bombe.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "code",
   5    "execution_count": 797,
   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": 798,
  21    "metadata": {
  22     "collapsed": true
  23    },
  24    "outputs": [],
  25    "source": [
  26     "# wheel_i_spec = 'ekmflgdqvzntowyhxuspaibrcj'\n",
  27     "# wheel_ii_spec = 'ajdksiruxblhwtmcqgznpyfvoe'\n",
  28     "# wheel_iii_spec = 'bdfhjlcprtxvznyeiwgakmusqo'\n",
  29     "# wheel_iv_spec = 'esovpzjayquirhxlnftgkdcmwb'\n",
  30     "# wheel_v_spec = 'vzbrgityupsdnhlxawmjqofeck'\n",
  31     "# wheel_vi_spec = 'jpgvoumfyqbenhzrdkasxlictw'\n",
  32     "# wheel_vii_spec = 'nzjhgrcxmyswboufaivlpekqdt'\n",
  33     "# wheel_viii_spec = 'fkqhtlxocbjspdzramewniuygv'\n",
  34     "# beta_wheel_spec = 'leyjvcnixwpbqmdrtakzgfuhos'\n",
  35     "# gamma_wheel_spec = 'fsokanuerhmbtiycwlqpzxvgjd'\n",
  36     "\n",
  37     "# wheel_i_pegs = ['q']\n",
  38     "# wheel_ii_pegs = ['e']\n",
  39     "# wheel_iii_pegs = ['v']\n",
  40     "# wheel_iv_pegs = ['j']\n",
  41     "# wheel_v_pegs = ['z']\n",
  42     "# wheel_vi_pegs = ['z', 'm']\n",
  43     "# wheel_vii_pegs = ['z', 'm']\n",
  44     "# wheel_viii_pegs = ['z', 'm']\n",
  45     "\n",
  46     "# reflector_b_spec = 'ay br cu dh eq fs gl ip jx kn mo tz vw'\n",
  47     "# reflector_c_spec = 'af bv cp dj ei go hy kr lz mx nw tq su'"
  48    ]
  49   },
  50   {
  51    "cell_type": "code",
  52    "execution_count": 799,
  53    "metadata": {
  54     "collapsed": true
  55    },
  56    "outputs": [],
  57    "source": [
  58     "class Bank(object):\n",
  59     "    def __init__(self):\n",
  60     "        self.signals = dict(zip(string.ascii_lowercase, [False]*len(string.ascii_lowercase)))"
  61    ]
  62   },
  63   {
  64    "cell_type": "code",
  65    "execution_count": 800,
  66    "metadata": {
  67     "collapsed": false
  68    },
  69    "outputs": [
  70     {
  71      "data": {
  72       "text/plain": [
  73        "{'a': False,\n",
  74        " 'b': False,\n",
  75        " 'c': False,\n",
  76        " 'd': False,\n",
  77        " 'e': False,\n",
  78        " 'f': False,\n",
  79        " 'g': False,\n",
  80        " 'h': False,\n",
  81        " 'i': False,\n",
  82        " 'j': False,\n",
  83        " 'k': False,\n",
  84        " 'l': False,\n",
  85        " 'm': False,\n",
  86        " 'n': False,\n",
  87        " 'o': False,\n",
  88        " 'p': False,\n",
  89        " 'q': False,\n",
  90        " 'r': False,\n",
  91        " 's': False,\n",
  92        " 't': False,\n",
  93        " 'u': False,\n",
  94        " 'v': False,\n",
  95        " 'w': False,\n",
  96        " 'x': False,\n",
  97        " 'y': False,\n",
  98        " 'z': False}"
  99       ]
 100      },
 101      "execution_count": 800,
 102      "metadata": {},
 103      "output_type": "execute_result"
 104     }
 105    ],
 106    "source": [
 107     "c1 = Bank()\n",
 108     "c1.signals"
 109    ]
 110   },
 111   {
 112    "cell_type": "code",
 113    "execution_count": 801,
 114    "metadata": {
 115     "collapsed": true
 116    },
 117    "outputs": [],
 118    "source": [
 119     "Signal = collections.namedtuple('Signal', ['bank', 'wire'])\n",
 120     "Connection = collections.namedtuple('Connection', ['banks', 'scrambler'])\n",
 121     "MenuItem = collections.namedtuple('MenuIem', ['before', 'after', 'number'])"
 122    ]
 123   },
 124   {
 125    "cell_type": "code",
 126    "execution_count": 802,
 127    "metadata": {
 128     "collapsed": true
 129    },
 130    "outputs": [],
 131    "source": [
 132     "class Scrambler(object):\n",
 133     "    def __init__(self, wheel1_spec, wheel2_spec, wheel3_spec, reflector_spec,\n",
 134     "                 wheel1_pos='a', wheel2_pos='a', wheel3_pos='a'):\n",
 135     "        self.wheel1 = SimpleWheel(wheel1_spec, position=wheel1_pos)\n",
 136     "        self.wheel2 = SimpleWheel(wheel2_spec, position=wheel2_pos)\n",
 137     "        self.wheel3 = SimpleWheel(wheel3_spec, position=wheel3_pos)\n",
 138     "        self.reflector = Reflector(reflector_spec)\n",
 139     "    \n",
 140     "    def __getattribute__(self, name):\n",
 141     "        if name=='wheel_positions':\n",
 142     "            return self.wheel1.position, self.wheel2.position, self.wheel3.position \n",
 143     "        elif name=='wheel_positions_l':\n",
 144     "            return self.wheel1.position_l, self.wheel2.position_l, self.wheel3.position_l \n",
 145     "        else:\n",
 146     "            return object.__getattribute__(self, name)\n",
 147     "    \n",
 148     "    def advance(self, wheel1=False, wheel2=False, wheel3=True):\n",
 149     "        if wheel1: self.wheel1.advance()\n",
 150     "        if wheel2: self.wheel2.advance()\n",
 151     "        if wheel3: self.wheel3.advance()\n",
 152     "            \n",
 153     "    def lookup(self, letter):\n",
 154     "        a = self.wheel3.forward(letter)\n",
 155     "        b = self.wheel2.forward(a)\n",
 156     "        c = self.wheel1.forward(b)\n",
 157     "        d = self.reflector.forward(c)\n",
 158     "        e = self.wheel1.backward(d)\n",
 159     "        f = self.wheel2.backward(e)\n",
 160     "        g = self.wheel3.backward(f)\n",
 161     "        return g\n",
 162     "    \n",
 163     "    def set_positions(self, wheel1_pos, wheel2_pos, wheel3_pos):\n",
 164     "        self.wheel1.set_position(wheel1_pos)\n",
 165     "        self.wheel2.set_position(wheel2_pos)\n",
 166     "        self.wheel3.set_position(wheel3_pos)        "
 167    ]
 168   },
 169   {
 170    "cell_type": "code",
 171    "execution_count": 803,
 172    "metadata": {
 173     "collapsed": false
 174    },
 175    "outputs": [],
 176    "source": [
 177     "class Bombe(object):\n",
 178     "    def __init__(self, wheel1_spec, wheel2_spec, wheel3_spec, reflector_spec,\n",
 179     "                menu=None, start_signal=None, use_diagonal_board=True, verify_plugboard=True):\n",
 180     "        self.connections = []\n",
 181     "        self.wheel1_spec = wheel1_spec\n",
 182     "        self.wheel2_spec = wheel2_spec\n",
 183     "        self.wheel3_spec = wheel3_spec\n",
 184     "        self.reflector_spec = reflector_spec\n",
 185     "        if menu:\n",
 186     "            self.read_menu(menu)\n",
 187     "        if start_signal:\n",
 188     "            self.test_start = start_signal\n",
 189     "        self.use_diagonal_board = use_diagonal_board\n",
 190     "        self.verify_plugboard = verify_plugboard\n",
 191     "        \n",
 192     "    def __getattribute__(self, name):\n",
 193     "        if name=='wheel_positions':\n",
 194     "            return self.connections[0].scrambler.wheel_positions\n",
 195     "        elif name=='wheel_positions_l':\n",
 196     "            return self.connections[0].scrambler.wheel_positions_l\n",
 197     "        else:\n",
 198     "            return object.__getattribute__(self, name)\n",
 199     "        \n",
 200     "    def __call__(self, start_positions):\n",
