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# -*- coding: utf-8 -*-
#
# PubKey/RSA/_slowmath.py : Pure Python implementation of the RSA portions of _fastmath
#
# Written in 2008 by Dwayne C. Litzenberger <dlitz@dlitz.net>
#
# ===================================================================
# The contents of this file are dedicated to the public domain. To
# the extent that dedication to the public domain is not available,
# everyone is granted a worldwide, perpetual, royalty-free,
# non-exclusive license to exercise all rights associated with the
# contents of this file for any purpose whatsoever.
# No rights are reserved.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
# BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
# ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
# ===================================================================
"""Pure Python implementation of the RSA-related portions of Crypto.PublicKey._fastmath."""
__revision__ = "$Id$"
__all__ = ['rsa_construct']
import sys
if sys.version_info[0] == 2 and sys.version_info[1] == 1:
from Crypto.Util.py21compat import *
from Crypto.Util.number import size, inverse, GCD
class error(Exception):
pass
class _RSAKey(object):
def _blind(self, m, r):
# compute r**e * m (mod n)
return (m * pow(r, self.e, self.n)) % self.n
def _unblind(self, m, r):
# compute m / r (mod n)
return inverse(r, self.n) * m % self.n
def _decrypt(self, c):
# compute c**d (mod n)
if not self.has_private():
raise TypeError("No private key")
if (hasattr(self,'p') and hasattr(self,'q') and hasattr(self,'u')):
m1 = pow(c, self.d % (self.p-1), self.p)
m2 = pow(c, self.d % (self.q-1), self.q)
h = m2 - m1
if (h<0):
h = h + self.q
h = h*self.u % self.q
return h*self.p+m1
return pow(c, self.d, self.n)
def _encrypt(self, m):
# compute m**d (mod n)
return pow(m, self.e, self.n)
def _sign(self, m): # alias for _decrypt
if not self.has_private():
raise TypeError("No private key")
return self._decrypt(m)
def _verify(self, m, sig):
return self._encrypt(sig) == m
def has_private(self):
return hasattr(self, 'd')
def size(self):
"""Return the maximum number of bits that can be encrypted"""
return size(self.n) - 1
def rsa_construct(n, e, d=None, p=None, q=None, u=None):
"""Construct an RSAKey object"""
assert isinstance(n, long)
assert isinstance(e, long)
assert isinstance(d, (long, type(None)))
assert isinstance(p, (long, type(None)))
assert isinstance(q, (long, type(None)))
assert isinstance(u, (long, type(None)))
obj = _RSAKey()
obj.n = n
obj.e = e
if d is None:
return obj
obj.d = d
if p is not None and q is not None:
obj.p = p
obj.q = q
else:
# Compute factors p and q from the private exponent d.
# We assume that n has no more than two factors.
# See 8.2.2(i) in Handbook of Applied Cryptography.
ktot = d*e-1
# The quantity d*e-1 is a multiple of phi(n), even,
# and can be represented as t*2^s.
t = ktot
while t%2==0:
t=divmod(t,2)[0]
# Cycle through all multiplicative inverses in Zn.
# The algorithm is non-deterministic, but there is a 50% chance
# any candidate a leads to successful factoring.
# See "Digitalized Signatures and Public Key Functions as Intractable
# as Factorization", M. Rabin, 1979
spotted = 0
a = 2
while not spotted and a<100:
k = t
# Cycle through all values a^{t*2^i}=a^k
while k<ktot:
cand = pow(a,k,n)
# Check if a^k is a non-trivial root of unity (mod n)
if cand!=1 and cand!=(n-1) and pow(cand,2,n)==1:
# We have found a number such that (cand-1)(cand+1)=0 (mod n).
# Either of the terms divides n.
obj.p = GCD(cand+1,n)
spotted = 1
break
k = k*2
# This value was not any good... let's try another!
a = a+2
if not spotted:
raise ValueError("Unable to compute factors p and q from exponent d.")
# Found !
assert ((n % obj.p)==0)
obj.q = divmod(n,obj.p)[0]
if u is not None:
obj.u = u
else:
obj.u = inverse(obj.p, obj.q)
return obj
class _DSAKey(object):
def size(self):
"""Return the maximum number of bits that can be encrypted"""
return size(self.p) - 1
def has_private(self):
return hasattr(self, 'x')
def _sign(self, m, k, blind): # 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_blind_k = inverse(blind * k, self.q) # Compute (blind * k)**-1 mod q
blind_x = self.x * blind
r = pow(self.g, k, self.p) % self.q # r = (g**k mod p) mod q
s = (inv_blind_k * (m * blind + blind_x * r)) % self.q
return (r, s)
def _verify(self, m, r, s):
# SECURITY TODO - We _should_ be computing SHA1(m), but we don't because that's the API.
if not (0 < r < self.q) or not (0 < s < self.q):
return False
w = inverse(s, self.q)
u1 = (m*w) % self.q
u2 = (r*w) % self.q
v = (pow(self.g, u1, self.p) * pow(self.y, u2, self.p) % self.p) % self.q
return v == r
def dsa_construct(y, g, p, q, x=None):
assert isinstance(y, long)
assert isinstance(g, long)
assert isinstance(p, long)
assert isinstance(q, long)
assert isinstance(x, (long, type(None)))
obj = _DSAKey()
obj.y = y
obj.g = g
obj.p = p
obj.q = q
if x is not None: obj.x = x
return obj
# vim:set ts=4 sw=4 sts=4 expandtab:
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