bombe.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "code",
   5    "execution_count": 1,
   6    "metadata": {
   7     "collapsed": true
   8    },
   9    "outputs": [],
  10    "source": [
  11     "import string\n",
  12     "import collections\n",
  13     "import multiprocessing\n",
  14     "import itertools\n",
  15     "from enigma import *"
  16    ]
  17   },
  18   {
  19    "cell_type": "code",
  20    "execution_count": 2,
  21    "metadata": {
  22     "collapsed": true
  23    },
  24    "outputs": [],
  25    "source": [
  26     "Signal = collections.namedtuple('Signal', ['bank', 'wire'])\n",
  27     "Connection = collections.namedtuple('Connection', ['banks', 'scrambler'])\n",
  28     "MenuItem = collections.namedtuple('MenuIem', ['before', 'after', 'number'])"
  29    ]
  30   },
  31   {
  32    "cell_type": "code",
  33    "execution_count": 3,
  34    "metadata": {
  35     "collapsed": true
  36    },
  37    "outputs": [],
  38    "source": [
  39     "class Scrambler(object):\n",
  40     "    def __init__(self, wheel1_spec, wheel2_spec, wheel3_spec, reflector_spec,\n",
  41     "                 wheel1_pos='a', wheel2_pos='a', wheel3_pos='a'):\n",
  42     "        self.wheel1 = SimpleWheel(wheel1_spec, position=wheel1_pos)\n",
  43     "        self.wheel2 = SimpleWheel(wheel2_spec, position=wheel2_pos)\n",
  44     "        self.wheel3 = SimpleWheel(wheel3_spec, position=wheel3_pos)\n",
  45     "        self.reflector = Reflector(reflector_spec)\n",
  46     "    \n",
  47     "    def __getattribute__(self, name):\n",
  48     "        if name=='wheel_positions':\n",
  49     "            return self.wheel1.position, self.wheel2.position, self.wheel3.position \n",
  50     "        elif name=='wheel_positions_l':\n",
  51     "            return self.wheel1.position_l, self.wheel2.position_l, self.wheel3.position_l \n",
  52     "        else:\n",
  53     "            return object.__getattribute__(self, name)\n",
  54     "    \n",
  55     "    def advance(self, wheel1=False, wheel2=False, wheel3=True):\n",
  56     "        if wheel1: self.wheel1.advance()\n",
  57     "        if wheel2: self.wheel2.advance()\n",
  58     "        if wheel3: self.wheel3.advance()\n",
  59     "            \n",
  60     "    def lookup(self, letter):\n",
  61     "        a = self.wheel3.forward(letter)\n",
  62     "        b = self.wheel2.forward(a)\n",
  63     "        c = self.wheel1.forward(b)\n",
  64     "        d = self.reflector.forward(c)\n",
  65     "        e = self.wheel1.backward(d)\n",
  66     "        f = self.wheel2.backward(e)\n",
  67     "        g = self.wheel3.backward(f)\n",
  68     "        return g\n",
  69     "    \n",
  70     "    def set_positions(self, wheel1_pos, wheel2_pos, wheel3_pos):\n",
  71     "        self.wheel1.set_position(wheel1_pos)\n",
  72     "        self.wheel2.set_position(wheel2_pos)\n",
  73     "        self.wheel3.set_position(wheel3_pos)        "
  74    ]
  75   },
  76   {
  77    "cell_type": "code",
  78    "execution_count": 4,
  79    "metadata": {
  80     "collapsed": true
  81    },
  82    "outputs": [],
  83    "source": [
  84     "class Bombe(object):\n",
  85     "    \n",
  86     "    def __init__(self, wheel1_spec, wheel2_spec, wheel3_spec, reflector_spec,\n",
  87     "                menu=None, start_signal=None, use_diagonal_board=True, \n",
  88     "                verify_plugboard=True):\n",
  89     "        self.connections = []\n",
  90     "        self.wheel1_spec = wheel1_spec\n",
  91     "        self.wheel2_spec = wheel2_spec\n",
  92     "        self.wheel3_spec = wheel3_spec\n",
  93     "        self.reflector_spec = reflector_spec\n",
  94     "        if menu:\n",
  95     "            self.read_menu(menu)\n",
  96     "        if start_signal:\n",
  97     "            self.test_start = start_signal\n",
  98     "        self.use_diagonal_board = use_diagonal_board\n",
  99     "        self.verify_plugboard = verify_plugboard\n",
 100     "        \n",
 101     "    def __getattribute__(self, name):\n",
 102     "        if name=='wheel_positions':\n",
 103     "            return self.connections[0].scrambler.wheel_positions\n",
 104     "        elif name=='wheel_positions_l':\n",
 105     "            return self.connections[0].scrambler.wheel_positions_l\n",
 106     "        else:\n",
 107     "            return object.__getattribute__(self, name)\n",
 108     "        \n",
 109     "    def __call__(self, start_positions):\n",
 110     "        return start_positions, self.test(initial_signal=self.test_start,\n",
 111     "            start_positions=start_positions, \n",
 112     "            use_diagonal_board=self.use_diagonal_board,\n",
 113     "            verify_plugboard=self.verify_plugboard)\n",
 114     "        \n",
 115     "    def add_connection(self, bank_before, bank_after, scrambler):\n",
 116     "        self.connections += [Connection([bank_before, bank_after], scrambler)]\n",
 117     "        \n",
 118     "    def read_menu(self, menu):\n",
 119     "        self.connections = []\n",
 120     "        for item in menu:\n",
 121     "            scrambler = Scrambler(self.wheel1_spec, self.wheel2_spec, self.wheel3_spec,\n",
 122     "                                  self.reflector_spec,\n",
 123     "                                  wheel3_pos=unpos(item.number - 1))\n",
 124     "            self.add_connection(item.before, item.after, scrambler)\n",
 125     "        most_common_letter = (collections.Counter(m.before for m in menu) + \\\n",
 126     "                              collections.Counter(m.after for m in menu)).most_common(1)[0][0]\n",
 127     "        self.test_start = Signal(most_common_letter, most_common_letter)\n",
 128     "        \n",
 129     "    def set_positions(self, wheel1_pos, wheel2_pos, wheel3_pos):\n",
 130     "        for i, c in enumerate(self.connections):\n",
 131     "            c.scrambler.set_positions(wheel1_pos, wheel2_pos, unpos(pos(wheel3_pos) + i))\n",
 132     "    \n",
 133     "    def test(self, initial_signal=None, start_positions=None, use_diagonal_board=True,\n",
 134     "            verify_plugboard=True):\n",
 135     "        self.banks = {label: \n",
 136     "                      dict(zip(string.ascii_lowercase, [False]*len(string.ascii_lowercase)))\n",
 137     "                      for label in string.ascii_lowercase}\n",
 138     "        if start_positions:\n",
 139     "            self.set_positions(*start_positions)\n",
 140     "        if not initial_signal:\n",
 141     "            initial_signal = self.test_start\n",
 142     "        self.pending = [initial_signal]\n",
 143     "        self.propagate(use_diagonal_board)\n",
 144     "        live_wire_count = len([self.banks[self.test_start.bank][w] \n",
 145     "                    for w in self.banks[self.test_start.bank] \n",
 146     "                    if self.banks[self.test_start.bank][w]])\n",
 147     "        if live_wire_count < 26:\n",
 148     "            if verify_plugboard:\n",
 149     "                possibles = self.possible_plugboards()\n",
 150     "                return all(s0.isdisjoint(s1) for s0 in possibles for s1 in possibles if s0 != s1)\n",
 151     "            else:\n",
 152     "                return True\n",
 153     "        else:\n",
 154     "            return False\n",
 155     "        \n",
 156     "    def propagate(self, use_diagonal_board):\n",
 157     "        while self.pending:\n",
 158     "            current = self.pending[0]\n",
 159     "            # print(\"processing\", current)\n",
 160     "            self.pending = self.pending[1:]\n",
 161     "            if not self.banks[current.bank][current.wire]:\n",
 162     "                self.banks[current.bank][current.wire] = True\n",
