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": 31,
  79    "metadata": {
  80     "collapsed": false
  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     "                        other_bank = [b for b in c.banks if b != current.bank][0]\n",
 168     "                        other_wire = c.scrambler.lookup(current.wire)\n",
 169     "                        # print(\"  adding\", other_bank, other_wire, \"because\", c.banks)\n",
 170     "                        self.pending += [Signal(other_bank, other_wire)]\n",
 171     "    \n",
 172     "    def run(self, run_start=None, wheel1_pos='a', wheel2_pos='a', wheel3_pos='a', use_diagonal_board=True):\n",
 173     "        if not run_start:\n",
 174     "            run_start = self.test_start\n",
 175     "        self.solutions = []\n",
 176     "        self.set_positions(wheel1_pos, wheel2_pos, wheel3_pos)\n",
 177     "        for run_index in range(26*26*26):\n",
 178     "            if self.test(initial_signal=run_start, use_diagonal_board=use_diagonal_board):\n",
 179     "                self.solutions += [self.connections[0].scrambler.wheel_positions_l]\n",
 180     "            advance3 = True\n",
 181     "            advance2 = False\n",
 182     "            advance1 = False\n",
 183     "            if (run_index + 1) % 26 == 0: advance2 = True\n",
 184     "            if (run_index + 1) % (26*26) == 0: advance1 = True\n",
 185     "            for c in self.connections:\n",
 186     "                c.scrambler.advance(advance1, advance2, advance3)\n",
 187     "        return self.solutions\n",
 188     "    \n",
 189     "    def possible_plugboards(self):\n",
 190     "        possibles = set()\n",
 191     "        for b in self.banks:\n",
 192     "            active = [w for w in self.banks[b] if self.banks[b][w]]\n",
 193     "            inactive = [w for w in self.banks[b] if not self.banks[b][w]]\n",
 194     "            if len(active) == 1:\n",
 195     "                possibles = possibles.union({frozenset((b, active[0]))})\n",
 196     "            if len(inactive) == 1:\n",
 197     "                possibles = possibles.union({frozenset((b, inactive[0]))})\n",
 198     "        return possibles\n"
 199    ]
 200   },
 201   {
 202    "cell_type": "code",
 203    "execution_count": 32,
 204    "metadata": {
 205     "collapsed": false
 206    },
 207    "outputs": [],
 208    "source": [
 209     "bombe = Bombe(wheel_i_spec, wheel_ii_spec, wheel_iii_spec, reflector_b_spec)\n",
 210     "# len(bombe.banks), bombe.banks['a'] == bombe.banks['b']"
 211    ]
 212   },
 213   {
 214    "cell_type": "code",
 215    "execution_count": 33,
 216    "metadata": {
 217     "collapsed": true
 218    },
 219    "outputs": [],
 220    "source": [
 221     "test_enigma = Enigma(reflector_b_spec, \n",
 222     "                wheel_i_spec, wheel_i_pegs,\n",
 223     "                wheel_ii_spec, wheel_ii_pegs,\n",
 224     "                wheel_iii_spec, wheel_iii_pegs,\n",
 225     "                1, 1, 1,\n",
 226     "                '')"
 227    ]
 228   },
 229   {
 230    "cell_type": "code",
 231    "execution_count": 34,
 232    "metadata": {
 233     "collapsed": false
 234    },
 235    "outputs": [
 236     {
 237      "data": {
 238       "text/plain": [
 239        "'opgndxcrwomnlnecjz'"
 240       ]
 241      },
 242      "execution_count": 34,
 243      "metadata": {},
 244      "output_type": "execute_result"
 245     }
 246    ],
 247    "source": [
 248     "test_enigma.set_wheels('a', 'a', 'a')\n",
 249     "pt = 'thisisatestmessage'\n",
 250     "ct = test_enigma.encipher(pt)\n",
 251     "ct"
 252    ]
 253   },
 254   {
 255    "cell_type": "code",
 256    "execution_count": 35,
 257    "metadata": {
 258     "collapsed": false
 259    },
 260    "outputs": [
 261     {
 262      "data": {
 263       "text/plain": [
 264        "'aas'"
 265       ]
 266      },
 267      "execution_count": 35,
 268      "metadata": {},
 269      "output_type": "execute_result"
 270     }
 271    ],
 272    "source": [
 273     "cat(test_enigma.wheel_positions_l)"
 274    ]
 275   },
 276   {
 277    "cell_type": "code",