 201     "        return start_positions, self.test(start_positions=start_positions, \n",
 202     "                                          use_diagonal_board=self.use_diagonal_board,\n",
 203     "                                          verify_plugboard=self.verify_plugboard)\n",
 204     "        \n",
 205     "    def add_connection(self, bank_before, bank_after, scrambler):\n",
 206     "        self.connections += [Connection([bank_before, bank_after], scrambler)]\n",
 207     "        \n",
 208     "    def read_menu(self, menu):\n",
 209     "        for item in menu:\n",
 210     "            scrambler = Scrambler(self.wheel1_spec, self.wheel2_spec, self.wheel3_spec,\n",
 211     "                                  self.reflector_spec,\n",
 212     "                                  wheel3_pos=unpos(item.number - 1))\n",
 213     "            self.add_connection(item.before, item.after, scrambler)\n",
 214     "        most_common_letter = (collections.Counter(m.before for m in menu) + \\\n",
 215     "                              collections.Counter(m.after for m in menu)).most_common(1)[0][0]\n",
 216     "        self.test_start = Signal(most_common_letter, most_common_letter)\n",
 217     "        \n",
 218     "    def set_positions(self, wheel1_pos, wheel2_pos, wheel3_pos):\n",
 219     "        for i, c in enumerate(self.connections):\n",
 220     "            c.scrambler.set_positions(wheel1_pos, wheel2_pos, unpos(pos(wheel3_pos) + i))\n",
 221     "    \n",
 222     "    def test(self, initial_signal=None, start_positions=None, use_diagonal_board=True,\n",
 223     "            verify_plugboard=True):\n",
 224     "        self.banks = {label: \n",
 225     "                      dict(zip(string.ascii_lowercase, [False]*len(string.ascii_lowercase)))\n",
 226     "                      for label in string.ascii_lowercase}\n",
 227     "        if start_positions:\n",
 228     "            self.set_positions(*start_positions)\n",
 229     "        if not initial_signal:\n",
 230     "            initial_signal = self.test_start\n",
 231     "        self.pending = [initial_signal]\n",
 232     "        self.propagate(use_diagonal_board)\n",
 233     "        live_wire_count = len([self.banks[self.test_start.bank][w] \n",
 234     "                    for w in self.banks[self.test_start.bank] \n",
 235     "                    if self.banks[self.test_start.bank][w]])\n",
 236     "        if live_wire_count < 26:\n",
 237     "            if verify_plugboard:\n",
 238     "                possibles = self.possible_plugboards()\n",
 239     "                return all(s0.isdisjoint(s1) for s0 in possibles for s1 in possibles if s0 != s1)\n",
 240     "            else:\n",
 241     "                return True\n",
 242     "        else:\n",
 243     "            return False\n",
 244     "        \n",
 245     "    def propagate(self, use_diagonal_board):\n",
 246     "        while self.pending:\n",
 247     "            current = self.pending[0]\n",
 248     "            # print(\"processing\", current)\n",
 249     "            self.pending = self.pending[1:]\n",
 250     "            if not self.banks[current.bank][current.wire]:\n",
 251     "                self.banks[current.bank][current.wire] = True\n",
 252     "                if use_diagonal_board:\n",
 253     "                    self.pending += [Signal(current.wire, current.bank)]\n",
 254     "                for c in self.connections:\n",
 255     "                    if current.bank in c.banks:\n",
 256     "                        other_bank = [b for b in c.banks if b != current.bank][0]\n",
 257     "                        other_wire = c.scrambler.lookup(current.wire)\n",
 258     "                        # print(\"  adding\", other_bank, other_wire, \"because\", c.banks)\n",
 259     "                        self.pending += [Signal(other_bank, other_wire)]\n",
 260     "    \n",
 261     "    def run(self, run_start=None, wheel1_pos='a', wheel2_pos='a', wheel3_pos='a', use_diagonal_board=True):\n",
 262     "        if not run_start:\n",
 263     "            run_start = self.test_start\n",
 264     "        self.solutions = []\n",
 265     "        self.set_positions(wheel1_pos, wheel2_pos, wheel3_pos)\n",
 266     "        for run_index in range(26*26*26):\n",
 267     "            if self.test(initial_signal=run_start, use_diagonal_board=use_diagonal_board):\n",
 268     "                self.solutions += [self.connections[0].scrambler.wheel_positions_l]\n",
 269     "            advance3 = True\n",
 270     "            advance2 = False\n",
 271     "            advance1 = False\n",
 272     "            if (run_index + 1) % 26 == 0: advance2 = True\n",
 273     "            if (run_index + 1) % (26*26) == 0: advance1 = True\n",
 274     "            for c in self.connections:\n",
 275     "                c.scrambler.advance(advance1, advance2, advance3)\n",
 276     "        return self.solutions\n",
 277     "    \n",
 278     "    def possible_plugboards(self):\n",
 279     "        possibles = set()\n",
 280     "        for b in self.banks:\n",
 281     "            active = [w for w in self.banks[b] if self.banks[b][w]]\n",
 282     "            inactive = [w for w in self.banks[b] if not self.banks[b][w]]\n",
 283     "            if len(active) == 1:\n",
 284     "                possibles = possibles.union({frozenset((b, active[0]))})\n",
 285     "            if len(inactive) == 1:\n",
 286     "                possibles = possibles.union({frozenset((b, inactive[0]))})\n",
 287     "        return possibles"
 288    ]
 289   },
 290   {
 291    "cell_type": "code",
 292    "execution_count": 804,
 293    "metadata": {
 294     "collapsed": false
 295    },
 296    "outputs": [],
 297    "source": [
 298     "bombe = Bombe(wheel_i_spec, wheel_ii_spec, wheel_iii_spec, reflector_b_spec)\n",
 299     "# len(bombe.banks), bombe.banks['a'] == bombe.banks['b']"
 300    ]
 301   },
 302   {
 303    "cell_type": "code",
 304    "execution_count": 805,
 305    "metadata": {
 306     "collapsed": true
 307    },
 308    "outputs": [],
 309    "source": [
 310     "test_enigma = Enigma(reflector_b_spec, \n",
 311     "                wheel_i_spec, wheel_i_pegs,\n",
 312     "                wheel_ii_spec, wheel_ii_pegs,\n",
 313     "                wheel_iii_spec, wheel_iii_pegs,\n",
 314     "                1, 1, 1,\n",
 315     "                '')"
 316    ]
 317   },
 318   {
 319    "cell_type": "code",
 320    "execution_count": 806,
 321    "metadata": {
 322     "collapsed": false
 323    },
 324    "outputs": [
 325     {
 326      "data": {
 327       "text/plain": [
 328        "'opgndxcrwomnlnecjz'"
 329       ]
 330      },
 331      "execution_count": 806,
 332      "metadata": {},
 333      "output_type": "execute_result"
 334     }
 335    ],
 336    "source": [
 337     "test_enigma.set_wheels('a', 'a', 'a')\n",
 338     "pt = 'thisisatestmessage'\n",
 339     "ct = test_enigma.encipher(pt)\n",
 340     "ct"
 341    ]
 342   },
 343   {
 344    "cell_type": "code",
 345    "execution_count": 807,
 346    "metadata": {
 347     "collapsed": false