 163     "                if use_diagonal_board:\n",
 164     "                    self.pending += [Signal(current.wire, current.bank)]\n",
 165     "                for c in self.connections:\n",
 166     "                    if current.bank in c.banks:\n",
 167     "                        if len(set(c.banks)) == 1:\n",
 168     "                            other_bank = c.banks[0]\n",
 169     "                        else:\n",
 170     "                            other_bank = [b for b in c.banks if b != current.bank][0]\n",
 171     "                        other_wire = c.scrambler.lookup(current.wire)\n",
 172     "                        # print(\"  adding\", other_bank, other_wire, \"because\", c.banks)\n",
 173     "                        self.pending += [Signal(other_bank, other_wire)]\n",
 174     "    \n",
 175     "    def run(self, run_start=None, wheel1_pos='a', wheel2_pos='a', wheel3_pos='a', use_diagonal_board=True):\n",
 176     "        if not run_start:\n",
 177     "            run_start = self.test_start\n",
 178     "        self.solutions = []\n",
 179     "        self.set_positions(wheel1_pos, wheel2_pos, wheel3_pos)\n",
 180     "        for run_index in range(26*26*26):\n",
 181     "            if self.test(initial_signal=run_start, use_diagonal_board=use_diagonal_board):\n",
 182     "                self.solutions += [self.connections[0].scrambler.wheel_positions_l]\n",
 183     "            advance3 = True\n",
 184     "            advance2 = False\n",
 185     "            advance1 = False\n",
 186     "            if (run_index + 1) % 26 == 0: advance2 = True\n",
 187     "            if (run_index + 1) % (26*26) == 0: advance1 = True\n",
 188     "            for c in self.connections:\n",
 189     "                c.scrambler.advance(advance1, advance2, advance3)\n",
 190     "        return self.solutions\n",
 191     "    \n",
 192     "    def possible_plugboards(self):\n",
 193     "        possibles = set()\n",
 194     "        for b in self.banks:\n",
 195     "            active = [w for w in self.banks[b] if self.banks[b][w]]\n",
 196     "            inactive = [w for w in self.banks[b] if not self.banks[b][w]]\n",
 197     "            if len(active) == 1:\n",
 198     "                possibles = possibles.union({frozenset((b, active[0]))})\n",
 199     "            if len(inactive) == 1:\n",
 200     "                possibles = possibles.union({frozenset((b, inactive[0]))})\n",
 201     "        return possibles\n"
 202    ]
 203   },
 204   {
 205    "cell_type": "code",
 206    "execution_count": 5,
 207    "metadata": {
 208     "collapsed": true
 209    },
 210    "outputs": [],
 211    "source": [
 212     "bombe = Bombe(wheel_i_spec, wheel_ii_spec, wheel_iii_spec, reflector_b_spec)\n",
 213     "# len(bombe.banks), bombe.banks['a'] == bombe.banks['b']"
 214    ]
 215   },
 216   {
 217    "cell_type": "code",
 218    "execution_count": 6,
 219    "metadata": {
 220     "collapsed": true
 221    },
 222    "outputs": [],
 223    "source": [
 224     "test_enigma = Enigma(reflector_b_spec, \n",
 225     "                wheel_i_spec, wheel_i_pegs,\n",
 226     "                wheel_ii_spec, wheel_ii_pegs,\n",
 227     "                wheel_iii_spec, wheel_iii_pegs,\n",
 228     "                1, 1, 1,\n",
 229     "                '')"
 230    ]
 231   },
 232   {
 233    "cell_type": "code",
 234    "execution_count": 7,
 235    "metadata": {},
 236    "outputs": [
 237     {
 238      "data": {
 239       "text/plain": [
 240        "'opgndxcrwomnlnecjz'"
 241       ]
 242      },
 243      "execution_count": 7,
 244      "metadata": {},
 245      "output_type": "execute_result"
 246     }
 247    ],
 248    "source": [
 249     "test_enigma.set_wheels('a', 'a', 'a')\n",
 250     "pt = 'thisisatestmessage'\n",
 251     "ct = test_enigma.encipher(pt)\n",
 252     "ct"
 253    ]
 254   },
 255   {
 256    "cell_type": "code",
 257    "execution_count": 8,
 258    "metadata": {},
 259    "outputs": [
 260     {
 261      "data": {
 262       "text/plain": [
 263        "'aas'"
 264       ]
 265      },
 266      "execution_count": 8,
 267      "metadata": {},
 268      "output_type": "execute_result"
 269     }
 270    ],
 271    "source": [
 272     "cat(test_enigma.wheel_positions_l)"
 273    ]
 274   },
 275   {
 276    "cell_type": "code",
 277    "execution_count": 9,
 278    "metadata": {},
 279    "outputs": [
 280     {
 281      "data": {
 282       "text/plain": [
 283        "[MenuIem(before='t', after='o', number=1),\n",
 284        " MenuIem(before='h', after='p', number=2),\n",
 285        " MenuIem(before='i', after='g', number=3),\n",
 286        " MenuIem(before='s', after='n', number=4),\n",
 287        " MenuIem(before='i', after='d', number=5),\n",
 288        " MenuIem(before='s', after='x', number=6),\n",
 289        " MenuIem(before='a', after='c', number=7),\n",
 290        " MenuIem(before='t', after='r', number=8),\n",
 291        " MenuIem(before='e', after='w', number=9),\n",
 292        " MenuIem(before='s', after='o', number=10),\n",
 293        " MenuIem(before='t', after='m', number=11),\n",
 294        " MenuIem(before='m', after='n', number=12),\n",
 295        " MenuIem(before='e', after='l', number=13),\n",
 296        " MenuIem(before='s', after='n', number=14),\n",
 297        " MenuIem(before='s', after='e', number=15),\n",
 298        " MenuIem(before='a', after='c', number=16),\n",
 299        " MenuIem(before='g', after='j', number=17),\n",
 300        " MenuIem(before='e', after='z', number=18)]"
 301       ]
 302      },
 303      "execution_count": 9,
 304      "metadata": {},
 305      "output_type": "execute_result"
 306     }
 307    ],
 308    "source": [
 309     "menu = [MenuItem(p, c, i+1) for i, (p, c) in enumerate(zip(pt, ct))]\n",
 310     "menu"
 311    ]
 312   },
 313   {
 314    "cell_type": "code",
 315    "execution_count": 10,
 316    "metadata": {
 317     "collapsed": true
 318    },
 319    "outputs": [],
 320    "source": [
 321     "def make_menu(plaintext, ciphertext):\n",
 322     "    return [MenuItem(p, c, i+1) \n",
 323     "            for i, (p, c) in enumerate(zip(plaintext, ciphertext))]"
 324    ]
 325   },
 326   {
 327    "cell_type": "code",
 328    "execution_count": 11,
 329    "metadata": {},
 330    "outputs": [
 331     {
 332      "data": {
 333       "text/plain": [
 334        "[MenuIem(before='t', after='o', number=1),\n",
 335        " MenuIem(before='h', after='p', number=2),\n",
 336        " MenuIem(before='i', after='g', number=3),\n",
 337        " MenuIem(before='s', after='n', number=4),\n",
 338        " MenuIem(before='i', after='d', number=5),\n",
 339        " MenuIem(before='s', after='x', number=6),\n",
 340        " MenuIem(before='a', after='c', number=7),\n",
 341        " MenuIem(before='t', after='r', number=8),\n",
 342        " MenuIem(before='e', after='w', number=9),\n",
 343        " MenuIem(before='s', after='o', number=10),\n",
 344        " MenuIem(before='t', after='m', number=11),\n",
 345        " MenuIem(before='m', after='n', number=12),\n",
 346        " MenuIem(before='e', after='l', number=13),\n",
 347        " MenuIem(before='s', after='n', number=14),\n",
 348        " MenuIem(before='s', after='e', number=15),\n",
 349        " MenuIem(before='a', after='c', number=16),\n",
 350        " MenuIem(before='g', after='j', number=17),\n",
 351        " MenuIem(before='e', after='z', number=18)]"
 352       ]
 353      },
 354      "execution_count": 11,
 355      "metadata": {},
 356      "output_type": "execute_result"
 357     }
 358    ],
 359    "source": [
 360     "make_menu(pt, ct)"
 361    ]
 362   },
 363   {
 364    "cell_type": "code",
 365    "execution_count": 12,
 366    "metadata": {},
 367    "outputs": [
 368     {
 369      "data": {
 370       "text/plain": [