 278    "execution_count": 36,
 279    "metadata": {
 280     "collapsed": false
 281    },
 282    "outputs": [
 283     {
 284      "data": {
 285       "text/plain": [
 286        "[MenuIem(before='t', after='o', number=1),\n",
 287        " MenuIem(before='h', after='p', number=2),\n",
 288        " MenuIem(before='i', after='g', number=3),\n",
 289        " MenuIem(before='s', after='n', number=4),\n",
 290        " MenuIem(before='i', after='d', number=5),\n",
 291        " MenuIem(before='s', after='x', number=6),\n",
 292        " MenuIem(before='a', after='c', number=7),\n",
 293        " MenuIem(before='t', after='r', number=8),\n",
 294        " MenuIem(before='e', after='w', number=9),\n",
 295        " MenuIem(before='s', after='o', number=10),\n",
 296        " MenuIem(before='t', after='m', number=11),\n",
 297        " MenuIem(before='m', after='n', number=12),\n",
 298        " MenuIem(before='e', after='l', number=13),\n",
 299        " MenuIem(before='s', after='n', number=14),\n",
 300        " MenuIem(before='s', after='e', number=15),\n",
 301        " MenuIem(before='a', after='c', number=16),\n",
 302        " MenuIem(before='g', after='j', number=17),\n",
 303        " MenuIem(before='e', after='z', number=18)]"
 304       ]
 305      },
 306      "execution_count": 36,
 307      "metadata": {},
 308      "output_type": "execute_result"
 309     }
 310    ],
 311    "source": [
 312     "menu = [MenuItem(p, c, i+1) for i, (p, c) in enumerate(zip(pt, ct))]\n",
 313     "menu"
 314    ]
 315   },
 316   {
 317    "cell_type": "code",
 318    "execution_count": 37,
 319    "metadata": {
 320     "collapsed": true
 321    },
 322    "outputs": [],
 323    "source": [
 324     "def make_menu(plaintext, ciphertext):\n",
 325     "    return [MenuItem(p, c, i+1) \n",
 326     "            for i, (p, c) in enumerate(zip(plaintext, ciphertext))]"
 327    ]
 328   },
 329   {
 330    "cell_type": "code",
 331    "execution_count": 38,
 332    "metadata": {
 333     "collapsed": false
 334    },
 335    "outputs": [
 336     {
 337      "data": {
 338       "text/plain": [
 339        "[MenuIem(before='t', after='o', number=1),\n",
 340        " MenuIem(before='h', after='p', number=2),\n",
 341        " MenuIem(before='i', after='g', number=3),\n",
 342        " MenuIem(before='s', after='n', number=4),\n",
 343        " MenuIem(before='i', after='d', number=5),\n",
 344        " MenuIem(before='s', after='x', number=6),\n",
 345        " MenuIem(before='a', after='c', number=7),\n",
 346        " MenuIem(before='t', after='r', number=8),\n",
 347        " MenuIem(before='e', after='w', number=9),\n",
 348        " MenuIem(before='s', after='o', number=10),\n",
 349        " MenuIem(before='t', after='m', number=11),\n",
 350        " MenuIem(before='m', after='n', number=12),\n",
 351        " MenuIem(before='e', after='l', number=13),\n",
 352        " MenuIem(before='s', after='n', number=14),\n",
 353        " MenuIem(before='s', after='e', number=15),\n",
 354        " MenuIem(before='a', after='c', number=16),\n",
 355        " MenuIem(before='g', after='j', number=17),\n",
 356        " MenuIem(before='e', after='z', number=18)]"
 357       ]
 358      },
 359      "execution_count": 38,
 360      "metadata": {},
 361      "output_type": "execute_result"
 362     }
 363    ],
 364    "source": [
 365     "make_menu(pt, ct)"
 366    ]
 367   },
 368   {
 369    "cell_type": "code",
 370    "execution_count": 39,
 371    "metadata": {
 372     "collapsed": false
 373    },
 374    "outputs": [
 375     {
 376      "data": {
 377       "text/plain": [
 378        "'s'"
 379       ]
 380      },
 381      "execution_count": 39,
 382      "metadata": {},
 383      "output_type": "execute_result"
 384     }
 385    ],
 386    "source": [
 387     "(collections.Counter(m.before for m in menu) + collections.Counter(m.after for m in menu)).most_common(1)[0][0]"
 388    ]
 389   },
 390   {
 391    "cell_type": "code",
 392    "execution_count": 42,
 393    "metadata": {
 394     "collapsed": false
 395    },
 396    "outputs": [],
 397    "source": [
 398     "bombe.read_menu(menu)"
 399    ]
 400   },