 348    },
 349    "outputs": [
 350     {
 351      "data": {
 352       "text/plain": [
 353        "'aas'"
 354       ]
 355      },
 356      "execution_count": 807,
 357      "metadata": {},
 358      "output_type": "execute_result"
 359     }
 360    ],
 361    "source": [
 362     "cat(test_enigma.wheel_positions_l)"
 363    ]
 364   },
 365   {
 366    "cell_type": "code",
 367    "execution_count": 808,
 368    "metadata": {
 369     "collapsed": false
 370    },
 371    "outputs": [
 372     {
 373      "data": {
 374       "text/plain": [
 375        "[MenuIem(before='t', after='o', number=1),\n",
 376        " MenuIem(before='h', after='p', number=2),\n",
 377        " MenuIem(before='i', after='g', number=3),\n",
 378        " MenuIem(before='s', after='n', number=4),\n",
 379        " MenuIem(before='i', after='d', number=5),\n",
 380        " MenuIem(before='s', after='x', number=6),\n",
 381        " MenuIem(before='a', after='c', number=7),\n",
 382        " MenuIem(before='t', after='r', number=8),\n",
 383        " MenuIem(before='e', after='w', number=9),\n",
 384        " MenuIem(before='s', after='o', number=10),\n",
 385        " MenuIem(before='t', after='m', number=11),\n",
 386        " MenuIem(before='m', after='n', number=12),\n",
 387        " MenuIem(before='e', after='l', number=13),\n",
 388        " MenuIem(before='s', after='n', number=14),\n",
 389        " MenuIem(before='s', after='e', number=15),\n",
 390        " MenuIem(before='a', after='c', number=16),\n",
 391        " MenuIem(before='g', after='j', number=17),\n",
 392        " MenuIem(before='e', after='z', number=18)]"
 393       ]
 394      },
 395      "execution_count": 808,
 396      "metadata": {},
 397      "output_type": "execute_result"
 398     }
 399    ],
 400    "source": [
 401     "menu = [MenuItem(p, c, i+1) for i, (p, c) in enumerate(zip(pt, ct))]\n",
 402     "menu"
 403    ]
 404   },
 405   {
 406    "cell_type": "code",
 407    "execution_count": 809,
 408    "metadata": {
 409     "collapsed": true
 410    },
 411    "outputs": [],
 412    "source": [
 413     "def make_menu(plaintext, ciphertext):\n",
 414     "    return [MenuItem(p, c, i+1) \n",
 415     "            for i, (p, c) in enumerate(zip(plaintext, ciphertext))]"
 416    ]
 417   },
 418   {
 419    "cell_type": "code",
 420    "execution_count": 810,
 421    "metadata": {
 422     "collapsed": false
 423    },
 424    "outputs": [
 425     {
 426      "data": {
 427       "text/plain": [
 428        "[MenuIem(before='t', after='o', number=1),\n",
 429        " MenuIem(before='h', after='p', number=2),\n",
 430        " MenuIem(before='i', after='g', number=3),\n",
 431        " MenuIem(before='s', after='n', number=4),\n",
 432        " MenuIem(before='i', after='d', number=5),\n",
 433        " MenuIem(before='s', after='x', number=6),\n",
 434        " MenuIem(before='a', after='c', number=7),\n",
 435        " MenuIem(before='t', after='r', number=8),\n",
 436        " MenuIem(before='e', after='w', number=9),\n",
 437        " MenuIem(before='s', after='o', number=10),\n",
 438        " MenuIem(before='t', after='m', number=11),\n",
 439        " MenuIem(before='m', after='n', number=12),\n",
 440        " MenuIem(before='e', after='l', number=13),\n",
 441        " MenuIem(before='s', after='n', number=14),\n",
 442        " MenuIem(before='s', after='e', number=15),\n",
 443        " MenuIem(before='a', after='c', number=16),\n",
 444        " MenuIem(before='g', after='j', number=17),\n",
 445        " MenuIem(before='e', after='z', number=18)]"
 446       ]
 447      },
 448      "execution_count": 810,
 449      "metadata": {},
 450      "output_type": "execute_result"
 451     }
 452    ],
 453    "source": [
 454     "make_menu(pt, ct)"
 455    ]
 456   },
 457   {
 458    "cell_type": "code",
 459    "execution_count": 811,
 460    "metadata": {
 461     "collapsed": false
 462    },
 463    "outputs": [
 464     {
 465      "data": {
 466       "text/plain": [
 467        "'s'"
 468       ]
 469      },
 470      "execution_count": 811,
 471      "metadata": {},
 472      "output_type": "execute_result"
 473     }
 474    ],
 475    "source": [
 476     "(collections.Counter(m.before for m in menu) + collections.Counter(m.after for m in menu)).most_common(1)[0][0]"
 477    ]
 478   },
 479   {
 480    "cell_type": "code",
 481    "execution_count": 812,
 482    "metadata": {
 483     "collapsed": false
 484    },
 485    "outputs": [],
 486    "source": [
 487     "bombe.read_menu(menu)"
 488    ]
 489   },
 490   {
 491    "cell_type": "code",
 492    "execution_count": 813,
 493    "metadata": {
 494     "collapsed": false
 495    },
 496    "outputs": [
 497     {
 498      "data": {
 499       "text/plain": [
 500        "18"
 501       ]
 502      },
 503      "execution_count": 813,
 504      "metadata": {},
 505      "output_type": "execute_result"
 506     }
 507    ],
 508    "source": [
 509     "len(bombe.connections)"
 510    ]
 511   },
 512   {
 513    "cell_type": "code",
 514    "execution_count": 814,
 515    "metadata": {
 516     "collapsed": false
 517    },
 518    "outputs": [
 519     {
 520      "name": "stdout",
 521      "output_type": "stream",
 522      "text": [
 523       "['t', 'o'] aaa\n",
 524       "['h', 'p'] aab\n",
 525       "['i', 'g'] aac\n",
 526       "['s', 'n'] aad\n",
 527       "['i', 'd'] aae\n",
 528       "['s', 'x'] aaf\n",
 529       "['a', 'c'] aag\n",
 530       "['t', 'r'] aah\n",
 531       "['e', 'w'] aai\n",
 532       "['s', 'o'] aaj\n",
 533       "['t', 'm'] aak\n",
 534       "['m', 'n'] aal\n",
 535       "['e', 'l'] aam\n",
 536       "['s', 'n'] aan\n",
 537       "['s', 'e'] aao\n",
 538       "['a', 'c'] aap\n",
 539       "['g', 'j'] aaq\n",
 540       "['e', 'z'] aar\n"
 541      ]
 542     }
 543    ],
 544    "source": [
 545     "for c in bombe.connections:\n",
 546     "    print(c.banks, cat(c.scrambler.wheel_positions_l))"
 547    ]
 548   },
 549   {
 550    "cell_type": "code",
 551    "execution_count": 815,
 552    "metadata": {
 553     "collapsed": false
 554    },
 555    "outputs": [
 556     {
 557      "data": {
 558       "text/plain": [
 559        "False"
 560       ]
 561      },
 562      "execution_count": 815,
 563      "metadata": {},
 564      "output_type": "execute_result"
 565     }
 566    ],
 567    "source": [
 568     "bombe.test(Signal('t', 't'))"
 569    ]
 570   },
 571   {
 572    "cell_type": "code",
 573    "execution_count": 816,
 574    "metadata": {
 575     "collapsed": false
 576    },
 577    "outputs": [
 578     {
 579      "data": {
 580       "text/plain": [
 581        "{'a': True,\n",
 582        " 'b': True,\n",
 583        " 'c': True,\n",
 584        " 'd': True,\n",
 585        " 'e': True,\n",
 586        " 'f': True,\n",
 587        " 'g': True,\n",
 588        " 'h': True,\n",
 589        " 'i': True,\n",
 590        " 'j': True,\n",
 591        " 'k': True,\n",
 592        " 'l': True,\n",
 593        " 'm': True,\n",
 594        " 'n': True,\n",
 595        " 'o': True,\n",
 596        " 'p': True,\n",