 371        "'s'"
 372       ]
 373      },
 374      "execution_count": 12,
 375      "metadata": {},
 376      "output_type": "execute_result"
 377     }
 378    ],
 379    "source": [
 380     "(collections.Counter(m.before for m in menu) + collections.Counter(m.after for m in menu)).most_common(1)[0][0]"
 381    ]
 382   },
 383   {
 384    "cell_type": "code",
 385    "execution_count": 13,
 386    "metadata": {
 387     "collapsed": true
 388    },
 389    "outputs": [],
 390    "source": [
 391     "bombe.read_menu(menu)"
 392    ]
 393   },
 394   {
 395    "cell_type": "code",
 396    "execution_count": 14,
 397    "metadata": {},
 398    "outputs": [
 399     {
 400      "data": {
 401       "text/plain": [
 402        "18"
 403       ]
 404      },
 405      "execution_count": 14,
 406      "metadata": {},
 407      "output_type": "execute_result"
 408     }
 409    ],
 410    "source": [
 411     "len(bombe.connections)"
 412    ]
 413   },
 414   {
 415    "cell_type": "code",
 416    "execution_count": 15,
 417    "metadata": {},
 418    "outputs": [
 419     {
 420      "name": "stdout",
 421      "output_type": "stream",
 422      "text": [
 423       "['t', 'o'] aaa\n",
 424       "['h', 'p'] aab\n",
 425       "['i', 'g'] aac\n",
 426       "['s', 'n'] aad\n",
 427       "['i', 'd'] aae\n",
 428       "['s', 'x'] aaf\n",
 429       "['a', 'c'] aag\n",
 430       "['t', 'r'] aah\n",
 431       "['e', 'w'] aai\n",
 432       "['s', 'o'] aaj\n",
 433       "['t', 'm'] aak\n",
 434       "['m', 'n'] aal\n",
 435       "['e', 'l'] aam\n",
 436       "['s', 'n'] aan\n",
 437       "['s', 'e'] aao\n",
 438       "['a', 'c'] aap\n",
 439       "['g', 'j'] aaq\n",
 440       "['e', 'z'] aar\n"
 441      ]
 442     }
 443    ],
 444    "source": [
 445     "for c in bombe.connections:\n",
 446     "    print(c.banks, cat(c.scrambler.wheel_positions_l))"
 447    ]
 448   },
 449   {
 450    "cell_type": "code",
 451    "execution_count": 16,
 452    "metadata": {},
 453    "outputs": [
 454     {
 455      "data": {
 456       "text/plain": [
 457        "'ot:hp:gi:ns:di:sx:ac:rt:ew:os:mt:mn:el:ns:es:ac:gj:ez'"
 458       ]
 459      },
 460      "execution_count": 16,
 461      "metadata": {},
 462      "output_type": "execute_result"
 463     }
 464    ],
 465    "source": [
 466     "':'.join(cat(sorted(c.banks)) for c in bombe.connections)"
 467    ]
 468   },
 469   {
 470    "cell_type": "code",
 471    "execution_count": 17,
 472    "metadata": {},
 473    "outputs": [
 474     {
 475      "data": {
 476       "text/plain": [
 477        "'aaa:aab:aac:aad:aae:aaf:aag:aah:aai:aaj:aak:aal:aam:aan:aao:aap:aaq:aar'"
 478       ]
 479      },
 480      "execution_count": 17,
 481      "metadata": {},
 482      "output_type": "execute_result"
 483     }
 484    ],
 485    "source": [
 486     "':'.join(cat(c.scrambler.wheel_positions_l) for c in bombe.connections)"
 487    ]
 488   },
 489   {
 490    "cell_type": "code",
 491    "execution_count": 18,
 492    "metadata": {},
 493    "outputs": [
 494     {
 495      "data": {
 496       "text/plain": [
 497        "False"
 498       ]
 499      },
 500      "execution_count": 18,
 501      "metadata": {},
 502      "output_type": "execute_result"
 503     }
 504    ],
 505    "source": [
 506     "bombe.test(Signal('t', 't'))"
 507    ]
 508   },
 509   {
 510    "cell_type": "code",
 511    "execution_count": 19,
 512    "metadata": {},
 513    "outputs": [
 514     {
 515      "data": {
 516       "text/plain": [
 517        "{'a': True,\n",
 518        " 'b': True,\n",
 519        " 'c': True,\n",
 520        " 'd': True,\n",
 521        " 'e': True,\n",
 522        " 'f': True,\n",
 523        " 'g': True,\n",
 524        " 'h': True,\n",
 525        " 'i': True,\n",
 526        " 'j': True,\n",
 527        " 'k': True,\n",
 528        " 'l': True,\n",
 529        " 'm': True,\n",
 530        " 'n': True,\n",
 531        " 'o': True,\n",
 532        " 'p': True,\n",
 533        " 'q': True,\n",
 534        " 'r': True,\n",
 535        " 's': True,\n",
 536        " 't': True,\n",
 537        " 'u': True,\n",
 538        " 'v': True,\n",
 539        " 'w': True,\n",
 540        " 'x': True,\n",
 541        " 'y': True,\n",
 542        " 'z': True}"
 543       ]
 544      },
 545      "execution_count": 19,
 546      "metadata": {},
 547      "output_type": "execute_result"
 548     }
 549    ],
 550    "source": [
 551     "bombe.banks['t']"
 552    ]
 553   },
 554   {
 555    "cell_type": "code",
 556    "execution_count": 20,
 557    "metadata": {},
 558    "outputs": [
 559     {
 560      "name": "stdout",
 561      "output_type": "stream",
 562      "text": [
 563       "a : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 564       "b : AbCDEfGHIJkLMNOPqRSTuvWXyZ\n",
 565       "c : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 566       "d : ABCDEFGHIJKLMNOPQRSTUVWXyZ\n",
 567       "e : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 568       "f : AbCDEfGHIJkLMNOPqRSTuvWXyZ\n",
 569       "g : ABCDEFGHIJKLMNOPQRSTuVWXYZ\n",
 570       "h : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 571       "i : ABCDEFGHIJKLMNOPQRSTUvWXYZ\n",
 572       "j : ABCDEFGHIjKLMNOPQRSTUVWXYZ\n",
 573       "k : AbCDEfGHIJkLMNOPqRSTuvWXyZ\n",
 574       "l : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 575       "m : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 576       "n : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 577       "o : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 578       "p : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 579       "q : AbCDEfGHIJkLMNOPqRSTuvWXyZ\n",
 580       "r : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 581       "s : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 582       "t : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 583       "u : AbCDEfgHIJkLMNOPqRSTuvWXyZ\n",
 584       "v : AbCDEfGHiJkLMNOPqRSTuvWXyZ\n",
 585       "w : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 586       "x : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 587       "y : AbCdEfGHIJkLMNOPqRSTuvWXyZ\n",
 588       "z : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n"
 589      ]
 590     }
 591    ],
 592    "source": [
 593     "for b in sorted(bombe.banks):\n",
 594     "    print(b, ': ', end='')\n",
 595     "    for w in sorted(bombe.banks[b]):\n",
 596     "        if bombe.banks[b][w]:\n",
 597     "            print(w.upper(), end='')\n",
 598     "        else:\n",
 599     "            print(w, end='')\n",
 600     "    print('')"
 601    ]
 602   },
 603   {
 604    "cell_type": "code",
 605    "execution_count": 21,
 606    "metadata": {},
 607    "outputs": [
 608     {
 609      "name": "stdout",
 610      "output_type": "stream",
 611      "text": [
 612       "a : abcdefghijklmnopqrstuvwxyz\n",
 613       "b : a.cde.ghij.lmnop.rst..wx.z\n",
 614       "c : abcdefghijklmnopqrstuvwxyz\n",
 615       "d : abcdefghijklmnopqrstuvwx.z\n",
 616       "e : abcdefghijklmnopqrstuvwxyz\n",
 617       "f : a.cde.ghij.lmnop.rst..wx.z\n",
 618       "g : abcdefghijklmnopqrst.vwxyz\n",
 619       "h : abcdefghijklmnopqrstuvwxyz\n",
 620       "i : abcdefghijklmnopqrstu.wxyz\n",
 621       "j : abcdefghi.klmnopqrstuvwxyz\n",
 622       "k : a.cde.ghij.lmnop.rst..wx.z\n",
 623       "l : abcdefghijklmnopqrstuvwxyz\n",
 624       "m : abcdefghijklmnopqrstuvwxyz\n",
 625       "n : abcdefghijklmnopqrstuvwxyz\n",
 626       "o : abcdefghijklmnopqrstuvwxyz\n",
 627       "p : abcdefghijklmnopqrstuvwxyz\n",
 628       "q : a.cde.ghij.lmnop.rst..wx.z\n",
 629       "r : abcdefghijklmnopqrstuvwxyz\n",
 630       "s : abcdefghijklmnopqrstuvwxyz\n",
 631       "t : abcdefghijklmnopqrstuvwxyz\n",
 632       "u : a.cde..hij.lmnop.rst..wx.z\n",
 633       "v : a.cde.gh.j.lmnop.rst..wx.z\n",