 401   {
 402    "cell_type": "code",
 403    "execution_count": 43,
 404    "metadata": {
 405     "collapsed": false
 406    },
 407    "outputs": [
 408     {
 409      "data": {
 410       "text/plain": [
 411        "18"
 412       ]
 413      },
 414      "execution_count": 43,
 415      "metadata": {},
 416      "output_type": "execute_result"
 417     }
 418    ],
 419    "source": [
 420     "len(bombe.connections)"
 421    ]
 422   },
 423   {
 424    "cell_type": "code",
 425    "execution_count": 27,
 426    "metadata": {
 427     "collapsed": false
 428    },
 429    "outputs": [
 430     {
 431      "name": "stdout",
 432      "output_type": "stream",
 433      "text": [
 434       "['t', 'o'] aaa\n",
 435       "['h', 'p'] aab\n",
 436       "['i', 'g'] aac\n",
 437       "['s', 'n'] aad\n",
 438       "['i', 'd'] aae\n",
 439       "['s', 'x'] aaf\n",
 440       "['a', 'c'] aag\n",
 441       "['t', 'r'] aah\n",
 442       "['e', 'w'] aai\n",
 443       "['s', 'o'] aaj\n",
 444       "['t', 'm'] aak\n",
 445       "['m', 'n'] aal\n",
 446       "['e', 'l'] aam\n",
 447       "['s', 'n'] aan\n",
 448       "['s', 'e'] aao\n",
 449       "['a', 'c'] aap\n",
 450       "['g', 'j'] aaq\n",
 451       "['e', 'z'] aar\n",
 452       "['t', 'o'] aaa\n",
 453       "['h', 'p'] aab\n",
 454       "['i', 'g'] aac\n",
 455       "['s', 'n'] aad\n",
 456       "['i', 'd'] aae\n",
 457       "['s', 'x'] aaf\n",
 458       "['a', 'c'] aag\n",
 459       "['t', 'r'] aah\n",
 460       "['e', 'w'] aai\n",
 461       "['s', 'o'] aaj\n",
 462       "['t', 'm'] aak\n",
 463       "['m', 'n'] aal\n",
 464       "['e', 'l'] aam\n",
 465       "['s', 'n'] aan\n",
 466       "['s', 'e'] aao\n",
 467       "['a', 'c'] aap\n",
 468       "['g', 'j'] aaq\n",
 469       "['e', 'z'] aar\n"
 470      ]
 471     }
 472    ],
 473    "source": [
 474     "for c in bombe.connections:\n",
 475     "    print(c.banks, cat(c.scrambler.wheel_positions_l))"
 476    ]
 477   },
 478   {
 479    "cell_type": "code",
 480    "execution_count": 44,
 481    "metadata": {
 482     "collapsed": false
 483    },
 484    "outputs": [
 485     {
 486      "data": {
 487       "text/plain": [
 488        "'ot:hp:gi:ns:di:sx:ac:rt:ew:os:mt:mn:el:ns:es:ac:gj:ez'"
 489       ]
 490      },
 491      "execution_count": 44,
 492      "metadata": {},
 493      "output_type": "execute_result"
 494     }
 495    ],
 496    "source": [
 497     "':'.join(cat(sorted(c.banks)) for c in bombe.connections)"
 498    ]
 499   },
 500   {
 501    "cell_type": "code",
 502    "execution_count": 45,
 503    "metadata": {
 504     "collapsed": false
 505    },
 506    "outputs": [
 507     {
 508      "data": {
 509       "text/plain": [
 510        "'aaa:aab:aac:aad:aae:aaf:aag:aah:aai:aaj:aak:aal:aam:aan:aao:aap:aaq:aar'"
 511       ]
 512      },
 513      "execution_count": 45,
 514      "metadata": {},
 515      "output_type": "execute_result"
 516     }
 517    ],
 518    "source": [
 519     "':'.join(cat(c.scrambler.wheel_positions_l) for c in bombe.connections)"
 520    ]
 521   },
 522   {
 523    "cell_type": "code",
 524    "execution_count": 56,
 525    "metadata": {
 526     "collapsed": false
 527    },
 528    "outputs": [
 529     {
 530      "data": {
 531       "text/plain": [
 532        "True"
 533       ]
 534      },
 535      "execution_count": 56,
 536      "metadata": {},
 537      "output_type": "execute_result"
 538     }
 539    ],
 540    "source": [
 541     "bombe.test(Signal('t', 't'))"
 542    ]
 543   },
 544   {
 545    "cell_type": "code",
 546    "execution_count": 57,
 547    "metadata": {
 548     "collapsed": false
 549    },
 550    "outputs": [
 551     {
 552      "data": {
 553       "text/plain": [
 554        "{'a': False,\n",
 555        " 'b': False,\n",
 556        " 'c': False,\n",
 557        " 'd': False,\n",
 558        " 'e': False,\n",
 559        " 'f': False,\n",
 560        " 'g': False,\n",
 561        " 'h': False,\n",
 562        " 'i': False,\n",
 563        " 'j': False,\n",
 564        " 'k': False,\n",
 565        " 'l': False,\n",
 566        " 'm': False,\n",
 567        " 'n': False,\n",