 597        " 'q': True,\n",
 598        " 'r': True,\n",
 599        " 's': True,\n",
 600        " 't': True,\n",
 601        " 'u': True,\n",
 602        " 'v': True,\n",
 603        " 'w': True,\n",
 604        " 'x': True,\n",
 605        " 'y': True,\n",
 606        " 'z': True}"
 607       ]
 608      },
 609      "execution_count": 816,
 610      "metadata": {},
 611      "output_type": "execute_result"
 612     }
 613    ],
 614    "source": [
 615     "bombe.banks['t']"
 616    ]
 617   },
 618   {
 619    "cell_type": "code",
 620    "execution_count": 817,
 621    "metadata": {
 622     "collapsed": false
 623    },
 624    "outputs": [
 625     {
 626      "name": "stdout",
 627      "output_type": "stream",
 628      "text": [
 629       "a : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 630       "b : AbCDEfGHIJkLMNOPqRSTuvWXyZ\n",
 631       "c : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 632       "d : ABCDEFGHIJKLMNOPQRSTUVWXyZ\n",
 633       "e : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 634       "f : AbCDEfGHIJkLMNOPqRSTuvWXyZ\n",
 635       "g : ABCDEFGHIJKLMNOPQRSTuVWXYZ\n",
 636       "h : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 637       "i : ABCDEFGHIJKLMNOPQRSTUvWXYZ\n",
 638       "j : ABCDEFGHIjKLMNOPQRSTUVWXYZ\n",
 639       "k : AbCDEfGHIJkLMNOPqRSTuvWXyZ\n",
 640       "l : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 641       "m : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 642       "n : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 643       "o : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 644       "p : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 645       "q : AbCDEfGHIJkLMNOPqRSTuvWXyZ\n",
 646       "r : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 647       "s : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 648       "t : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 649       "u : AbCDEfgHIJkLMNOPqRSTuvWXyZ\n",
 650       "v : AbCDEfGHiJkLMNOPqRSTuvWXyZ\n",
 651       "w : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 652       "x : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 653       "y : AbCdEfGHIJkLMNOPqRSTuvWXyZ\n",
 654       "z : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n"
 655      ]
 656     }
 657    ],
 658    "source": [
 659     "for b in sorted(bombe.banks):\n",
 660     "    print(b, ': ', end='')\n",
 661     "    for w in sorted(bombe.banks[b]):\n",
 662     "        if bombe.banks[b][w]:\n",
 663     "            print(w.upper(), end='')\n",
 664     "        else:\n",
 665     "            print(w, end='')\n",
 666     "    print('')"
 667    ]
 668   },
 669   {
 670    "cell_type": "code",
 671    "execution_count": 818,
 672    "metadata": {
 673     "collapsed": false
 674    },
 675    "outputs": [
 676     {
 677      "data": {
 678       "text/plain": [
 679        "('a', 'a', 'a')"
 680       ]
 681      },
 682      "execution_count": 818,
 683      "metadata": {},
 684      "output_type": "execute_result"
 685     }
 686    ],
 687    "source": [
 688     "bombe.wheel_positions_l"
 689    ]
 690   },
 691   {
 692    "cell_type": "code",
 693    "execution_count": 819,
 694    "metadata": {
 695     "collapsed": false
 696    },
 697    "outputs": [
 698     {
 699      "name": "stdout",
 700      "output_type": "stream",
 701      "text": [
 702       "['t', 'o'] pqr\n",
 703       "['h', 'p'] pqs\n",
 704       "['i', 'g'] pqt\n",
 705       "['s', 'n'] pqu\n",
 706       "['i', 'd'] pqv\n",
 707       "['s', 'x'] pqw\n",
 708       "['a', 'c'] pqx\n",
 709       "['t', 'r'] pqy\n",
 710       "['e', 'w'] pqz\n",
 711       "['s', 'o'] pqa\n",
 712       "['t', 'm'] pqb\n",
 713       "['m', 'n'] pqc\n",
 714       "['e', 'l'] pqd\n",
 715       "['s', 'n'] pqe\n",
 716       "['s', 'e'] pqf\n",
 717       "['a', 'c'] pqg\n",
 718       "['g', 'j'] pqh\n",
 719       "['e', 'z'] pqi\n"
 720      ]
 721     }
 722    ],
 723    "source": [
 724     "bombe.set_positions('p', 'q', 'r')\n",
 725     "for c in bombe.connections:\n",
 726     "    print(c.banks, cat(c.scrambler.wheel_positions_l))"
 727    ]
 728   },
 729   {
 730    "cell_type": "code",
 731    "execution_count": 820,
 732    "metadata": {
 733     "collapsed": false
 734    },
 735    "outputs": [],
 736    "source": [
 737     "# bombe.run()\n",
 738     "# print('x')"
 739    ]
 740   },
 741   {
 742    "cell_type": "code",
 743    "execution_count": 821,
 744    "metadata": {
 745     "collapsed": false
 746    },
 747    "outputs": [
 748     {
 749      "name": "stdout",
 750      "output_type": "stream",
 751      "text": [
 752       "a : .b.defghijklmnopqrstuvwxyz\n",
 753       "b : a.cde.ghij.lmnop.rst..wx.z\n",
 754       "c : .b.defghijklmnopqrstuvwxyz\n",
 755       "d : abc.e.gh.jklmnopqrstuvwxyz\n",
 756       "e : abcd.fghijklmnopqrstuvwxyz\n",
 757       "f : a.c.e.g.ij.lmno..rst..wx.z\n",
 758       "g : abcdef.h..klmnopqrstuvwxyz\n",
 759       "h : abcde.g.ij.lmno.qrst..wxyz\n",
 760       "i : abc.ef.h.jklmnopqrstuvwxyz\n",
 761       "j : abcdef.hi.klmnopqrstuvwx.z\n",
 762       "k : a.cde.g.ij.lmno..rst..wx.z\n",
 763       "l : abcdefghijk.mnopqrstuvwxyz\n",
 764       "m : abcdefghijkl.nopqrstuvwxyz\n",
 765       "n : abcdefghijklm.opqrstuvwxyz\n",
 766       "o : abcdefghijklmn.pqrstuvwxyz\n",
 767       "p : abcde.g.ij.lmno.qrst..wxyz\n",
 768       "q : a.cde.ghij.lmnop.rst..wx.z\n",
 769       "r : abcdefghijklmnopq.stuvwxyz\n",
 770       "s : abcdefghijklmnopqr.tuvwxyz\n",
 771       "t : abcdefghijklmnopqrs.uvwxyz\n",
 772       "u : a.cde.g.ij.lmno..rst..wx.z\n",
 773       "v : a.cde.g.ij.lmno..rst..wx.z\n",
 774       "w : abcdefghijklmnopqrstuv.xyz\n",
 775       "x : abcdefghijklmnopqrstuvw.yz\n",
 776       "y : a.cde.ghi..lmnop.rst..wx.z\n",
 777       "z : abcdefghijklmnopqrstuvwxy.\n"
 778      ]
 779     }
 780    ],
 781    "source": [
 782     "bombe.set_positions('a', 'a', 'b')\n",
 783     "bombe.test(Signal('s', 'a'))\n",
 784     "\n",
 785     "for b in sorted(bombe.banks):\n",
 786     "    print(b, ': ', end='')\n",
 787     "    for w in sorted(bombe.banks[b]):\n",
 788     "        if bombe.banks[b][w]:\n",
 789     "            print(w, end='')\n",
 790     "        else:\n",
 791     "            print('.', end='')\n",
 792     "    print('')"
 793    ]
 794   },
 795   {
 796    "cell_type": "code",
 797    "execution_count": 822,
 798    "metadata": {
 799     "collapsed": false
 800    },
 801    "outputs": [
 802     {
 803      "name": "stdout",
 804      "output_type": "stream",
 805      "text": [
 806       "a : ..........................\n",
 807       "b : ..........................\n",
 808       "c : ..........................\n",
 809       "d : ..........................\n",
 810       "e : ....e.....................\n",
 811       "f : ..........................\n",
 812       "g : ..........................\n",
 813       "h : ..........................\n",
 814       "i : ..........................\n",
 815       "j : ..........................\n",
 816       "k : ..........................\n",