 634       "w : abcdefghijklmnopqrstuvwxyz\n",
 635       "x : abcdefghijklmnopqrstuvwxyz\n",
 636       "y : a.c.e.ghij.lmnop.rst..wx.z\n",
 637       "z : abcdefghijklmnopqrstuvwxyz\n"
 638      ]
 639     }
 640    ],
 641    "source": [
 642     "for b in sorted(bombe.banks):\n",
 643     "    print(b, ': ', end='')\n",
 644     "    for w in sorted(bombe.banks[b]):\n",
 645     "        if bombe.banks[b][w]:\n",
 646     "            print(w, end='')\n",
 647     "        else:\n",
 648     "            print('.', end='')\n",
 649     "    print('')"
 650    ]
 651   },
 652   {
 653    "cell_type": "code",
 654    "execution_count": 22,
 655    "metadata": {},
 656    "outputs": [
 657     {
 658      "data": {
 659       "text/plain": [
 660        "('a', 'a', 'a')"
 661       ]
 662      },
 663      "execution_count": 22,
 664      "metadata": {},
 665      "output_type": "execute_result"
 666     }
 667    ],
 668    "source": [
 669     "bombe.wheel_positions_l"
 670    ]
 671   },
 672   {
 673    "cell_type": "code",
 674    "execution_count": 23,
 675    "metadata": {},
 676    "outputs": [
 677     {
 678      "name": "stdout",
 679      "output_type": "stream",
 680      "text": [
 681       "['t', 'o'] pqr\n",
 682       "['h', 'p'] pqs\n",
 683       "['i', 'g'] pqt\n",
 684       "['s', 'n'] pqu\n",
 685       "['i', 'd'] pqv\n",
 686       "['s', 'x'] pqw\n",
 687       "['a', 'c'] pqx\n",
 688       "['t', 'r'] pqy\n",
 689       "['e', 'w'] pqz\n",
 690       "['s', 'o'] pqa\n",
 691       "['t', 'm'] pqb\n",
 692       "['m', 'n'] pqc\n",
 693       "['e', 'l'] pqd\n",
 694       "['s', 'n'] pqe\n",
 695       "['s', 'e'] pqf\n",
 696       "['a', 'c'] pqg\n",
 697       "['g', 'j'] pqh\n",
 698       "['e', 'z'] pqi\n"
 699      ]
 700     }
 701    ],
 702    "source": [
 703     "bombe.set_positions('p', 'q', 'r')\n",
 704     "for c in bombe.connections:\n",
 705     "    print(c.banks, cat(c.scrambler.wheel_positions_l))"
 706    ]
 707   },
 708   {
 709    "cell_type": "code",
 710    "execution_count": 24,
 711    "metadata": {
 712     "collapsed": true
 713    },
 714    "outputs": [],
 715    "source": [
 716     "# bombe.run()\n",
 717     "# print('x')"
 718    ]
 719   },
 720   {
 721    "cell_type": "code",
 722    "execution_count": 25,
 723    "metadata": {},
 724    "outputs": [
 725     {
 726      "name": "stdout",
 727      "output_type": "stream",
 728      "text": [
 729       "a : .b.defghijklmnopqrstuvwxyz\n",
 730       "b : a.cde.ghij.lmnop.rst..wx.z\n",
 731       "c : .b.defghijklmnopqrstuvwxyz\n",
 732       "d : abc.e.gh.jklmnopqrstuvwxyz\n",
 733       "e : abcd.fghijklmnopqrstuvwxyz\n",
 734       "f : a.c.e.g.ij.lmno..rst..wx.z\n",
 735       "g : abcdef.h..klmnopqrstuvwxyz\n",
 736       "h : abcde.g.ij.lmno.qrst..wxyz\n",
 737       "i : abc.ef.h.jklmnopqrstuvwxyz\n",
 738       "j : abcdef.hi.klmnopqrstuvwx.z\n",
 739       "k : a.cde.g.ij.lmno..rst..wx.z\n",
 740       "l : abcdefghijk.mnopqrstuvwxyz\n",
 741       "m : abcdefghijkl.nopqrstuvwxyz\n",
 742       "n : abcdefghijklm.opqrstuvwxyz\n",
 743       "o : abcdefghijklmn.pqrstuvwxyz\n",
 744       "p : abcde.g.ij.lmno.qrst..wxyz\n",
 745       "q : a.cde.ghij.lmnop.rst..wx.z\n",
 746       "r : abcdefghijklmnopq.stuvwxyz\n",
 747       "s : abcdefghijklmnopqr.tuvwxyz\n",
 748       "t : abcdefghijklmnopqrs.uvwxyz\n",
 749       "u : a.cde.g.ij.lmno..rst..wx.z\n",
 750       "v : a.cde.g.ij.lmno..rst..wx.z\n",
 751       "w : abcdefghijklmnopqrstuv.xyz\n",
 752       "x : abcdefghijklmnopqrstuvw.yz\n",
 753       "y : a.cde.ghi..lmnop.rst..wx.z\n",
 754       "z : abcdefghijklmnopqrstuvwxy.\n"
 755      ]
 756     }
 757    ],
 758    "source": [
 759     "bombe.set_positions('a', 'a', 'b')\n",
 760     "bombe.test(Signal('s', 'a'))\n",
 761     "\n",
 762     "for b in sorted(bombe.banks):\n",
 763     "    print(b, ': ', end='')\n",
 764     "    for w in sorted(bombe.banks[b]):\n",
 765     "        if bombe.banks[b][w]:\n",
 766     "            print(w, end='')\n",
 767     "        else:\n",
 768     "            print('.', end='')\n",
 769     "    print('')"
 770    ]
 771   },
 772   {
 773    "cell_type": "code",
 774    "execution_count": 26,
 775    "metadata": {},
 776    "outputs": [
 777     {
 778      "name": "stdout",
 779      "output_type": "stream",
 780      "text": [
 781       "a : ..........................\n",
 782       "b : ..........................\n",
 783       "c : ..........................\n",
 784       "d : ..........................\n",
 785       "e : ....e.....................\n",
 786       "f : ..........................\n",
 787       "g : ..........................\n",
 788       "h : ..........................\n",
 789       "i : ..........................\n",
 790       "j : ..........................\n",
 791       "k : ..........................\n",
 792       "l : ...........l..............\n",
 793       "m : ............m.............\n",
 794       "n : .............n............\n",
 795       "o : ..............o...........\n",
 796       "p : ..........................\n",
 797       "q : ..........................\n",
 798       "r : .................r........\n",
 799       "s : ..................s.......\n",
 800       "t : ...................t......\n",
 801       "u : ..........................\n",
 802       "v : ..........................\n",
 803       "w : ......................w...\n",
 804       "x : .......................x..\n",
 805       "y : ..........................\n",
 806       "z : .........................z\n"
 807      ]
 808     }
 809    ],
 810    "source": [
 811     "bombe.set_positions('a', 'a', 'b')\n",
 812     "bombe.test()\n",
 813     "\n",
 814     "for b in sorted(bombe.banks):\n",
 815     "    print(b, ': ', end='')\n",
 816     "    for w in sorted(bombe.banks[b]):\n",
 817     "        if bombe.banks[b][w]:\n",
 818     "            print(w, end='')\n",
 819     "        else:\n",
 820     "            print('.', end='')\n",
 821     "    print('')"
 822    ]
 823   },
 824   {
 825    "cell_type": "code",
 826    "execution_count": 27,
 827    "metadata": {},
 828    "outputs": [
 829     {
 830      "data": {
 831       "text/plain": [
 832        "1"
 833       ]
 834      },
 835      "execution_count": 27,
 836      "metadata": {},
 837      "output_type": "execute_result"
 838     }
 839    ],
 840    "source": [
 841     "len([bombe.banks['t'][w] for w in bombe.banks['t'] if bombe.banks['t'][w]])"
 842    ]
 843   },
 844   {
 845    "cell_type": "code",
 846    "execution_count": 28,
 847    "metadata": {
 848     "collapsed": true
 849    },
 850    "outputs": [],
 851    "source": [
 852     "# %%timeit\n",
 853     "# results = bombe.run()\n",
 854     "# print(len(results), ('a', 'a', 'b') in results)"
 855    ]
 856   },
 857   {
 858    "cell_type": "code",
 859    "execution_count": 29,
 860    "metadata": {
 861     "collapsed": true
 862    },
 863    "outputs": [],
 864    "source": [
 865     "# %%timeit\n",
 866     "# results = bombe.run(use_diagonal_board=False)\n",
 867     "# print(len(results), ('a', 'a', 'b') in results)"
 868    ]
 869   },
 870   {
 871    "cell_type": "code",
 872    "execution_count": 30,
 873    "metadata": {},
 874    "outputs": [
 875     {
 876      "data": {
 877       "text/plain": [
 878        "('a', 'a', 'b')"
 879       ]
 880      },
 881      "execution_count": 30,
 882      "metadata": {},
 883      "output_type": "execute_result"
 884     }
 885    ],
 886    "source": [
 887     "bombe.wheel_positions_l"
 888    ]
 889   },
 890   {
 891    "cell_type": "code",
 892    "execution_count": 31,
 893    "metadata": {},
 894    "outputs": [
 895     {
 896      "data": {
 897       "text/plain": [
 898        "False"
 899       ]
 900      },
 901      "execution_count": 31,
