# 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 SHA1 = 0 SHA224 = 1 SHA256 = 2 SHA384 = 3 SHA512 = 4 NG_1024 = 0 NG_2048 = 1 NG_4096 = 2 NG_8192 = 3 NG_CUSTOM = 4 _hash_map = { SHA1 : hashlib.sha1, SHA224 : hashlib.sha224, SHA256 : hashlib.sha256, SHA384 : hashlib.sha384, SHA512 : hashlib.sha512 } _ng_const = ( # 1024-bit ('''\ EEAF0AB9ADB38DD69C33F80AFA8FC5E86072618775FF3C0B9EA2314C9C256576D674DF7496\ EA81D3383B4813D692C6E0E0D5D8E250B98BE48E495C1D6089DAD15DC7D7B46154D6B6CE8E\ F4AD69B15D4982559B297BCF1885C529F566660E57EC68EDBC3C05726CC02FD4CBF4976EAA\ 9AFD5138FE8376435B9FC61D2FC0EB06E3''', "2"), # 2048 ('''\ AC6BDB41324A9A9BF166DE5E1389582FAF72B6651987EE07FC3192943DB56050A37329CBB4\ A099ED8193E0757767A13DD52312AB4B03310DCD7F48A9DA04FD50E8083969EDB767B0CF60\ 95179A163AB3661A05FBD5FAAAE82918A9962F0B93B855F97993EC975EEAA80D740ADBF4FF\ 747359D041D5C33EA71D281E446B14773BCA97B43A23FB801676BD207A436C6481F1D2B907\ 8717461A5B9D32E688F87748544523B524B0D57D5EA77A2775D2ECFA032CFBDBF52FB37861\ 60279004E57AE6AF874E7303CE53299CCC041C7BC308D82A5698F3A8D0C38271AE35F8E9DB\ FBB694B5C803D89F7AE435DE236D525F54759B65E372FCD68EF20FA7111F9E4AFF73''', "2"), # 4096 ('''\ FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E08\ 8A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B\ 302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9\ A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE6\ 49286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A69163FA8\ FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D\ 670C354E4ABC9804F1746C08CA18217C32905E462E36CE3BE39E772C\ 180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718\ 3995497CEA956AE515D2261898FA051015728E5A8AAAC42DAD33170D\ 04507A33A85521ABDF1CBA64ECFB850458DBEF0A8AEA71575D060C7D\ B3970F85A6E1E4C7ABF5AE8CDB0933D71E8C94E04A25619DCEE3D226\ 1AD2EE6BF12FFA06D98A0864D87602733EC86A64521F2B18177B200C\ BBE117577A615D6C770988C0BAD946E208E24FA074E5AB3143DB5BFC\ E0FD108E4B82D120A92108011A723C12A787E6D788719A10BDBA5B26\ 99C327186AF4E23C1A946834B6150BDA2583E9CA2AD44CE8DBBBC2DB\ 04DE8EF92E8EFC141FBECAA6287C59474E6BC05D99B2964FA090C3A2\ 233BA186515BE7ED1F612970CEE2D7AFB81BDD762170481CD0069127\ D5B05AA993B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934063199\ FFFFFFFFFFFFFFFF''', "5"), # 8192 ('''\ FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E08\ 8A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B\ 302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9\ A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE6\ 49286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A69163FA8\ FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D\ 670C354E4ABC9804F1746C08CA18217C32905E462E36CE3BE39E772C\ 180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718\ 3995497CEA956AE515D2261898FA051015728E5A8AAAC42DAD33170D\ 04507A33A85521ABDF1CBA64ECFB850458DBEF0A8AEA71575D060C7D\ B3970F85A6E1E4C7ABF5AE8CDB0933D71E8C94E04A25619DCEE3D226\ 1AD2EE6BF12FFA06D98A0864D87602733EC86A64521F2B18177B200C\ BBE117577A615D6C770988C0BAD946E208E24FA074E5AB3143DB5BFC\ E0FD108E4B82D120A92108011A723C12A787E6D788719A10BDBA5B26\ 99C327186AF4E23C1A946834B6150BDA2583E9CA2AD44CE8DBBBC2DB\ 04DE8EF92E8EFC141FBECAA6287C59474E6BC05D99B2964FA090C3A2\ 233BA186515BE7ED1F612970CEE2D7AFB81BDD762170481CD0069127\ D5B05AA993B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492\ 36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BDF8FF9406\ AD9E530EE5DB382F413001AEB06A53ED9027D831179727B0865A8918\ DA3EDBEBCF9B14ED44CE6CBACED4BB1BDB7F1447E6CC254B33205151\ 2BD7AF426FB8F401378CD2BF5983CA01C64B92ECF032EA15D1721D03\ F482D7CE6E74FEF6D55E702F46980C82B5A84031900B1C9E59E7C97F\ BEC7E8F323A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA\ CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE32806A1D58B\ B7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55CDA56C9EC2EF29632\ 387FE8D76E3C0468043E8F663F4860EE12BF2D5B0B7474D6E694F91E\ 