bombe.py

   1 import string
   2 import collections
   3 import multiprocessing
   4 import itertools
   5 import logging
   6
   7 from szyfrow.enigma import *
   8
   9
  10 ##################################
  11 # # Bombe
  12 ##################################
  13 #
  14 # Good explanation of [how the bombe worked](http://www.ellsbury.com/enigmabombe.htm) by Graham Ellsbury
  15 #
  16
  17 Signal = collections.namedtuple('Signal', ['bank', 'wire'])
  18 Connection = collections.namedtuple('Connection', ['banks', 'scrambler'])
  19 MenuItem = collections.namedtuple('MenuIem', ['before', 'after', 'number'])
  20
  21
  22 def make_menu(plaintext, ciphertext):
  23     return [MenuItem(p, c, i+1)
  24             for i, (p, c) in enumerate(zip(plaintext, ciphertext))]
  25
  26
  27 class Scrambler(object):
  28     def __init__(self, wheel1_spec, wheel2_spec, wheel3_spec, reflector_spec,
  29                  wheel1_pos='a', wheel2_pos='a', wheel3_pos='a'):
  30         self.wheel1 = SimpleWheel(wheel1_spec, position=wheel1_pos)
  31         self.wheel2 = SimpleWheel(wheel2_spec, position=wheel2_pos)
  32         self.wheel3 = SimpleWheel(wheel3_spec, position=wheel3_pos)
  33         self.reflector = Reflector(reflector_spec)
  34
  35     def __getattribute__(self, name):
  36         if name=='wheel_positions':
  37             return self.wheel1.position, self.wheel2.position, self.wheel3.position
  38         elif name=='wheel_positions_l':
  39             return self.wheel1.position_l, self.wheel2.position_l, self.wheel3.position_l
  40         else:
  41             return object.__getattribute__(self, name)
  42
  43     def advance(self, wheel1=False, wheel2=False, wheel3=True):
  44         if wheel1: self.wheel1.advance()
  45         if wheel2: self.wheel2.advance()
  46         if wheel3: self.wheel3.advance()
  47
  48     def lookup(self, letter):
  49         a = self.wheel3.forward(letter)
  50         b = self.wheel2.forward(a)
  51         c = self.wheel1.forward(b)
  52         d = self.reflector.forward(c)
  53         e = self.wheel1.backward(d)
  54         f = self.wheel2.backward(e)
  55         g = self.wheel3.backward(f)
  56         return g
  57
  58     def set_positions(self, wheel1_pos, wheel2_pos, wheel3_pos):
  59         self.wheel1.set_position(wheel1_pos)
  60         self.wheel2.set_position(wheel2_pos)
  61         self.wheel3.set_position(wheel3_pos)
  62
  63
  64 class Bombe(object):
  65
  66     def __init__(self, wheel1_spec, wheel2_spec, wheel3_spec, reflector_spec,
  67                 menu=None, start_signal=None, use_diagonal_board=True,
  68                 verify_plugboard=True):
  69         self.connections = []
  70         self.wheel1_spec = wheel1_spec
  71         self.wheel2_spec = wheel2_spec
  72         self.wheel3_spec = wheel3_spec
  73         self.reflector_spec = reflector_spec
  74         if menu:
  75             self.read_menu(menu)
  76         if start_signal:
  77             self.test_start = start_signal
  78         self.use_diagonal_board = use_diagonal_board
  79         self.verify_plugboard = verify_plugboard
  80
  81     def __getattribute__(self, name):
  82         if name=='wheel_positions':
  83             return self.connections[0].scrambler.wheel_positions
  84         elif name=='wheel_positions_l':
  85             return self.connections[0].scrambler.wheel_positions_l
  86         else:
  87             return object.__getattribute__(self, name)
  88
  89     def __call__(self, start_positions):
  90         return start_positions, self.test(initial_signal=self.test_start,
  91             start_positions=start_positions,
  92             use_diagonal_board=self.use_diagonal_board,
  93             verify_plugboard=self.verify_plugboard)
  94
  95     def add_connection(self, bank_before, bank_after, scrambler):
  96         self.connections += [Connection([bank_before, bank_after], scrambler)]
  97
  98     def read_menu(self, menu):
  99         self.connections = []
 100         for item in menu:
 101             scrambler = Scrambler(self.wheel1_spec, self.wheel2_spec, self.wheel3_spec,
 102                                   self.reflector_spec,
 103                                   wheel3_pos=unpos(item.number - 1))
 104             self.add_connection(item.before, item.after, scrambler)
 105         most_common_letter = (collections.Counter(m.before for m in menu) +\
 106             collections.Counter(m.after for m in menu)).most_common(1)[0][0]