 902      "metadata": {},
 903      "output_type": "execute_result"
 904     }
 905    ],
 906    "source": [
 907     "bombe.test(Signal('t', 't'), ('p', 'p', 'p'))"
 908    ]
 909   },
 910   {
 911    "cell_type": "code",
 912    "execution_count": 32,
 913    "metadata": {},
 914    "outputs": [
 915     {
 916      "data": {
 917       "text/plain": [
 918        "('p', 'p', 'p')"
 919       ]
 920      },
 921      "execution_count": 32,
 922      "metadata": {},
 923      "output_type": "execute_result"
 924     }
 925    ],
 926    "source": [
 927     "bombe.wheel_positions_l"
 928    ]
 929   },
 930   {
 931    "cell_type": "code",
 932    "execution_count": 33,
 933    "metadata": {},
 934    "outputs": [
 935     {
 936      "name": "stdout",
 937      "output_type": "stream",
 938      "text": [
 939       "a : abcdefghijklmnop.rst.vwxyz\n",
 940       "b : a.cde.g.ij.lmno..rst..wx.z\n",
 941       "c : abcdefghijklmnop.rst.vwxyz\n",
 942       "d : abcdefghijklmnopqrstuvwxyz\n",
 943       "e : abcdefghijklmnopqrstuvwxyz\n",
 944       "f : a.cde.g.ij.lmno..rst..wx.z\n",
 945       "g : abcdefghijklmnopqrstuvwxyz\n",
 946       "h : a.cde.ghijklmnop.rst.vwxyz\n",
 947       "i : abcdefghijklmnopqrstuvwxyz\n",
 948       "j : abcdefghijklmnopqrstuvwxyz\n",
 949       "k : a.cde.ghij.lmnop.rst..wx.z\n",
 950       "l : abcdefghijklmnopqrstuvwxyz\n",
 951       "m : abcdefghijklmnopqrstuvwxyz\n",
 952       "n : abcdefghijklmnopqrstuvwxyz\n",
 953       "o : abcdefghijklmnopqrstuvwxyz\n",
 954       "p : a.cde.ghijklmnop.rst.vwxyz\n",
 955       "q : ...de.g.ij.lmno..rst..wx.z\n",
 956       "r : abcdefghijklmnopqrstuvwxyz\n",
 957       "s : abcdefghijklmnopqrstuvwxyz\n",
 958       "t : abcdefghijklmnopqrstuvwxyz\n",
 959       "u : ...de.g.ij.lmno..rst..wx.z\n",
 960       "v : a.cde.ghij.lmnop.rst..wx.z\n",
 961       "w : abcdefghijklmnopqrstuvwxyz\n",
 962       "x : abcdefghijklmnopqrstuvwxyz\n",
 963       "y : a.cde.ghij.lmnop.rst..wx.z\n",
 964       "z : abcdefghijklmnopqrstuvwxyz\n"
 965      ]
 966     }
 967    ],
 968    "source": [
 969     "for b in sorted(bombe.banks):\n",
 970     "    print(b, ': ', end='')\n",
 971     "    for w in sorted(bombe.banks[b]):\n",
 972     "        if bombe.banks[b][w]:\n",
 973     "            print(w, end='')\n",
 974     "        else:\n",
 975     "            print('.', end='')\n",
 976     "    print('')"
 977    ]
 978   },
 979   {
 980    "cell_type": "code",
 981    "execution_count": 34,
 982    "metadata": {},
 983    "outputs": [
 984     {
 985      "data": {
 986       "text/plain": [
 987        "17576"
 988       ]
 989      },
 990      "execution_count": 34,
 991      "metadata": {},
 992      "output_type": "execute_result"
 993     }
 994    ],
 995    "source": [
 996     "allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
 997     "len(list(allwheels))"
 998    ]
 999   },
1000   {
1001    "cell_type": "code",
1002    "execution_count": 35,
1003    "metadata": {},
1004    "outputs": [
1005     {
1006      "data": {
1007       "text/plain": [
1008        "(('a', 'a', 'b'), True)"
1009       ]
1010      },
1011      "execution_count": 35,
1012      "metadata": {},
1013      "output_type": "execute_result"
1014     }
1015    ],
1016    "source": [
1017     "b = Bombe(wheel_i_spec, wheel_ii_spec, wheel_iii_spec, reflector_b_spec, menu=menu)\n",
1018     "b(('a', 'a', 'b'))"
1019    ]
1020   },
1021   {
1022    "cell_type": "code",
1023    "execution_count": 36,
1024    "metadata": {
1025     "collapsed": true
1026    },
1027    "outputs": [],
1028    "source": [
1029     "b = Bombe(wheel_i_spec, wheel_ii_spec, wheel_iii_spec, reflector_b_spec, menu=menu)(('a', 'a', 'b'))"
1030    ]
1031   },
1032   {
1033    "cell_type": "code",
1034    "execution_count": 37,
1035    "metadata": {},
1036    "outputs": [
1037     {
1038      "data": {
1039       "text/plain": [
1040        "[('a', 'a', 'b')]"
1041       ]
1042      },
1043      "execution_count": 37,
1044      "metadata": {},
1045      "output_type": "execute_result"
1046     }
1047    ],
1048    "source": [
1049     "allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1050     "\n",
1051     "with multiprocessing.Pool() as pool:\n",
1052     "    res = pool.map(Bombe(wheel_i_spec, wheel_ii_spec, wheel_iii_spec, reflector_b_spec, menu=menu),\n",
1053     "                  allwheels)\n",
1054     "[r[0] for r in res if r[1]]"
1055    ]
1056   },
1057   {
1058    "cell_type": "code",
1059    "execution_count": 38,
1060    "metadata": {
1061     "collapsed": true
1062    },
1063    "outputs": [],
1064    "source": [
1065     "def run_multi_bombe(wheel1_spec, wheel2_spec, wheel3_spec, reflector_spec, menu,\n",
1066     "                    start_signal=None, use_diagonal_board=True, \n",
1067     "                    verify_plugboard=True):\n",
1068     "    allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1069     "\n",
1070     "    with multiprocessing.Pool() as pool:\n",
1071     "        res = pool.map(Bombe(wheel1_spec, wheel2_spec, wheel3_spec, \n",
1072     "            reflector_spec, menu=menu, start_signal=start_signal, \n",
1073     "            use_diagonal_board=use_diagonal_board, \n",
1074     "            verify_plugboard=verify_plugboard),\n",
1075     "                  allwheels)\n",
1076     "    return [r[0] for r in res if r[1]]"
1077    ]
1078   },
1079   {
1080    "cell_type": "code",
1081    "execution_count": 39,
1082    "metadata": {},
1083    "outputs": [
1084     {
1085      "data": {
1086       "text/plain": [
1087        "[('a', 'a', 'b')]"
1088       ]
1089      },
1090      "execution_count": 39,
1091      "metadata": {},
1092      "output_type": "execute_result"
1093     }
1094    ],
1095    "source": [
1096     "[r[0] for r in res if r[1]]"
1097    ]
1098   },
1099   {
1100    "cell_type": "code",
1101    "execution_count": 40,
1102    "metadata": {
1103     "collapsed": true
1104    },
1105    "outputs": [],
1106    "source": [
1107     "# Setting sheet line 31 from http://www.codesandciphers.org.uk/enigma/enigma3.htm\n",
1108     "# Enigma simulation settings are \n",
1109     "# http://enigma.louisedade.co.uk/enigma.html?m3;b;b153;AFTX;AJFE;AU-BG-EY-FP-HL-IN-JZ-OS-QR-TX\n",
1110     "w_enigma = Enigma(reflector_b_spec, \n",
1111     "                wheel_i_spec, wheel_i_pegs,\n",
1112     "                wheel_v_spec, wheel_v_pegs,\n",
1113     "                wheel_iii_spec, wheel_iii_pegs,\n",
1114     "                6, 20, 24,\n",
1115     "                'ua pf rq so ni ey bg hl tx zj')"
1116    ]
1117   },
1118   {
1119    "cell_type": "code",
1120    "execution_count": 41,
1121    "metadata": {},
1122    "outputs": [
1123     {
1124      "data": {
1125       "text/plain": [
1126        "('e', 'l', 'e')"
1127       ]
1128      },
1129      "execution_count": 41,
1130      "metadata": {},
1131      "output_type": "execute_result"
1132     }
1133    ],
1134    "source": [
1135     "w_enigma.set_wheels('j', 'e', 'b')\n",
1136     "tuple(unpos(p) for p in w_enigma.wheel_positions)"
1137    ]
1138   },
1139   {
1140    "cell_type": "code",
1141    "execution_count": 42,
1142    "metadata": {},
1143    "outputs": [
1144     {
1145      "data": {
1146       "text/plain": [
1147        "'dhnpforeeimgg'"
1148       ]
1149      },
1150      "execution_count": 42,
1151      "metadata": {},
1152      "output_type": "execute_result"
1153     }
1154    ],
1155    "source": [
1156     "w_enigma.set_wheels('j', 'e', 'b')\n",
1157     "pt = 'someplaintext'\n",
1158     "ct = w_enigma.encipher(pt)\n",
1159     "ct"
1160    ]
1161   },
1162   {
1163    "cell_type": "code",
1164    "execution_count": 43,
1165    "metadata": {},
1166    "outputs": [
1167     {
1168      "data": {
1169       "text/plain": [
1170        "('j', 'e', 'o')"
1171       ]
1172      },