 817       "l : ...........l..............\n",
 818       "m : ............m.............\n",
 819       "n : .............n............\n",
 820       "o : ..............o...........\n",
 821       "p : ..........................\n",
 822       "q : ..........................\n",
 823       "r : .................r........\n",
 824       "s : ..................s.......\n",
 825       "t : ...................t......\n",
 826       "u : ..........................\n",
 827       "v : ..........................\n",
 828       "w : ......................w...\n",
 829       "x : .......................x..\n",
 830       "y : ..........................\n",
 831       "z : .........................z\n"
 832      ]
 833     }
 834    ],
 835    "source": [
 836     "bombe.set_positions('a', 'a', 'b')\n",
 837     "bombe.test()\n",
 838     "\n",
 839     "for b in sorted(bombe.banks):\n",
 840     "    print(b, ': ', end='')\n",
 841     "    for w in sorted(bombe.banks[b]):\n",
 842     "        if bombe.banks[b][w]:\n",
 843     "            print(w, end='')\n",
 844     "        else:\n",
 845     "            print('.', end='')\n",
 846     "    print('')"
 847    ]
 848   },
 849   {
 850    "cell_type": "code",
 851    "execution_count": 823,
 852    "metadata": {
 853     "collapsed": false
 854    },
 855    "outputs": [
 856     {
 857      "data": {
 858       "text/plain": [
 859        "1"
 860       ]
 861      },
 862      "execution_count": 823,
 863      "metadata": {},
 864      "output_type": "execute_result"
 865     }
 866    ],
 867    "source": [
 868     "len([bombe.banks['t'][w] for w in bombe.banks['t'] if bombe.banks['t'][w]])"
 869    ]
 870   },
 871   {
 872    "cell_type": "code",
 873    "execution_count": 824,
 874    "metadata": {
 875     "collapsed": false
 876    },
 877    "outputs": [],
 878    "source": [
 879     "# %%timeit\n",
 880     "# results = bombe.run()\n",
 881     "# print(len(results), ('a', 'a', 'b') in results)"
 882    ]
 883   },
 884   {
 885    "cell_type": "code",
 886    "execution_count": 825,
 887    "metadata": {
 888     "collapsed": false
 889    },
 890    "outputs": [],
 891    "source": [
 892     "# %%timeit\n",
 893     "# results = bombe.run(use_diagonal_board=False)\n",
 894     "# print(len(results), ('a', 'a', 'b') in results)"
 895    ]
 896   },
 897   {
 898    "cell_type": "code",
 899    "execution_count": 826,
 900    "metadata": {
 901     "collapsed": false
 902    },
 903    "outputs": [
 904     {
 905      "data": {
 906       "text/plain": [
 907        "('a', 'a', 'b')"
 908       ]
 909      },
 910      "execution_count": 826,
 911      "metadata": {},
 912      "output_type": "execute_result"
 913     }
 914    ],
 915    "source": [
 916     "bombe.wheel_positions_l"
 917    ]
 918   },
 919   {
 920    "cell_type": "code",
 921    "execution_count": 827,
 922    "metadata": {
 923     "collapsed": false
 924    },
 925    "outputs": [
 926     {
 927      "data": {
 928       "text/plain": [
 929        "False"
 930       ]
 931      },
 932      "execution_count": 827,
 933      "metadata": {},
 934      "output_type": "execute_result"
 935     }
 936    ],
 937    "source": [
 938     "bombe.test(Signal('t', 't'), ('p', 'p', 'p'))"
 939    ]
 940   },
 941   {
 942    "cell_type": "code",
 943    "execution_count": 828,
 944    "metadata": {
 945     "collapsed": false
 946    },
 947    "outputs": [
 948     {
 949      "data": {
 950       "text/plain": [
 951        "('p', 'p', 'p')"
 952       ]
 953      },
 954      "execution_count": 828,
 955      "metadata": {},
 956      "output_type": "execute_result"
 957     }
 958    ],
 959    "source": [
 960     "bombe.wheel_positions_l"
 961    ]
 962   },
 963   {
 964    "cell_type": "code",
 965    "execution_count": 829,
 966    "metadata": {
 967     "collapsed": false
 968    },
 969    "outputs": [
 970     {
 971      "name": "stdout",
 972      "output_type": "stream",
 973      "text": [
 974       "a : abcdefghijklmnop.rst.vwxyz\n",
 975       "b : a.cde.g.ij.lmno..rst..wx.z\n",
 976       "c : abcdefghijklmnop.rst.vwxyz\n",
 977       "d : abcdefghijklmnopqrstuvwxyz\n",
 978       "e : abcdefghijklmnopqrstuvwxyz\n",
 979       "f : a.cde.g.ij.lmno..rst..wx.z\n",
 980       "g : abcdefghijklmnopqrstuvwxyz\n",
 981       "h : a.cde.ghijklmnop.rst.vwxyz\n",
 982       "i : abcdefghijklmnopqrstuvwxyz\n",
 983       "j : abcdefghijklmnopqrstuvwxyz\n",
 984       "k : a.cde.ghij.lmnop.rst..wx.z\n",
 985       "l : abcdefghijklmnopqrstuvwxyz\n",
 986       "m : abcdefghijklmnopqrstuvwxyz\n",
 987       "n : abcdefghijklmnopqrstuvwxyz\n",
 988       "o : abcdefghijklmnopqrstuvwxyz\n",
 989       "p : a.cde.ghijklmnop.rst.vwxyz\n",
 990       "q : ...de.g.ij.lmno..rst..wx.z\n",
 991       "r : abcdefghijklmnopqrstuvwxyz\n",
 992       "s : abcdefghijklmnopqrstuvwxyz\n",
 993       "t : abcdefghijklmnopqrstuvwxyz\n",
 994       "u : ...de.g.ij.lmno..rst..wx.z\n",
 995       "v : a.cde.ghij.lmnop.rst..wx.z\n",
 996       "w : abcdefghijklmnopqrstuvwxyz\n",
 997       "x : abcdefghijklmnopqrstuvwxyz\n",
 998       "y : a.cde.ghij.lmnop.rst..wx.z\n",
 999       "z : abcdefghijklmnopqrstuvwxyz\n"
1000      ]
1001     }
1002    ],
1003    "source": [
1004     "for b in sorted(bombe.banks):\n",
1005     "    print(b, ': ', end='')\n",
1006     "    for w in sorted(bombe.banks[b]):\n",
1007     "        if bombe.banks[b][w]:\n",
1008     "            print(w, end='')\n",
1009     "        else:\n",
1010     "            print('.', end='')\n",
1011     "    print('')"
1012    ]
1013   },
1014   {
1015    "cell_type": "code",
1016    "execution_count": 830,
1017    "metadata": {
1018     "collapsed": false
1019    },
1020    "outputs": [
1021     {
1022      "data": {
1023       "text/plain": [
1024        "17576"
1025       ]
1026      },
1027      "execution_count": 830,
1028      "metadata": {},
1029      "output_type": "execute_result"
1030     }
1031    ],
1032    "source": [
1033     "allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1034     "len(list(allwheels))"
1035    ]
1036   },
1037   {
1038    "cell_type": "code",
1039    "execution_count": 831,
1040    "metadata": {
1041     "collapsed": false
1042    },
1043    "outputs": [
1044     {
1045      "data": {
1046       "text/plain": [
1047        "(('a', 'a', 'b'), True)"
1048       ]
1049      },
1050      "execution_count": 831,
1051      "metadata": {},
1052      "output_type": "execute_result"
1053     }
1054    ],
1055    "source": [
1056     "b = Bombe(wheel_i_spec, wheel_ii_spec, wheel_iii_spec, reflector_b_spec, menu=menu)\n",
1057     "b(('a', 'a', 'b'))"
1058    ]
1059   },
1060   {
1061    "cell_type": "code",
1062    "execution_count": 832,
1063    "metadata": {
1064     "collapsed": false
1065    },
1066    "outputs": [],
1067    "source": [
1068     "b = Bombe(wheel_i_spec, wheel_ii_spec, wheel_iii_spec, reflector_b_spec, menu=menu)(('a', 'a', 'b'))"
1069    ]
1070   },
1071   {
1072    "cell_type": "code",
1073    "execution_count": 833,
1074    "metadata": {
1075     "collapsed": false
1076    },