6DBE115974A3926F12FEE5E438777CB6A932DF8CD8BEC4D073B931BA\ 3BC832B68D9DD300741FA7BF8AFC47ED2576F6936BA424663AAB639C\ 5AE4F5683423B4742BF1C978238F16CBE39D652DE3FDB8BEFC848AD9\ 22222E04A4037C0713EB57A81A23F0C73473FC646CEA306B4BCBC886\ 2F8385DDFA9D4B7FA2C087E879683303ED5BDD3A062B3CF5B3A278A6\ 6D2A13F83F44F82DDF310EE074AB6A364597E899A0255DC164F31CC5\ 0846851DF9AB48195DED7EA1B1D510BD7EE74D73FAF36BC31ECFA268\ 359046F4EB879F924009438B481C6CD7889A002ED5EE382BC9190DA6\ FC026E479558E4475677E9AA9E3050E2765694DFC81F56E880B96E71\ 60C980DD98EDD3DFFFFFFFFFFFFFFFFF''', '0x13') ) def get_ng( ng_type, n_hex, g_hex ): if ng_type < NG_CUSTOM: n_hex, g_hex = _ng_const[ ng_type ] return int(n_hex,16), int(g_hex,16) 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( hash_class, 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(hash_class(s).hexdigest(), 16) def H( hash_class, *args, **kwargs ): h = hash_class() 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) def HNxorg( hash_class, N, g ): hN = hash_class( long_to_bytes(N) ).digest() hg = hash_class( long_to_bytes(g) ).digest() return ''.join( chr( ord(hN[i]) ^ ord(hg[i]) ) for i in range(0,len(hN)) ) def gen_x( hash_class, salt, username, password ): return H( hash_class, salt, H( hash_class, username + ':' + password ) ) def create_salted_verification_key( username, password, hash_alg=SHA1, ng_type=NG_2048, n_hex=None, g_hex=None ): if ng_type == NG_CUSTOM and (n_hex is None or g_hex is None): raise ValueError("Both n_hex and g_hex are required when ng_type = NG_CUSTOM") hash_class = _hash_map[ hash_alg ] N,g = get_ng( ng_type, n_hex, g_hex ) _s = long_to_bytes( get_random( 4 ) ) _v = long_to_bytes( pow(g, gen_x( hash_class, _s, username, password ), N) ) return _s, _v def calculate_M( hash_class, N, g, I, s, A, B, K ): h = hash_class() h.update( HNxorg( hash_class, N, g ) ) h.update( hash_class(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( hash_class, A, M, K ): h = hash_class() 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, hash_alg=SHA1, ng_type=NG_2048, n_hex=None, g_hex=None): if ng_type == NG_CUSTOM and (n_hex is None or g_hex is None): raise ValueError("Both n_hex and g_hex are required when ng_type = NG_CUSTOM") self.s = bytes_to_long(bytes_s) self.v = bytes_to_long(bytes_v) self.I = username self.K = None self._authenticated = False N,g = get_ng( ng_type, n_hex, g_hex ) hash_class = _hash_map[ hash_alg ] k = H( hash_class, N, g ) self.hash_class = hash_class self.N = N self.g = g self.k = k 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(hash_class, self.A, self.B) self.S = pow(self.A*pow(self.v, self.u, N ), self.b, N) self.K = hash_class( long_to_bytes(self.S) ).digest() self.M = calculate_M( hash_class, N, g, self.I, self.s, self.A, self.B, self.K ) self.H_AMK = calculate_H_AMK( hash_class, 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, hash_alg=SHA1, ng_type=NG_2048, n_hex=None, g_hex=None): if ng_type == NG_CUSTOM and (n_hex is None or g_hex is None): raise ValueError("Both n_hex and g_hex are required when ng_type = NG_CUSTOM") N,g = get_ng( ng_type, n_hex, g_hex ) hash_class = _hash_map[ hash_alg ] k = H( hash_class, N, g ) 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 self.hash_class = hash_class self.N = N self.g = g self.k = 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 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 ) N = self.N g = self.g k = self.k hash_class = self.hash_class # SRP-6a safety check if (self.B % N) == 0: return None self.u = H( hash_class, self.A, self.B ) # SRP-6a safety check if self.u == 0: return None self.x = gen_x( hash_class, 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 = hash_class( long_to_bytes(self.S) ).digest() self.M = calculate_M( hash_class, N, g, self.I, self.s, self.A, self.B, self.K ) self.H_AMK = calculate_H_AMK(hash_class, self.A, self.M, self.K) return self.M def verify_session(self, host_HAMK): if self.H_AMK == host_HAMK: self._authenticated = True