 107         self.test_start = Signal(most_common_letter, most_common_letter)
 108
 109     def set_positions(self, wheel1_pos, wheel2_pos, wheel3_pos):
 110         for i, c in enumerate(self.connections):
 111             c.scrambler.set_positions(wheel1_pos, wheel2_pos, unpos(pos(wheel3_pos) + i))
 112
 113     def test(self, initial_signal=None, start_positions=None, use_diagonal_board=True,
 114             verify_plugboard=True):
 115         self.banks = {label:
 116                       dict(zip(string.ascii_lowercase, [False]*len(string.ascii_lowercase)))
 117                       for label in string.ascii_lowercase}
 118         if start_positions:
 119             self.set_positions(*start_positions)
 120         if not initial_signal:
 121             initial_signal = self.test_start
 122         self.pending = [initial_signal]
 123         self.propagate(use_diagonal_board)
 124         live_wire_count = len([self.banks[self.test_start.bank][w]
 125                     for w in self.banks[self.test_start.bank]
 126                     if self.banks[self.test_start.bank][w]])
 127         if live_wire_count < 26:
 128             if verify_plugboard:
 129                 possibles = self.possible_plugboards()
 130                 return all(s0.isdisjoint(s1) for s0 in possibles for s1 in possibles if s0 != s1)
 131             else:
 132                 return True
 133         else:
 134             return False
 135
 136     def propagate(self, use_diagonal_board):
 137         while self.pending:
 138             current = self.pending[0]
 139             # print("processing", current)
 140             self.pending = self.pending[1:]
 141             if not self.banks[current.bank][current.wire]:
 142                 self.banks[current.bank][current.wire] = True
 143                 if use_diagonal_board:
 144                     self.pending += [Signal(current.wire, current.bank)]
 145                 for c in self.connections:
 146                     if current.bank in c.banks:
 147                         other_bank = [b for b in c.banks if b != current.bank][0]
 148                         other_wire = c.scrambler.lookup(current.wire)
 149                         # print("  adding", other_bank, other_wire, "because", c.banks)
 150                         self.pending += [Signal(other_bank, other_wire)]
 151
 152     def run(self, run_start=None, wheel1_pos='a', wheel2_pos='a', wheel3_pos='a', use_diagonal_board=True):
 153         if not run_start:
 154             run_start = self.test_start
 155         self.solutions = []
 156         self.set_positions(wheel1_pos, wheel2_pos, wheel3_pos)
 157         for run_index in range(26*26*26):
 158             if self.test(initial_signal=run_start, use_diagonal_board=use_diagonal_board):
 159                 self.solutions += [self.connections[0].scrambler.wheel_positions_l]
 160             advance3 = True
 161             advance2 = False
 162             advance1 = False
 163             if (run_index + 1) % 26 == 0: advance2 = True
 164             if (run_index + 1) % (26*26) == 0: advance1 = True
 165             for c in self.connections:
 166                 c.scrambler.advance(advance1, advance2, advance3)
 167         return self.solutions
 168
 169     def possible_plugboards(self):
 170         possibles = set()
 171         for b in self.banks:
 172             active = [w for w in self.banks[b] if self.banks[b][w]]
 173             inactive = [w for w in self.banks[b] if not self.banks[b][w]]
 174             if len(active) == 1:
 175                 possibles = possibles.union({frozenset((b, active[0]))})
 176             if len(inactive) == 1:
 177                 possibles = possibles.union({frozenset((b, inactive[0]))})
 178         return possibles
 179
 180
 181 def run_multi_bombe(wheel1_spec, wheel2_spec, wheel3_spec, reflector_spec, menu,
 182                     start_signal=None, use_diagonal_board=True,
 183                     verify_plugboard=True):
 184     allwheels = itertools.product(string.ascii_lowercase, repeat=3)
 185
 186     with multiprocessing.Pool() as pool:
 187         res = pool.map(Bombe(wheel1_spec, wheel2_spec, wheel3_spec,
 188             reflector_spec, menu=menu, start_signal=start_signal,
 189             use_diagonal_board=use_diagonal_board,
 190             verify_plugboard=verify_plugboard),
 191                   allwheels)
 192     return [r[0] for r in res if r[1]]