1077    "outputs": [
1078     {
1079      "data": {
1080       "text/plain": [
1081        "[('a', 'a', 'b')]"
1082       ]
1083      },
1084      "execution_count": 833,
1085      "metadata": {},
1086      "output_type": "execute_result"
1087     }
1088    ],
1089    "source": [
1090     "allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1091     "\n",
1092     "with multiprocessing.Pool() as pool:\n",
1093     "    res = pool.map(Bombe(wheel_i_spec, wheel_ii_spec, wheel_iii_spec, reflector_b_spec, menu=menu),\n",
1094     "                  allwheels)\n",
1095     "[r[0] for r in res if r[1]]"
1096    ]
1097   },
1098   {
1099    "cell_type": "code",
1100    "execution_count": 857,
1101    "metadata": {
1102     "collapsed": true
1103    },
1104    "outputs": [],
1105    "source": [
1106     "def run_multi_bombe(wheel1_spec, wheel2_spec, wheel3_spec, reflector_spec, menu,\n",
1107     "                    start_signal=None, use_diagonal_board=True, \n",
1108     "                    verify_plugboard=True):\n",
1109     "    allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1110     "\n",
1111     "    with multiprocessing.Pool() as pool:\n",
1112     "        res = pool.map(Bombe(wheel1_spec, wheel2_spec, wheel3_spec, \n",
1113     "            reflector_spec, menu=menu, start_signal=start_signal, \n",
1114     "            use_diagonal_board=use_diagonal_board, \n",
1115     "            verify_plugboard=verify_plugboard),\n",
1116     "                  allwheels)\n",
1117     "    return [r[0] for r in res if r[1]]"
1118    ]
1119   },
1120   {
1121    "cell_type": "code",
1122    "execution_count": 835,
1123    "metadata": {
1124     "collapsed": false
1125    },
1126    "outputs": [
1127     {
1128      "data": {
1129       "text/plain": [
1130        "[('a', 'a', 'b')]"
1131       ]
1132      },
1133      "execution_count": 835,
1134      "metadata": {},
1135      "output_type": "execute_result"
1136     }
1137    ],
1138    "source": [
1139     "[r[0] for r in res if r[1]]"
1140    ]
1141   },
1142   {
1143    "cell_type": "code",
1144    "execution_count": 836,
1145    "metadata": {
1146     "collapsed": false
1147    },
1148    "outputs": [],
1149    "source": [
1150     "# Setting sheet line 31 from http://www.codesandciphers.org.uk/enigma/enigma3.htm\n",
1151     "# Enigma simulation settings are \n",
1152     "# http://enigma.louisedade.co.uk/enigma.html?m3;b;b153;AFTX;AJFE;AU-BG-EY-FP-HL-IN-JZ-OS-QR-TX\n",
1153     "w_enigma = Enigma(reflector_b_spec, \n",
1154     "                wheel_i_spec, wheel_i_pegs,\n",
1155     "                wheel_v_spec, wheel_v_pegs,\n",
1156     "                wheel_iii_spec, wheel_iii_pegs,\n",
1157     "                6, 20, 24,\n",
1158     "                'ua pf rq so ni ey bg hl tx zj')"
1159    ]
1160   },
1161   {
1162    "cell_type": "code",
1163    "execution_count": 837,
1164    "metadata": {
1165     "collapsed": false
1166    },
1167    "outputs": [
1168     {
1169      "data": {
1170       "text/plain": [
1171        "('e', 'l', 'e')"
1172       ]
1173      },
1174      "execution_count": 837,
1175      "metadata": {},
1176      "output_type": "execute_result"
1177     }
1178    ],
1179    "source": [
1180     "w_enigma.set_wheels('j', 'e', 'b')\n",
1181     "tuple(unpos(p) for p in w_enigma.wheel_positions)"
1182    ]
1183   },
1184   {
1185    "cell_type": "code",
1186    "execution_count": 838,
1187    "metadata": {
1188     "collapsed": false
1189    },
1190    "outputs": [
1191     {
1192      "data": {
1193       "text/plain": [
1194        "'dhnpforeeimgg'"
1195       ]
1196      },
1197      "execution_count": 838,
1198      "metadata": {},
1199      "output_type": "execute_result"
1200     }
1201    ],
1202    "source": [
1203     "w_enigma.set_wheels('j', 'e', 'b')\n",
1204     "pt = 'someplaintext'\n",
1205     "ct = w_enigma.encipher(pt)\n",
1206     "ct"
1207    ]
1208   },
1209   {
1210    "cell_type": "code",
1211    "execution_count": 839,
1212    "metadata": {
1213     "collapsed": false
1214    },
1215    "outputs": [
1216     {
1217      "data": {
1218       "text/plain": [
1219        "('j', 'e', 'o')"
1220       ]
1221      },
1222      "execution_count": 839,
1223      "metadata": {},
1224      "output_type": "execute_result"
1225     }
1226    ],
1227    "source": [
1228     "w_enigma.wheel_positions_l"
1229    ]
1230   },
1231   {
1232    "cell_type": "code",
1233    "execution_count": 840,
1234    "metadata": {
1235     "collapsed": false
1236    },
1237    "outputs": [
1238     {
1239      "data": {
1240       "text/plain": [
1241        "[MenuIem(before='s', after='d', number=1),\n",
1242        " MenuIem(before='o', after='h', number=2),\n",
1243        " MenuIem(before='m', after='n', number=3),\n",
1244        " MenuIem(before='e', after='p', number=4),\n",
1245        " MenuIem(before='p', after='f', number=5),\n",
1246        " MenuIem(before='l', after='o', number=6),\n",
1247        " MenuIem(before='a', after='r', number=7),\n",
1248        " MenuIem(before='i', after='e', number=8),\n",
1249        " MenuIem(before='n', after='e', number=9),\n",
1250        " MenuIem(before='t', after='i', number=10),\n",
1251        " MenuIem(before='e', after='m', number=11),\n",
1252        " MenuIem(before='x', after='g', number=12),\n",
1253        " MenuIem(before='t', after='g', number=13)]"
1254       ]
1255      },
1256      "execution_count": 840,
1257      "metadata": {},
1258      "output_type": "execute_result"
1259     }
1260    ],
1261    "source": [
1262     "w_menu = [MenuItem(p, c, i+1) for i, (p, c) in enumerate(zip(pt, ct))]\n",
1263     "w_menu"
1264    ]
1265   },
1266   {
1267    "cell_type": "code",
1268    "execution_count": 841,
1269    "metadata": {
1270     "collapsed": false,
1271     "scrolled": true
1272    },
1273    "outputs": [
1274     {
1275      "data": {
1276       "text/plain": [
1277        "[('a', 'y', 'm'),\n",
1278        " ('c', 'p', 'v'),\n",
1279        " ('c', 's', 'f'),\n",
1280        " ('c', 'w', 'j'),\n",
1281        " ('d', 'r', 'k'),\n",
1282        " ('e', 'l', 'f'),\n",
1283        " ('e', 's', 'v'),\n",
1284        " ('e', 'y', 'd'),\n",
1285        " ('e', 'y', 'o'),\n",
1286        " ('f', 'z', 'x'),\n",
1287        " ('g', 'b', 'l'),\n",
1288        " ('g', 'c', 'd'),\n",
1289        " ('g', 'c', 'f'),\n",
1290        " ('g', 'j', 'p'),\n",
1291        " ('h', 'c', 'i'),\n",
1292        " ('h', 'm', 'w'),\n",
1293        " ('h', 'o', 'd'),\n",
1294        " ('h', 'p', 'b'),\n",
1295        " ('h', 's', 't'),\n",
1296        " ('i', 'b', 's'),\n",
1297        " ('i', 'v', 'b'),\n",
1298        " ('j', 'y', 'u'),\n",
1299        " ('k', 'b', 'x'),\n",
1300        " ('k', 'f', 't'),\n",
1301        " ('k', 'l', 'e'),\n",
1302        " ('k', 'l', 'm'),\n",
1303        " ('k', 'r', 'z'),\n",
1304        " ('k', 's', 'p'),\n",
1305        " ('l', 'd', 'z'),\n",
1306        " ('l', 'i', 'y'),\n",
1307        " ('l', 'y', 'f'),\n",
1308        " ('m', 'b', 'h'),\n",
1309        " ('m', 'p', 'l'),\n",
1310        " ('n', 'l', 'r'),\n",
1311        " ('o', 'k', 'x'),\n",
