),), signature2)
# Test verification
self.assertEqual(1, rsaObj.verify(ciphertext, (bytes_to_long(plaintext),)))
def _unblind(self, m, r):
# compute m / r (mod n)
return inverse(r, self.n) * m % self.n
def _sign(self, m, k): # alias for _decrypt
# SECURITY TODO - We _should_ be computing SHA1(m), but we don't because that's the API.
if not self.has_private():
raise TypeError("No private key")
if not (1L < k < self.q):
raise ValueError("k is not between 2 and q-1")
inv_k = inverse(k, self.q) # Compute k**-1 mod q
r = pow(self.g, k, self.p) % self.q # r = (g**k mod p) mod q
s = (inv_k * (m + self.x * r)) % self.q
return (r, s)
def _decrypt(self, M):
if (not hasattr(self, 'x')):
raise TypeError('Private key not available in this object')
ax=pow(M[0], self.x, self.p)
plaintext=(M[1] * inverse(ax, self.p ) ) % self.p
return plaintext
def _sign(self, M, K):
if (not hasattr(self, 'x')):
raise TypeError('Private key not available in this object')
p1=self.p-1
if (GCD(K, p1)!=1):
raise ValueError('Bad K value: GCD(K,p-1)!=1')
a=pow(self.g, K, self.p)
t=(M-self.x*a) % p1
while t<0: t=t+p1
b=(t*inverse(K, p1)) % p1
return (a, b)
def setUp(self):
global RSA, Random, bytes_to_long
from Crypto.PublicKey import RSA
from Crypto import Random
from Crypto.Util.number import bytes_to_long, inverse
self.n = bytes_to_long(a2b_hex(self.modulus))
self.p = bytes_to_long(a2b_hex(self.prime_factor))
# Compute q, d, and u from n, e, and p
self.q = divmod(self.n, self.p)[0]
self.d = inverse(self.e, (self.p-1)*(self.q-1))
self.u = inverse(self.p, self.q) # u = e**-1 (mod q)
self.rsa = RSA
def _exercise_primitive(self, rsaObj):
# Since we're using a randomly-generated key, we can't check the test
# vector, but we can make sure encryption and decryption are inverse
# operations.
ciphertext = a2b_hex(self.ciphertext)
# Test decryption
plaintext = rsaObj.decrypt((ciphertext,))
# Test encryption (2 arguments)
(new_ciphertext2,) = rsaObj.encrypt(plaintext, b(""))
self.assertEqual(b2a_hex(ciphertext), b2a_hex(new_ciphertext2))
# Test blinded decryption
blinding_factor = Random.new().read(len(ciphertext)-1)
blinded_ctext = rsaObj.blind(ciphertext, blinding_factor)
blinded_ptext = rsaObj.decrypt((blinded_ctext,))
unblinded_plaintext = rsaObj.unblind(blinded_ptext, blinding_factor)
self.assertEqual(b2a_hex(plaintext), b2a_hex(unblinded_plaintext))
# Test signing (2 arguments)
signature2 = rsaObj.sign(ciphertext, b(""))
self.assertEqual((bytes_to_long(plaintext),), signature2)
# Test verification
self.assertEqual(1, rsaObj.verify(ciphertext, (bytes_to_long(plaintext),)))
def _unblind(self, m, r):
# compute m / r (mod n)
return inverse(r, self.n) * m % self.n
def _sign(self, m, k): # alias for _decrypt
# SECURITY TODO - We _should_ be computing SHA1(m), but we don't because that's the API.
if not self.has_private():
raise TypeError("No private key")
if not (1 < k < self.q):
raise ValueError("k is not between 2 and q-1")
inv_k = inverse(k, self.q) # Compute k**-1 mod q
r = pow(self.g, k, self.p) % self.q # r = (g**k mod p) mod q
s = (inv_k * (m + self.x * r)) % self.q
return (r, s)
def _decrypt(self, M):
if (not hasattr(self, 'x')):
raise TypeError('Private key not available in this object')
ax=pow(M[0], self.x, self.p)
plaintext=(M[1] * inverse(ax, self.p ) ) % self.p
return plaintext
def _sign(self, M, K):
if (not hasattr(self, 'x')):
raise TypeError('Private key not available in this object')
p1=self.p-1
if (GCD(K, p1)!=1):
raise ValueError('Bad K value: GCD(K,p-1)!=1')
a=pow(self.g, K, self.p)
t=(M-self.x*a) % p1
while t<0: t=t+p1
b=(t*inverse(K, p1)) % p1
return (a, b)
def setUp(self):
global RSA, Random, bytes_to_long
from Crypto.PublicKey import RSA
from Crypto import Random
from Crypto.Util.number import bytes_to_long, inverse
self.n = bytes_to_long(a2b_hex(self.modulus))
self.p = bytes_to_long(a2b_hex(self.prime_factor))
# Compute q, d, and u from n, e, and p
self.q = divmod(self.n, self.p)[0]
self.d = inverse(self.e, (self.p-1)*(self.q-1))
self.u = inverse(self.p, self.q) # u = e**-1 (mod q)
self.rsa = RSA
def _exercise_primitive(self, rsaObj):
# Since we're using a randomly-generated key, we can't check the test
# vector, but we can make sure encryption and decryption are inverse
# operations.
ciphertext = a2b_hex(self.ciphertext)
# Test decryption
plaintext = rsaObj.decrypt((ciphertext,))
# Test encryption (2 arguments)
(new_ciphertext2,) = rsaObj.encrypt(plaintext, b(""))
self.assertEqual(b2a_hex(ciphertext), b2a_hex(new_ciphertext2))
# Test blinded decryption
blinding_factor = Random.new().read(len(ciphertext)-1)
blinded_ctext = rsaObj.blind(ciphertext, blinding_factor)
blinded_ptext = rsaObj.decrypt((blinded_ctext,))
unblinded_plaintext = rsaObj.unblind(blinded_ptext, blinding_factor)
self.assertEqual(b2a_hex(plaintext), b2a_hex(unblinded_plaintext))
# Test signing (2 arguments)
signature2 = rsaObj.sign(ciphertext, b(""))
self.assertEqual((bytes_to_long(plaintext),), signature2)
# Test verification
self.assertEqual(1, rsaObj.verify(ciphertext, (bytes_to_long(plaintext),)))
def _unblind(self, m, r):
# compute m / r (mod n)
return inverse(r, self.n) * m % self.n
def _sign(self, m, k): # alias for _decrypt
# SECURITY TODO - We _should_ be computing SHA1(m), but we don't because that's the API.
if not self.has_private():
raise TypeError("No private key")
if not (1L < k < self.q):
raise ValueError("k is not between 2 and q-1")
inv_k = inverse(k, self.q) # Compute k**-1 mod q
r = pow(self.g, k, self.p) % self.q # r = (g**k mod p) mod q
s = (inv_k * (m + self.x * r)) % self.q
return (r, s)
def _decrypt(self, M):
if (not hasattr(self, 'x')):
raise TypeError('Private key not available in this object')
ax=pow(M[0], self.x, self.p)
plaintext=(M[1] * inverse(ax, self.p ) ) % self.p
return plaintext
def _sign(self, M, K):
if (not hasattr(self, 'x')):
raise TypeError('Private key not available in this object')
p1=self.p-1
if (GCD(K, p1)!=1):
raise ValueError('Bad K value: GCD(K,p-1)!=1')
a=pow(self.g, K, self.p)
t=(M-self.x*a) % p1
while t<0: t=t+p1
b=(t*inverse(K, p1)) % p1
return (a, b)
