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diff --git a/_pysrp.py b/_pysrp.py
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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