1173      "execution_count": 43,
1174      "metadata": {},
1175      "output_type": "execute_result"
1176     }
1177    ],
1178    "source": [
1179     "w_enigma.wheel_positions_l"
1180    ]
1181   },
1182   {
1183    "cell_type": "code",
1184    "execution_count": 44,
1185    "metadata": {},
1186    "outputs": [
1187     {
1188      "data": {
1189       "text/plain": [
1190        "[MenuIem(before='s', after='d', number=1),\n",
1191        " MenuIem(before='o', after='h', number=2),\n",
1192        " MenuIem(before='m', after='n', number=3),\n",
1193        " MenuIem(before='e', after='p', number=4),\n",
1194        " MenuIem(before='p', after='f', number=5),\n",
1195        " MenuIem(before='l', after='o', number=6),\n",
1196        " MenuIem(before='a', after='r', number=7),\n",
1197        " MenuIem(before='i', after='e', number=8),\n",
1198        " MenuIem(before='n', after='e', number=9),\n",
1199        " MenuIem(before='t', after='i', number=10),\n",
1200        " MenuIem(before='e', after='m', number=11),\n",
1201        " MenuIem(before='x', after='g', number=12),\n",
1202        " MenuIem(before='t', after='g', number=13)]"
1203       ]
1204      },
1205      "execution_count": 44,
1206      "metadata": {},
1207      "output_type": "execute_result"
1208     }
1209    ],
1210    "source": [
1211     "w_menu = [MenuItem(p, c, i+1) for i, (p, c) in enumerate(zip(pt, ct))]\n",
1212     "w_menu"
1213    ]
1214   },
1215   {
1216    "cell_type": "code",
1217    "execution_count": 45,
1218    "metadata": {
1219     "scrolled": true
1220    },
1221    "outputs": [
1222     {
1223      "data": {
1224       "text/plain": [
1225        "[('a', 'y', 'm'),\n",
1226        " ('c', 'p', 'v'),\n",
1227        " ('c', 's', 'f'),\n",
1228        " ('c', 'w', 'j'),\n",
1229        " ('d', 'r', 'k'),\n",
1230        " ('e', 'l', 'f'),\n",
1231        " ('e', 's', 'v'),\n",
1232        " ('e', 'y', 'd'),\n",
1233        " ('e', 'y', 'o'),\n",
1234        " ('f', 'z', 'x'),\n",
1235        " ('g', 'b', 'l'),\n",
1236        " ('g', 'c', 'd'),\n",
1237        " ('g', 'c', 'f'),\n",
1238        " ('g', 'j', 'p'),\n",
1239        " ('h', 'c', 'i'),\n",
1240        " ('h', 'm', 'w'),\n",
1241        " ('h', 'o', 'd'),\n",
1242        " ('h', 'p', 'b'),\n",
1243        " ('h', 's', 't'),\n",
1244        " ('i', 'b', 's'),\n",
1245        " ('i', 'v', 'b'),\n",
1246        " ('j', 'y', 'u'),\n",
1247        " ('k', 'b', 'x'),\n",
1248        " ('k', 'f', 't'),\n",
1249        " ('k', 'l', 'e'),\n",
1250        " ('k', 'l', 'm'),\n",
1251        " ('k', 'r', 'z'),\n",
1252        " ('k', 's', 'p'),\n",
1253        " ('l', 'd', 'z'),\n",
1254        " ('l', 'i', 'y'),\n",
1255        " ('l', 'y', 'f'),\n",
1256        " ('m', 'b', 'h'),\n",
1257        " ('m', 'p', 'l'),\n",
1258        " ('n', 'l', 'r'),\n",
1259        " ('o', 'k', 'x'),\n",
1260        " ('p', 'a', 'g'),\n",
1261        " ('p', 'c', 'v'),\n",
1262        " ('p', 'f', 'o'),\n",
1263        " ('p', 'm', 'i'),\n",
1264        " ('p', 'x', 'n'),\n",
1265        " ('p', 'x', 'p'),\n",
1266        " ('q', 'q', 'n'),\n",
1267        " ('q', 'r', 'w'),\n",
1268        " ('q', 'v', 'l'),\n",
1269        " ('q', 'x', 't'),\n",
1270        " ('s', 'a', 'h'),\n",
1271        " ('s', 'h', 'v'),\n",
1272        " ('s', 'l', 'p'),\n",
1273        " ('s', 'l', 's'),\n",
1274        " ('u', 'r', 'h'),\n",
1275        " ('v', 'v', 'v'),\n",
1276        " ('v', 'x', 'a'),\n",
1277        " ('w', 'j', 'z'),\n",
1278        " ('w', 'k', 'u'),\n",
1279        " ('x', 'f', 'p'),\n",
1280        " ('x', 'j', 'n'),\n",
1281        " ('x', 'o', 'q'),\n",
1282        " ('x', 'x', 'x'),\n",
1283        " ('y', 'n', 'c'),\n",
1284        " ('y', 'r', 'f'),\n",
1285        " ('z', 't', 'y'),\n",
1286        " ('z', 'z', 'k')]"
1287       ]
1288      },
1289      "execution_count": 45,
1290      "metadata": {},
1291      "output_type": "execute_result"
1292     }
1293    ],
1294    "source": [
1295     "allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1296     "\n",
1297     "with multiprocessing.Pool() as pool:\n",
1298     "    res = pool.map(Bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, \n",
1299     "                         menu=w_menu, verify_plugboard=False),\n",
1300     "                  allwheels)\n",
1301     "[r[0] for r in res if r[1]]"
1302    ]
1303   },
1304   {
1305    "cell_type": "code",
1306    "execution_count": 46,
1307    "metadata": {},
1308    "outputs": [
1309     {
1310      "data": {
1311       "text/plain": [
1312        "62"
1313       ]
1314      },
1315      "execution_count": 46,
1316      "metadata": {},
1317      "output_type": "execute_result"
1318     }
1319    ],
1320    "source": [
1321     "len([r[0] for r in res if r[1]])"
1322    ]
1323   },
1324   {
1325    "cell_type": "code",
1326    "execution_count": 47,
1327    "metadata": {
1328     "scrolled": true
1329    },
1330    "outputs": [
1331     {
1332      "data": {
1333       "text/plain": [
1334        "[('c', 'p', 'v'),\n",
1335        " ('c', 's', 'f'),\n",
1336        " ('e', 'l', 'f'),\n",
1337        " ('g', 'c', 'f'),\n",
1338        " ('j', 'y', 'u'),\n",
1339        " ('o', 'k', 'x'),\n",
1340        " ('p', 'a', 'g'),\n",
1341        " ('q', 'q', 'n'),\n",
1342        " ('q', 'v', 'l'),\n",
1343        " ('q', 'x', 't'),\n",
1344        " ('s', 'l', 'p'),\n",
1345        " ('u', 'r', 'h'),\n",
1346        " ('y', 'n', 'c')]"
1347       ]
1348      },
1349      "execution_count": 47,
1350      "metadata": {},
1351      "output_type": "execute_result"
1352     }
1353    ],
1354    "source": [
1355     "allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1356     "\n",
1357     "with multiprocessing.Pool() as pool:\n",
1358     "    res = pool.map(Bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, \n",
1359     "                         menu=w_menu, verify_plugboard=True),\n",
1360     "                  allwheels)\n",
1361     "[r[0] for r in res if r[1]]"
1362    ]
1363   },
1364   {
1365    "cell_type": "code",
1366    "execution_count": 48,
1367    "metadata": {},
1368    "outputs": [
1369     {
1370      "data": {
1371       "text/plain": [
1372        "[('c', 'p', 'v'),\n",
1373        " ('c', 's', 'f'),\n",
1374        " ('e', 'l', 'f'),\n",
1375        " ('g', 'c', 'f'),\n",
1376        " ('j', 'y', 'u'),\n",
1377        " ('o', 'k', 'x'),\n",
1378        " ('p', 'a', 'g'),\n",
1379        " ('q', 'q', 'n'),\n",
1380        " ('q', 'v', 'l'),\n",
1381        " ('q', 'x', 't'),\n",
1382        " ('s', 'l', 'p'),\n",
1383        " ('u', 'r', 'h'),\n",
1384        " ('y', 'n', 'c')]"
1385       ]
1386      },
1387      "execution_count": 48,
1388      "metadata": {},
1389      "output_type": "execute_result"
1390     }
1391    ],
1392    "source": [
1393     "run_multi_bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, w_menu)"
1394    ]
1395   },
1396   {
1397    "cell_type": "code",
1398    "execution_count": 49,
1399    "metadata": {
1400     "collapsed": true
1401    },
1402    "outputs": [],
1403    "source": [
1404     "# allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1405     "\n",
1406     "# with multiprocessing.Pool() as pool:\n",
1407     "#     res = pool.map(Bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, \n",
1408     "#                          menu=w_menu, start_signal=Signal('t', 'x')),\n",
1409     "#                   allwheels)\n",
1410     "# [r[0] for r in res if r[1]]"
1411    ]
1412   },
1413   {
1414    "cell_type": "code",
1415    "execution_count": 50,
1416    "metadata": {},
1417    "outputs": [
1418     {
1419      "data": {
1420       "text/plain": [
1421        "13"
1422       ]
1423      },
1424      "execution_count": 50,
1425      "metadata": {},
1426      "output_type": "execute_result"
1427     }
1428    ],
1429    "source": [
