text:   # 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 math
  import os
  import binascii
  import six
  
  
  _rfc5054_compat = False
  
  def rfc5054_enable(enable=True):
      global _rfc5054_compat
      _rfc5054_compat = enable
  
  
  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 = 0
      for b in six.iterbytes(s):
          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 six.b(''.join(l))
  
  
  def hex_to_long(s):
      return int(s, 16)
  
  
  def long_to_hex(n):
      return hex(n)[2:]
  
  
  def get_random( nbytes ):
      return bytes_to_long( os.urandom( nbytes ) )
  
  
  def get_random_of_length( nbytes ):
      offset = (nbytes*8) - 1
      return get_random( nbytes ) | (1 << offset)
  
  
  def H( hash_class, *args, **kwargs ):
      width = kwargs.get('width', None)
      
      h = hash_class()
  
      for s in args:
          if s is not None:
              data = long_to_bytes(s) if isinstance(s, six.integer_types) else s
              if width is not None and _rfc5054_compat:
                  h.update( bytes(width - len(data)))
              h.update( data )
  
      return int( h.hexdigest(), 16 )
  
  
  def gen_x( hash_class, salt, username, password ):
      username = username.encode() if hasattr(username, 'encode') else username
      password = password.encode() if hasattr(password, 'encode') else password
      return H( hash_class, salt, H( hash_class, username + six.b(':') + password ) )
  
  
  def calculate_M(hash_class, A, B, S):
      h = hash_class()
  
      h.update( A )
      h.update( B )
      h.update( S )
      return h.hexdigest().lstrip("0")
  
  
  class Verifier (object):
      def __init__(self, bytes_s, bytes_v, bytes_A, hash_alg=SHA1, ng_type=NG_2048, n_hex=None, g_hex=None, bytes_b=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")
  
          if bytes_b and len(bytes_b) != 32:
              raise ValueError("32 bytes required for bytes_b")
  
          self.s = bytes_to_long(bytes_s)
          self.v = bytes_to_long(bytes_v)
          self._authenticated = False
  
          N,g        = get_ng( ng_type, n_hex, g_hex )
          width = math.ceil(math.log2(N))
          hash_class = _hash_map[ hash_alg ]
          k          = H( hash_class, N, g, width=width )
  
          self.hash_class = hash_class
          self.N          = N
          self.g          = g
          self.k          = k
  
          self.A = bytes_to_long(bytes_A)
          self.AA = long_to_hex(self.A).encode("utf-8")
  
          # SRP-6a safety check
          self.safety_failed = self.A % N == 0
  
          if not self.safety_failed:
              if bytes_b:
                  self.b = bytes_to_long(bytes_b)
              else:
                  self.b = get_random_of_length( 32 )
  
              self.B = (k*self.v + pow(g, self.b, N)) % N
              self.BB = long_to_hex(self.B).encode("utf-8")
  
              self.u = H(hash_class, self.AA, self.BB, width=width)
  
              self.S = long_to_hex(pow(self.A*pow(self.v, self.u, N), self.b, N)).encode("utf-8")
              self.M = calculate_M(hash_class, self.AA, self.BB, self.S)
  
  
      def authenticated(self):
          return self._authenticated
  
  
      def get_ephemeral_secret(self):
          return long_to_bytes(self.b)
  
  
      # 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_hex(self.s), long_to_hex(self.B))
  
  
      def verify_session(self, user_M):
          if not self.safety_failed and user_M == self.M:
              self._authenticated = True
              return True
  
          return False
  