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# N A large safe prime (N = 2q+1, where q is prime)
# All arithmetic is done modulo N.
# g A generator modulo N
# k Multiplier parameter (k = H(N, g) in SRP-6a, k = 3 for legacy SRP-6)
# s User's salt
# I Username
# p Cleartext Password
# H() One-way hash function
# ^ (Modular) Exponentiation
# u Random scrambling parameter
# a,b Secret ephemeral values
# A,B Public ephemeral values
# x Private key (derived from p and s)
# v Password verifier
import hashlib
import os
import binascii
def bytes_to_long(s):
n = ord(s[0])
for b in ( ord(x) for x in s[1:] ):
n = (n << 8) | b
return n
def long_to_bytes(n):
l = list()
x = 0
off = 0
while x != n:
b = (n >> off) & 0xFF
l.append( chr(b) )
x = x | (b << off)
off += 8
l.reverse()
return ''.join(l)
def get_random( nbytes ):
return bytes_to_long( os.urandom( nbytes ) )
def old_H( s1, s2 = '', s3=''):
if isinstance(s1, (long, int)):
s1 = long_to_bytes(s1)
if s2 and isinstance(s2, (long, int)):
s2 = long_to_bytes(s2)
if s3 and isinstance(s3, (long, int)):
s3 = long_to_bytes(s3)
s = s1 + s2 + s3
return long(hashlib.sha256(s).hexdigest(), 16)
def H( *args, **kwargs ):
h = hashlib.sha256()
for s in args:
if s is not None:
h.update( long_to_bytes(s) if isinstance(s, (long, int)) else s )
return long( h.hexdigest(), 16 )
N = 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
g = 2;
k = H(N,g)
hN = hashlib.sha256( long_to_bytes(N) ).digest()
hg = hashlib.sha256( long_to_bytes(g) ).digest()
HNxorg = ''.join( chr( ord(hN[i]) ^ ord(hg[i]) ) for i in range(0,len(hN)) )
def gen_x( salt, username, password ):
return H( salt, H( username + ':' + password ) )
def gen_sv( username, password ):
_s = long_to_bytes( get_random( 4 ) )
_v = long_to_bytes( pow(g, gen_x( _s, username, password ), N) )
return _s, _v
def calculate_M( I, s, A, B, K ):
h = hashlib.sha256()
h.update( HNxorg )
h.update( hashlib.sha256(I).digest() )
h.update( long_to_bytes(s) )
h.update( long_to_bytes(A) )
h.update( long_to_bytes(B) )
h.update( K )
return h.digest()
def calculate_H_AMK( A, M, K ):
h = hashlib.sha256()
h.update( long_to_bytes(A) )
h.update( M )
h.update( K )
return h.digest()
class Verifier (object):
def __init__(self, username, bytes_s, bytes_v, bytes_A):
self.s = bytes_to_long(bytes_s)
self.v = bytes_to_long(bytes_v)
self.I = username
self.K = None
self._authenticated = False
self.A = bytes_to_long(bytes_A)
# SRP-6a safety check
self.safety_failed = self.A % N == 0
if not self.safety_failed:
self.b = get_random( 32 )
self.B = (k*self.v + pow(g, self.b, N)) % N
self.u = H(self.A, self.B)
self.S = pow(self.A*pow(self.v, self.u, N ), self.b, N)
self.K = hashlib.sha256( long_to_bytes(self.S) ).digest()
self.M = calculate_M( self.I, self.s, self.A, self.B, self.K )
self.H_AMK = calculate_H_AMK(self.A, self.M, self.K)
def authenticated(self):
return self._authenticated
def get_username(self):
return self.I
def get_session_key(self):
return self.K if self._authenticated else None
# returns (bytes_s, bytes_B) on success, (None,None) if SRP-6a safety check fails
def get_challenge(self):
if self.safety_failed:
return None,None
else:
return (long_to_bytes(self.s), long_to_bytes(self.B))
# returns H_AMK on success, None on failure
def verify_session(self, user_M):
if not self.safety_failed and user_M == self.M:
self._authenticated = True
return self.H_AMK
class User (object):
def __init__(self, username, password):
self.I = username
self.p = password
self.a = get_random( 32 )
self.A = pow(g, self.a, N)
self.v = None
self.M = None
self.K = None
self.H_AMK = None
self._authenticated = False
def authenticated(self):
return self._authenticated
def get_username(self):
return self.username
def get_session_key(self):
return self.K if self._authenticated else None
def start_authentication(self):
return (self.I, long_to_bytes(self.A))
# Returns M or None if SRP-6a safety check is violated
def process_challenge(self, bytes_s, bytes_B):
self.s = bytes_to_long( bytes_s )
self.B = bytes_to_long( bytes_B )
# SRP-6a safety check
if (self.B % N) == 0:
return None
self.u = H( self.A, self.B )
# SRP-6a safety check
if self.u == 0:
return None
self.x = gen_x( self.s, self.I, self.p )
self.v = pow(g, self.x, N)
self.S = pow((self.B - k*self.v), (self.a + self.u*self.x), N)
self.K = hashlib.sha256( long_to_bytes(self.S) ).digest()
self.M = calculate_M( self.I, self.s, self.A, self.B, self.K )
self.H_AMK = calculate_H_AMK(self.A, self.M, self.K)
return self.M
def verify_session(self, host_HAMK):
if self.H_AMK == host_HAMK:
self._authenticated = True
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