1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
|
# 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
|