1430     "len([r[0] for r in res if r[1]])"
1431    ]
1432   },
1433   {
1434    "cell_type": "code",
1435    "execution_count": 51,
1436    "metadata": {
1437     "collapsed": true
1438    },
1439    "outputs": [],
1440    "source": [
1441     "w_bombe = Bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, \n",
1442     "                         menu=w_menu)"
1443    ]
1444   },
1445   {
1446    "cell_type": "code",
1447    "execution_count": 52,
1448    "metadata": {},
1449    "outputs": [
1450     {
1451      "data": {
1452       "text/plain": [
1453        "Signal(bank='e', wire='e')"
1454       ]
1455      },
1456      "execution_count": 52,
1457      "metadata": {},
1458      "output_type": "execute_result"
1459     }
1460    ],
1461    "source": [
1462     "w_bombe.test_start"
1463    ]
1464   },
1465   {
1466    "cell_type": "code",
1467    "execution_count": 53,
1468    "metadata": {},
1469    "outputs": [
1470     {
1471      "data": {
1472       "text/plain": [
1473        "True"
1474       ]
1475      },
1476      "execution_count": 53,
1477      "metadata": {},
1478      "output_type": "execute_result"
1479     }
1480    ],
1481    "source": [
1482     "w_bombe.test(start_positions=('e', 'l', 'f'))"
1483    ]
1484   },
1485   {
1486    "cell_type": "code",
1487    "execution_count": 54,
1488    "metadata": {},
1489    "outputs": [
1490     {
1491      "data": {
1492       "text/plain": [
1493        "True"
1494       ]
1495      },
1496      "execution_count": 54,
1497      "metadata": {},
1498      "output_type": "execute_result"
1499     }
1500    ],
1501    "source": [
1502     "w_bombe.test(Signal('t', 'x'), ('e', 'l', 'f'))"
1503    ]
1504   },
1505   {
1506    "cell_type": "code",
1507    "execution_count": 55,
1508    "metadata": {},
1509    "outputs": [
1510     {
1511      "name": "stdout",
1512      "output_type": "stream",
1513      "text": [
1514       "True\n",
1515       "a : a.cdefghi..l.nopqrst.vwx..\n",
1516       "b : ....efghi...mnop.......x..\n",
1517       "c : a....fg.i..lmn.p.r.t...x..\n",
1518       "d : a...efghij.lmn...rstu..xyz\n",
1519       "e : ab.defghijklmnopqrstuvwxyz\n",
1520       "f : abcde.ghijklmnopqrstuvwxyz\n",
1521       "g : abcdef.hijklmnopqrstuvwxyz\n",
1522       "h : ab.defghi...mnopq.stuvwx..\n",
1523       "i : abcdefgh.jklmnopqrstuvwxyz\n",
1524       "j : ...defg.i...mn.p...t...x..\n",
1525       "k : ....efg.i..lmnop.r.t...x..\n",
1526       "l : a.cdefg.i.k.mnopqr.t..wxyz\n",
1527       "m : .bcdefghijklmnopqrstuvwxyz\n",
1528       "n : abcdefghijklmnopqr.tuvwxyz\n",
1529       "o : ab..efghi.klmnopqr.t...xyz\n",
1530       "p : abc.efghijklmnopqrstuvwxyz\n",
1531       "q : a...efghi..lmnop.r.t...x..\n",
1532       "r : a.cdefg.i.klmnopqrst..w..z\n",
1533       "s : a..defghi...m..p.rstuv.xyz\n",
1534       "t : a.cdefghijklmnopqrstuvwxyz\n",
1535       "u : ...defghi...mn.p..st...x..\n",
1536       "v : a...efghi...mn.p..st...x..\n",
1537       "w : a...efghi..lmn.p.r.t...x..\n",
1538       "x : abcdefghijklmnopq.stuvwxyz\n",
1539       "y : ...defg.i..lmnop..st...x..\n",
1540       "z : ...defg.i..lmnop.rst...x..\n"
1541      ]
1542     }
1543    ],
1544    "source": [
1545     "r = w_bombe.test(start_positions=('c', 'p', 'v'))\n",
1546     "print(r)\n",
1547     "for b in sorted(w_bombe.banks):\n",
1548     "    print(b, ': ', end='')\n",
1549     "    for w in sorted(w_bombe.banks[b]):\n",
1550     "        if w_bombe.banks[b][w]:\n",
1551     "            print(w, end='')\n",
1552     "        else:\n",
1553     "            print('.', end='')\n",
1554     "    print('')"
1555    ]
1556   },
1557   {
1558    "cell_type": "code",
1559    "execution_count": 56,
1560    "metadata": {},
1561    "outputs": [
1562     {
1563      "name": "stdout",
1564      "output_type": "stream",
1565      "text": [
1566       "True\n",
1567       "a : abcdefghi..lmnop.rst.v.x.z\n",
1568       "b : a...ef.hi..lmnop.r.t...x..\n",
1569       "c : a..defg.i..lmn.p.rst...x..\n",
1570       "d : a.c.efghi.klmnopqrstu.wxyz\n",
1571       "e : abcdefghijklmnopqrstuvwx.z\n",
1572       "f : abcdefghijklmno.qrstuvwxyz\n",
1573       "g : a.cdefghijklmnopqrstuvwxyz\n",
1574       "h : ab.defghi...mnopqrstuvwxyz\n",
1575       "i : abcdefghijklm.opqrstuvwxyz\n",
1576       "j : ....efg.i..lmnop...t...x..\n",
1577       "k : ...defg.i..lmn.p..st...x..\n",
1578       "l : abcdefg.ijklmnopqrstuv.x..\n",
1579       "m : abcdefghijkl.nopqrstuvwxyz\n",
1580       "n : abcdefgh.jklmnopqrstuvwxyz\n",
1581       "o : ab.defghij.lmnop.r.tuvwxyz\n",
1582       "p : abcde.ghijklmnopqrstuvwxyz\n",
1583       "q : ...defghi..lmn.p..st...x..\n",
1584       "r : abcdefghi..lmnop.rst.v.x.z\n",
1585       "s : a.cdefghi.klmn.pqr.tuvwxyz\n",
1586       "t : abcdefghijklmnopqrstuvw.yz\n",
1587       "u : ...defghi..lmnop..st...x..\n",
1588       "v : a...efghi..lmnop.rst...x..\n",
1589       "w : ...defghi...mnop..st...x..\n",
1590       "x : abcdefghijklmnopqrs.uvwxyz\n",
1591       "y : ...d.fghi...mnop..st...x..\n",
1592       "z : a..defghi...mnop.rst...x..\n"
1593      ]
1594     }
1595    ],
1596    "source": [
1597     "r = w_bombe.test(start_positions=('e', 'l', 'f'))\n",
1598     "print(r)\n",
1599     "for b in sorted(w_bombe.banks):\n",
1600     "    print(b, ': ', end='')\n",
1601     "    for w in sorted(w_bombe.banks[b]):\n",
1602     "        if w_bombe.banks[b][w]:\n",
1603     "            print(w, end='')\n",
1604     "        else:\n",
1605     "            print('.', end='')\n",
1606     "    print('')"
1607    ]
1608   },
1609   {
1610    "cell_type": "code",
1611    "execution_count": 57,
1612    "metadata": {},
1613    "outputs": [
1614     {
1615      "data": {
1616       "text/plain": [
1617        "{frozenset({'t', 'x'}),\n",
1618        " frozenset({'i', 'n'}),\n",
1619        " frozenset({'m'}),\n",
1620        " frozenset({'e', 'y'}),\n",
1621        " frozenset({'f', 'p'}),\n",
1622        " frozenset({'b', 'g'})}"
1623       ]
1624      },
1625      "execution_count": 57,
1626      "metadata": {},
1627      "output_type": "execute_result"
1628     }
1629    ],
1630    "source": [
1631     "ps = w_bombe.possible_plugboards()\n",
1632     "ps"
1633    ]
1634   },
1635   {
1636    "cell_type": "code",
1637    "execution_count": 58,
1638    "metadata": {},
1639    "outputs": [
1640     {
1641      "data": {
1642       "text/plain": [
1643        "True"
1644       ]
1645      },
1646      "execution_count": 58,
1647      "metadata": {},
1648      "output_type": "execute_result"
1649     }
1650    ],
1651    "source": [
1652     "all(s0.isdisjoint(s1) for s0 in ps for s1 in ps if s0 != s1)"
1653    ]
1654   },
1655   {
1656    "cell_type": "code",
1657    "execution_count": 59,
1658    "metadata": {},
1659    "outputs": [
1660     {
1661      "data": {
1662       "text/plain": [
1663        "({frozenset({1, 2}), frozenset({2, 3}), frozenset({3, 4})},\n",
1664        " frozenset({1, 2}),\n",
1665        " frozenset({3, 4}),\n",
1666        " frozenset({2, 3}))"
1667       ]
1668      },
1669      "execution_count": 59,
1670      "metadata": {},
1671      "output_type": "execute_result"
1672     }
1673    ],
1674    "source": [
1675     "s = set()\n",
1676     "f1 = frozenset((1, 2))\n",
1677     "f2 = frozenset((3, 4))\n",
1678     "f3 = frozenset((2, 3))\n",
1679     "s = s.union({f1})\n",
1680     "s = s.union({f2})\n",
1681     "s = s.union({f1})\n",
1682     "s = s.union({f3})\n",
1683     "s, f1, f2, f3"
1684    ]
1685   },
1686   {
1687    "cell_type": "code",
1688    "execution_count": 60,
1689    "metadata": {},
1690    "outputs": [
1691     {
1692      "data": {
1693       "text/plain": [
1694        "False"
1695       ]
1696      },
1697      "execution_count": 60,
1698      "metadata": {},
1699      "output_type": "execute_result"
1700     }
1701    ],
1702    "source": [