1312        " ('p', 'a', 'g'),\n",
1313        " ('p', 'c', 'v'),\n",
1314        " ('p', 'f', 'o'),\n",
1315        " ('p', 'm', 'i'),\n",
1316        " ('p', 'x', 'n'),\n",
1317        " ('p', 'x', 'p'),\n",
1318        " ('q', 'q', 'n'),\n",
1319        " ('q', 'r', 'w'),\n",
1320        " ('q', 'v', 'l'),\n",
1321        " ('q', 'x', 't'),\n",
1322        " ('s', 'a', 'h'),\n",
1323        " ('s', 'h', 'v'),\n",
1324        " ('s', 'l', 'p'),\n",
1325        " ('s', 'l', 's'),\n",
1326        " ('u', 'r', 'h'),\n",
1327        " ('v', 'v', 'v'),\n",
1328        " ('v', 'x', 'a'),\n",
1329        " ('w', 'j', 'z'),\n",
1330        " ('w', 'k', 'u'),\n",
1331        " ('x', 'f', 'p'),\n",
1332        " ('x', 'j', 'n'),\n",
1333        " ('x', 'o', 'q'),\n",
1334        " ('x', 'x', 'x'),\n",
1335        " ('y', 'n', 'c'),\n",
1336        " ('y', 'r', 'f'),\n",
1337        " ('z', 't', 'y'),\n",
1338        " ('z', 'z', 'k')]"
1339       ]
1340      },
1341      "execution_count": 841,
1342      "metadata": {},
1343      "output_type": "execute_result"
1344     }
1345    ],
1346    "source": [
1347     "allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1348     "\n",
1349     "with multiprocessing.Pool() as pool:\n",
1350     "    res = pool.map(Bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, \n",
1351     "                         menu=w_menu, verify_plugboard=False),\n",
1352     "                  allwheels)\n",
1353     "[r[0] for r in res if r[1]]"
1354    ]
1355   },
1356   {
1357    "cell_type": "code",
1358    "execution_count": 842,
1359    "metadata": {
1360     "collapsed": false
1361    },
1362    "outputs": [
1363     {
1364      "data": {
1365       "text/plain": [
1366        "62"
1367       ]
1368      },
1369      "execution_count": 842,
1370      "metadata": {},
1371      "output_type": "execute_result"
1372     }
1373    ],
1374    "source": [
1375     "len([r[0] for r in res if r[1]])"
1376    ]
1377   },
1378   {
1379    "cell_type": "code",
1380    "execution_count": 843,
1381    "metadata": {
1382     "collapsed": false,
1383     "scrolled": true
1384    },
1385    "outputs": [
1386     {
1387      "data": {
1388       "text/plain": [
1389        "[('c', 'p', 'v'),\n",
1390        " ('c', 's', 'f'),\n",
1391        " ('e', 'l', 'f'),\n",
1392        " ('g', 'c', 'f'),\n",
1393        " ('j', 'y', 'u'),\n",
1394        " ('o', 'k', 'x'),\n",
1395        " ('p', 'a', 'g'),\n",
1396        " ('q', 'q', 'n'),\n",
1397        " ('q', 'v', 'l'),\n",
1398        " ('q', 'x', 't'),\n",
1399        " ('s', 'l', 'p'),\n",
1400        " ('u', 'r', 'h'),\n",
1401        " ('y', 'n', 'c')]"
1402       ]
1403      },
1404      "execution_count": 843,
1405      "metadata": {},
1406      "output_type": "execute_result"
1407     }
1408    ],
1409    "source": [
1410     "allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1411     "\n",
1412     "with multiprocessing.Pool() as pool:\n",
1413     "    res = pool.map(Bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, \n",
1414     "                         menu=w_menu, verify_plugboard=True),\n",
1415     "                  allwheels)\n",
1416     "[r[0] for r in res if r[1]]"
1417    ]
1418   },
1419   {
1420    "cell_type": "code",
1421    "execution_count": 858,
1422    "metadata": {
1423     "collapsed": false
1424    },
1425    "outputs": [
1426     {
1427      "data": {
1428       "text/plain": [
1429        "[('c', 'p', 'v'),\n",
1430        " ('c', 's', 'f'),\n",
1431        " ('e', 'l', 'f'),\n",
1432        " ('g', 'c', 'f'),\n",
1433        " ('j', 'y', 'u'),\n",
1434        " ('o', 'k', 'x'),\n",
1435        " ('p', 'a', 'g'),\n",
1436        " ('q', 'q', 'n'),\n",
1437        " ('q', 'v', 'l'),\n",
1438        " ('q', 'x', 't'),\n",
1439        " ('s', 'l', 'p'),\n",
1440        " ('u', 'r', 'h'),\n",
1441        " ('y', 'n', 'c')]"
1442       ]
1443      },
1444      "execution_count": 858,
1445      "metadata": {},
1446      "output_type": "execute_result"
1447     }
1448    ],
1449    "source": [
1450     "run_multi_bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, w_menu)"
1451    ]
1452   },
1453   {
1454    "cell_type": "code",
1455    "execution_count": 844,
1456    "metadata": {
1457     "collapsed": false
1458    },
1459    "outputs": [],
1460    "source": [
1461     "# allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1462     "\n",
1463     "# with multiprocessing.Pool() as pool:\n",
1464     "#     res = pool.map(Bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, \n",
1465     "#                          menu=w_menu, start_signal=Signal('t', 'x')),\n",
1466     "#                   allwheels)\n",
1467     "# [r[0] for r in res if r[1]]"
1468    ]
1469   },
1470   {
1471    "cell_type": "code",
1472    "execution_count": 845,
1473    "metadata": {
1474     "collapsed": false
1475    },
1476    "outputs": [
1477     {
1478      "data": {
1479       "text/plain": [
1480        "13"
1481       ]
1482      },
1483      "execution_count": 845,
1484      "metadata": {},
1485      "output_type": "execute_result"
1486     }
1487    ],
1488    "source": [
1489     "len([r[0] for r in res if r[1]])"
1490    ]
1491   },
1492   {
1493    "cell_type": "code",
1494    "execution_count": 846,
1495    "metadata": {
1496     "collapsed": false
1497    },
1498    "outputs": [],
1499    "source": [
1500     "w_bombe = Bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, \n",
1501     "                         menu=w_menu)"
1502    ]
1503   },
1504   {
1505    "cell_type": "code",
1506    "execution_count": 847,
1507    "metadata": {
1508     "collapsed": false
1509    },
1510    "outputs": [
1511     {
1512      "data": {
1513       "text/plain": [
1514        "Signal(bank='e', wire='e')"
1515       ]
1516      },
1517      "execution_count": 847,
1518      "metadata": {},
1519      "output_type": "execute_result"
1520     }
1521    ],
1522    "source": [
1523     "w_bombe.test_start"
1524    ]
1525   },
1526   {
1527    "cell_type": "code",
1528    "execution_count": 848,
1529    "metadata": {
1530     "collapsed": false
1531    },
1532    "outputs": [
1533     {
1534      "data": {
1535       "text/plain": [
1536        "True"
1537       ]
1538      },
1539      "execution_count": 848,
1540      "metadata": {},
1541      "output_type": "execute_result"
1542     }
1543    ],
1544    "source": [
1545     "w_bombe.test(start_positions=('e', 'l', 'f'))"
1546    ]
1547   },
1548   {
1549    "cell_type": "code",
1550    "execution_count": 849,
1551    "metadata": {
1552     "collapsed": false
1553    },
1554    "outputs": [
1555     {
1556      "data": {
1557       "text/plain": [
1558        "True"
1559       ]
1560      },
1561      "execution_count": 849,
1562      "metadata": {},
1563      "output_type": "execute_result"
1564     }
1565    ],
1566    "source": [
1567     "w_bombe.test(Signal('t', 'x'), ('e', 'l', 'f'))"
1568    ]
1569   },
1570   {
1571    "cell_type": "code",
1572    "execution_count": 850,
1573    "metadata": {
1574     "collapsed": false
1575    },
1576    "outputs": [
1577     {
1578      "name": "stdout",
1579      "output_type": "stream",
1580      "text": [
1581       "True\n",
1582       "a : a.cdefghi..l.nopqrst.vwx..\n",
1583       "b : ....efghi...mnop.......x..\n",
1584       "c : a....fg.i..lmn.p.r.t...x..\n",
1585       "d : a...efghij.lmn...rstu..xyz\n",
1586       "e : ab.defghijklmnopqrstuvwxyz\n",
1587       "f : abcde.ghijklmnopqrstuvwxyz\n",
1588       "g : abcdef.hijklmnopqrstuvwxyz\n",
1589       "h : ab.defghi...mnopq.stuvwx..\n",
1590       "i : abcdefgh.jklmnopqrstuvwxyz\n",
1591       "j : ...defg.i...mn.p...t...x..\n",
1592       "k : ....efg.i..lmnop.r.t...x..\n",
1593       "l : a.cdefg.i.k.mnopqr.t..wxyz\n",
1594       "m : .bcdefghijklmnopqrstuvwxyz\n",
1595       "n : abcdefghijklmnopqr.tuvwxyz\n",
1596       "o : ab..efghi.klmnopqr.t...xyz\n",
1597       "p : abc.efghijklmnopqrstuvwxyz\n",
1598       "q : a...efghi..lmnop.r.t...x..\n",
1599       "r : a.cdefg.i.klmnopqrst..w..z\n",
1600       "s : a..defghi...m..p.rstuv.xyz\n",
1601       "t : a.cdefghijklmnopqrstuvwxyz\n",
1602       "u : ...defghi...mn.p..st...x..\n",
1603       "v : a...efghi...mn.p..st...x..\n",
1604       "w : a...efghi..lmn.p.r.t...x..\n",
1605       "x : abcdefghijklmnopq.stuvwxyz\n",
1606       "y : ...defg.i..lmnop..st...x..\n",
1607       "z : ...defg.i..lmnop.rst...x..\n"
1608      ]
1609     }
1610    ],
1611    "source": [
1612     "r = w_bombe.test(start_positions=('c', 'p', 'v'))\n",
1613     "print(r)\n",
1614     "for b in sorted(w_bombe.banks):\n",
1615     "    print(b, ': ', end='')\n",
1616     "    for w in sorted(w_bombe.banks[b]):\n",
1617     "        if w_bombe.banks[b][w]:\n",
1618     "            print(w, end='')\n",
1619     "        else:\n",
1620     "            print('.', end='')\n",
1621     "    print('')"
1622    ]
1623   },
1624   {
1625    "cell_type": "code",
1626    "execution_count": 851,
1627    "metadata": {
1628     "collapsed": false
1629    },
1630    "outputs": [
1631     {
1632      "name": "stdout",
1633      "output_type": "stream",
1634      "text": [
1635       "True\n",
1636       "a : abcdefghi..lmnop.rst.v.x.z\n",
1637       "b : a...ef.hi..lmnop.r.t...x..\n",
1638       "c : a..defg.i..lmn.p.rst...x..\n",
1639       "d : a.c.efghi.klmnopqrstu.wxyz\n",
1640       "e : abcdefghijklmnopqrstuvwx.z\n",
1641       "f : abcdefghijklmno.qrstuvwxyz\n",
1642       "g : a.cdefghijklmnopqrstuvwxyz\n",
1643       "h : ab.defghi...mnopqrstuvwxyz\n",
1644       "i : abcdefghijklm.opqrstuvwxyz\n",
1645       "j : ....efg.i..lmnop...t...x..\n",
1646       "k : ...defg.i..lmn.p..st...x..\n",
1647       "l : abcdefg.ijklmnopqrstuv.x..\n",
1648       "m : abcdefghijkl.nopqrstuvwxyz\n",
1649       "n : abcdefgh.jklmnopqrstuvwxyz\n",
1650       "o : ab.defghij.lmnop.r.tuvwxyz\n",
1651       "p : abcde.ghijklmnopqrstuvwxyz\n",
1652       "q : ...defghi..lmn.p..st...x..\n",
1653       "r : abcdefghi..lmnop.rst.v.x.z\n",
1654       "s : a.cdefghi.klmn.pqr.tuvwxyz\n",
1655       "t : abcdefghijklmnopqrstuvw.yz\n",
1656       "u : ...defghi..lmnop..st...x..\n",
1657       "v : a...efghi..lmnop.rst...x..\n",
1658       "w : ...defghi...mnop..st...x..\n",
1659       "x : abcdefghijklmnopqrs.uvwxyz\n",
1660       "y : ...d.fghi...mnop..st...x..\n",
1661       "z : a..defghi...mnop.rst...x..\n"
1662      ]
1663     }
1664    ],
1665    "source": [
1666     "r = w_bombe.test(start_positions=('e', 'l', 'f'))\n",
1667     "print(r)\n",
1668     "for b in sorted(w_bombe.banks):\n",
1669     "    print(b, ': ', end='')\n",
1670     "    for w in sorted(w_bombe.banks[b]):\n",
1671     "        if w_bombe.banks[b][w]:\n",
1672     "            print(w, end='')\n",
1673     "        else:\n",
1674     "            print('.', end='')\n",
1675     "    print('')"
1676    ]
1677   },
1678   {
1679    "cell_type": "code",
1680    "execution_count": 852,
1681    "metadata": {
1682     "collapsed": false
1683    },
1684    "outputs": [
1685     {
1686      "data": {
1687       "text/plain": [
1688        "{frozenset({'e', 'y'}),\n",
1689        " frozenset({'t', 'x'}),\n",
1690        " frozenset({'i', 'n'}),\n",
1691        " frozenset({'m'}),\n",
1692        " frozenset({'b', 'g'}),\n",
1693        " frozenset({'f', 'p'})}"
1694       ]
1695      },
1696      "execution_count": 852,
1697      "metadata": {},
1698      "output_type": "execute_result"
1699     }
1700    ],
1701    "source": [
1702     "ps = w_bombe.possible_plugboards()\n",
1703     "ps"
1704    ]
1705   },
1706   {
1707    "cell_type": "code",
1708    "execution_count": 853,
1709    "metadata": {
1710     "collapsed": false
1711    },
1712    "outputs": [
1713     {
1714      "data": {
1715       "text/plain": [
1716        "True"
1717       ]
1718      },
1719      "execution_count": 853,
1720      "metadata": {},
1721      "output_type": "execute_result"
1722     }
1723    ],
1724    "source": [
1725     "all(s0.isdisjoint(s1) for s0 in ps for s1 in ps if s0 != s1)"
1726    ]
1727   },
1728   {
1729    "cell_type": "code",
1730    "execution_count": 854,
1731    "metadata": {
1732     "collapsed": false
1733    },
1734    "outputs": [
1735     {
1736      "data": {
1737       "text/plain": [
1738        "({frozenset({1, 2}), frozenset({2, 3}), frozenset({3, 4})},\n",
1739        " frozenset({1, 2}),\n",
1740        " frozenset({3, 4}),\n",
1741        " frozenset({2, 3}))"
1742       ]
1743      },
1744      "execution_count": 854,
1745      "metadata": {},
1746      "output_type": "execute_result"
1747     }
1748    ],
1749    "source": [
1750     "s = set()\n",
1751     "f1 = frozenset((1, 2))\n",
1752     "f2 = frozenset((3, 4))\n",
1753     "f3 = frozenset((2, 3))\n",
1754     "s = s.union({f1})\n",
1755     "s = s.union({f2})\n",
1756     "s = s.union({f1})\n",
1757     "s = s.union({f3})\n",
1758     "s, f1, f2, f3"
1759    ]
1760   },
1761   {
1762    "cell_type": "code",
1763    "execution_count": 855,
1764    "metadata": {
1765     "collapsed": false
1766    },
1767    "outputs": [
1768     {
1769      "data": {
1770       "text/plain": [
1771        "False"
1772       ]
1773      },
1774      "execution_count": 855,
1775      "metadata": {},
1776      "output_type": "execute_result"
1777     }
1778    ],
1779    "source": [
1780     "all(s0.isdisjoint(s1) for s0 in s for s1 in s if s0 != s1)"
1781    ]
1782   },
1783   {
1784    "cell_type": "code",
1785    "execution_count": 856,
1786    "metadata": {
1787     "collapsed": false
1788    },
1789    "outputs": [
1790     {
1791      "data": {
1792       "text/plain": [
1793        "False"
1794       ]
1795      },
1796      "execution_count": 856,
1797      "metadata": {},
1798      "output_type": "execute_result"
1799     }
1800    ],
1801    "source": [
1802     "{1, 2}.isdisjoint({1, 6})"
1803    ]
1804   },
1805   {
1806    "cell_type": "code",
1807    "execution_count": null,
1808    "metadata": {
1809     "collapsed": true
1810    },
1811    "outputs": [],
1812    "source": []
1813   }
1814  ],
1815  "metadata": {
1816   "kernelspec": {
1817    "display_name": "Python 3",
1818    "language": "python",
1819    "name": "python3"
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