1703     "all(s0.isdisjoint(s1) for s0 in s for s1 in s if s0 != s1)"
1704    ]
1705   },
1706   {
1707    "cell_type": "code",
1708    "execution_count": 61,
1709    "metadata": {},
1710    "outputs": [
1711     {
1712      "data": {
1713       "text/plain": [
1714        "False"
1715       ]
1716      },
1717      "execution_count": 61,
1718      "metadata": {},
1719      "output_type": "execute_result"
1720     }
1721    ],
1722    "source": [
1723     "{1, 2}.isdisjoint({1, 6})"
1724    ]
1725   },
1726   {
1727    "cell_type": "markdown",
1728    "metadata": {
1729     "collapsed": true
1730    },
1731    "source": [
1732     "# Tsest"
1733    ]
1734   },
1735   {
1736    "cell_type": "code",
1737    "execution_count": 62,
1738    "metadata": {},
1739    "outputs": [
1740     {
1741      "data": {
1742       "text/plain": [
1743        "'slgncszxltkzebghstgywdmpr'"
1744       ]
1745      },
1746      "execution_count": 62,
1747      "metadata": {},
1748      "output_type": "execute_result"
1749     }
1750    ],
1751    "source": [
1752     "target_ct = ''.join(c.lower() for c in 'SLGNC SZXLT KZEBG HSTGY WDMPR' if c in string.ascii_letters)\n",
1753     "target_ct"
1754    ]
1755   },
1756   {
1757    "cell_type": "code",
1758    "execution_count": 63,
1759    "metadata": {},
1760    "outputs": [
1761     {
1762      "data": {
1763       "text/plain": [
1764        "'theyweredetectedbybritishshipsinclud'"
1765       ]
1766      },
1767      "execution_count": 63,
1768      "metadata": {},
1769      "output_type": "execute_result"
1770     }
1771    ],
1772    "source": [
1773     "target_pt = ''.join(c.lower() for c in 'Theyw erede tecte d byBri tishs hipsi nclud' if c in string.ascii_letters)\n",
1774     "target_pt"
1775    ]
1776   },
1777   {
1778    "cell_type": "code",
1779    "execution_count": 64,
1780    "metadata": {},
1781    "outputs": [
1782     {
1783      "data": {
1784       "text/plain": [
1785        "[MenuIem(before='w', after='c', number=1),\n",
1786        " MenuIem(before='e', after='s', number=2),\n",
1787        " MenuIem(before='r', after='z', number=3),\n",
1788        " MenuIem(before='e', after='x', number=4),\n",
1789        " MenuIem(before='d', after='l', number=5),\n",
1790        " MenuIem(before='e', after='t', number=6),\n",
1791        " MenuIem(before='t', after='k', number=7),\n",
1792        " MenuIem(before='e', after='z', number=8),\n",
1793        " MenuIem(before='c', after='e', number=9),\n",
1794        " MenuIem(before='t', after='b', number=10),\n",
1795        " MenuIem(before='e', after='g', number=11),\n",
1796        " MenuIem(before='d', after='h', number=12),\n",
1797        " MenuIem(before='b', after='s', number=13),\n",
1798        " MenuIem(before='y', after='t', number=14),\n",
1799        " MenuIem(before='b', after='g', number=15),\n",
1800        " MenuIem(before='r', after='y', number=16),\n",
1801        " MenuIem(before='i', after='w', number=17),\n",
1802        " MenuIem(before='t', after='d', number=18),\n",
1803        " MenuIem(before='i', after='m', number=19),\n",
1804        " MenuIem(before='s', after='p', number=20)]"
1805       ]
1806      },
1807      "execution_count": 64,
1808      "metadata": {},
1809      "output_type": "execute_result"
1810     }
1811    ],
1812    "source": [
1813     "tbt_menu = [MenuItem(p, c, i+1) for i, (p, c) in enumerate(zip(target_pt[4:24], target_ct[4:24]))]\n",
1814     "tbt_menu"
1815    ]
1816   },
1817   {
1818    "cell_type": "code",
1819    "execution_count": 65,
1820    "metadata": {
1821     "collapsed": true
1822    },
1823    "outputs": [],
1824    "source": [
1825     "tbt_bombe = Bombe(wheel_iii_spec, wheel_i_spec, wheel_ii_spec, reflector_b_spec, \n",
1826     "                         menu=tbt_menu)"
1827    ]
1828   },
1829   {
1830    "cell_type": "code",
1831    "execution_count": 66,
1832    "metadata": {},
1833    "outputs": [
1834     {
1835      "data": {
1836       "text/plain": [
1837        "[('k', 'r', 'n')]"
1838       ]
1839      },
1840      "execution_count": 66,
1841      "metadata": {},
1842      "output_type": "execute_result"
1843     }
1844    ],
1845    "source": [
1846     "tbt_wheel_posns = run_multi_bombe(wheel_iii_spec, wheel_i_spec, wheel_ii_spec, reflector_b_spec, tbt_menu)\n",
1847     "tbt_wheel_posns"
1848    ]
1849   },
1850   {
1851    "cell_type": "code",
1852    "execution_count": 67,
1853    "metadata": {},
1854    "outputs": [
1855     {
1856      "data": {
1857       "text/plain": [
1858        "Signal(bank='e', wire='e')"
1859       ]
1860      },
1861      "execution_count": 67,
1862      "metadata": {},
1863      "output_type": "execute_result"
1864     }
1865    ],
1866    "source": [
1867     "tbt_bombe.test_start"
1868    ]
1869   },
1870   {
1871    "cell_type": "code",
1872    "execution_count": 68,
1873    "metadata": {},
1874    "outputs": [
1875     {
1876      "name": "stdout",
1877      "output_type": "stream",
1878      "text": [
1879       "False\n",
1880       "a : abcdefghi..lmnop.rst.v.x.z\n",
1881       "b : a...ef.hi..lmnop.r.t...x..\n",
1882       "c : a..defg.i..lmn.p.rst...x..\n",
1883       "d : a.c.efghi.klmnopqrstu.wxyz\n",
1884       "e : abcdefghijklmnopqrstuvwx.z\n",
1885       "f : abcdefghijklmno.qrstuvwxyz\n",
1886       "g : a.cdefghijklmnopqrstuvwxyz\n",
1887       "h : ab.defghi...mnopqrstuvwxyz\n",
1888       "i : abcdefghijklm.opqrstuvwxyz\n",
1889       "j : ....efg.i..lmnop...t...x..\n",
1890       "k : ...defg.i..lmn.p..st...x..\n",
1891       "l : abcdefg.ijklmnopqrstuv.x..\n",
1892       "m : abcdefghijkl.nopqrstuvwxyz\n",
1893       "n : abcdefgh.jklmnopqrstuvwxyz\n",
1894       "o : ab.defghij.lmnop.r.tuvwxyz\n",
1895       "p : abcde.ghijklmnopqrstuvwxyz\n",
1896       "q : ...defghi..lmn.p..st...x..\n",
1897       "r : abcdefghi..lmnop.rst.v.x.z\n",
1898       "s : a.cdefghi.klmn.pqr.tuvwxyz\n",
1899       "t : abcdefghijklmnopqrstuvw.yz\n",
1900       "u : ...defghi..lmnop..st...x..\n",
1901       "v : a...efghi..lmnop.rst...x..\n",
1902       "w : ...defghi...mnop..st...x..\n",
1903       "x : abcdefghijklmnopqrs.uvwxyz\n",
1904       "y : ...d.fghi...mnop..st...x..\n",
1905       "z : a..defghi...mnop.rst...x..\n"
1906      ]
1907     }
1908    ],
1909    "source": [
1910     "r = tbt_bombe.test(start_positions=('l', 's', 'd'))\n",
1911     "print(r)\n",
1912     "for b in sorted(w_bombe.banks):\n",
1913     "    print(b, ': ', end='')\n",
1914     "    for w in sorted(w_bombe.banks[b]):\n",
1915     "        if w_bombe.banks[b][w]:\n",
1916     "            print(w, end='')\n",
1917     "        else:\n",
1918     "            print('.', end='')\n",
1919     "    print('')\n"
1920    ]
1921   },
1922   {
1923    "cell_type": "code",
1924    "execution_count": 69,
1925    "metadata": {},
1926    "outputs": [
1927     {
1928      "data": {
1929       "text/plain": [
1930        "set()"
1931       ]
1932      },
1933      "execution_count": 69,
1934      "metadata": {},
1935      "output_type": "execute_result"
1936     }
1937    ],
1938    "source": [
1939     "ps = tbt_bombe.possible_plugboards()\n",
1940     "ps"
1941    ]
1942   },
1943   {
1944    "cell_type": "code",
1945    "execution_count": null,
1946    "metadata": {
1947     "collapsed": true
1948    },
1949    "outputs": [],
1950    "source": []
1951   }
1952  ],
1953  "metadata": {
1954   "kernelspec": {
1955    "display_name": "Python 3",
1956    "language": "python",
1957    "name": "python3"
1958   },
1959   "language_info": {
1960    "codemirror_mode": {
1961     "name": "ipython",
1962     "version": 3
1963    },
1964    "file_extension": ".py",
1965    "mimetype": "text/x-python",
1966    "name": "python",
1967    "nbconvert_exporter": "python",
1968    "pygments_lexer": "ipython3",
1969    "version": "3.5.3"
1970   }
1971  },
1972  "nbformat": 4,
1973  "nbformat_minor": 1
1974 }