 568        " 'o': False,\n",
 569        " 'p': False,\n",
 570        " 'q': False,\n",
 571        " 'r': False,\n",
 572        " 's': False,\n",
 573        " 't': True,\n",
 574        " 'u': False,\n",
 575        " 'v': False,\n",
 576        " 'w': False,\n",
 577        " 'x': False,\n",
 578        " 'y': False,\n",
 579        " 'z': False}"
 580       ]
 581      },
 582      "execution_count": 57,
 583      "metadata": {},
 584      "output_type": "execute_result"
 585     }
 586    ],
 587    "source": [
 588     "bombe.banks['t']"
 589    ]
 590   },
 591   {
 592    "cell_type": "code",
 593    "execution_count": 48,
 594    "metadata": {
 595     "collapsed": false
 596    },
 597    "outputs": [
 598     {
 599      "name": "stdout",
 600      "output_type": "stream",
 601      "text": [
 602       "a : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 603       "b : AbCDEfGHIJkLMNOPqRSTuvWXyZ\n",
 604       "c : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 605       "d : ABCDEFGHIJKLMNOPQRSTUVWXyZ\n",
 606       "e : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 607       "f : AbCDEfGHIJkLMNOPqRSTuvWXyZ\n",
 608       "g : ABCDEFGHIJKLMNOPQRSTuVWXYZ\n",
 609       "h : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 610       "i : ABCDEFGHIJKLMNOPQRSTUvWXYZ\n",
 611       "j : ABCDEFGHIjKLMNOPQRSTUVWXYZ\n",
 612       "k : AbCDEfGHIJkLMNOPqRSTuvWXyZ\n",
 613       "l : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 614       "m : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 615       "n : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 616       "o : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 617       "p : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 618       "q : AbCDEfGHIJkLMNOPqRSTuvWXyZ\n",
 619       "r : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 620       "s : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 621       "t : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 622       "u : AbCDEfgHIJkLMNOPqRSTuvWXyZ\n",
 623       "v : AbCDEfGHiJkLMNOPqRSTuvWXyZ\n",
 624       "w : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 625       "x : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
 626       "y : AbCdEfGHIJkLMNOPqRSTuvWXyZ\n",
 627       "z : ABCDEFGHIJKLMNOPQRSTUVWXYZ\n"
 628      ]
 629     }
 630    ],
 631    "source": [
 632     "for b in sorted(bombe.banks):\n",
 633     "    print(b, ': ', end='')\n",
 634     "    for w in sorted(bombe.banks[b]):\n",
 635     "        if bombe.banks[b][w]:\n",
 636     "            print(w.upper(), end='')\n",
 637     "        else:\n",
 638     "            print(w, end='')\n",
 639     "    print('')"
 640    ]
 641   },
 642   {
 643    "cell_type": "code",
 644    "execution_count": 49,
 645    "metadata": {
 646     "collapsed": false
 647    },
 648    "outputs": [
 649     {
 650      "name": "stdout",
 651      "output_type": "stream",
 652      "text": [
 653       "a : abcdefghijklmnopqrstuvwxyz\n",
 654       "b : a.cde.ghij.lmnop.rst..wx.z\n",
 655       "c : abcdefghijklmnopqrstuvwxyz\n",
 656       "d : abcdefghijklmnopqrstuvwx.z\n",
 657       "e : abcdefghijklmnopqrstuvwxyz\n",
 658       "f : a.cde.ghij.lmnop.rst..wx.z\n",
 659       "g : abcdefghijklmnopqrst.vwxyz\n",
 660       "h : abcdefghijklmnopqrstuvwxyz\n",
 661       "i : abcdefghijklmnopqrstu.wxyz\n",
 662       "j : abcdefghi.klmnopqrstuvwxyz\n",
 663       "k : a.cde.ghij.lmnop.rst..wx.z\n",
 664       "l : abcdefghijklmnopqrstuvwxyz\n",
 665       "m : abcdefghijklmnopqrstuvwxyz\n",
 666       "n : abcdefghijklmnopqrstuvwxyz\n",
 667       "o : abcdefghijklmnopqrstuvwxyz\n",
 668       "p : abcdefghijklmnopqrstuvwxyz\n",
 669       "q : a.cde.ghij.lmnop.rst..wx.z\n",
 670       "r : abcdefghijklmnopqrstuvwxyz\n",
 671       "s : abcdefghijklmnopqrstuvwxyz\n",
 672       "t : abcdefghijklmnopqrstuvwxyz\n",
 673       "u : a.cde..hij.lmnop.rst..wx.z\n",
 674       "v : a.cde.gh.j.lmnop.rst..wx.z\n",
 675       "w : abcdefghijklmnopqrstuvwxyz\n",
 676       "x : abcdefghijklmnopqrstuvwxyz\n",
 677       "y : a.c.e.ghij.lmnop.rst..wx.z\n",
 678       "z : abcdefghijklmnopqrstuvwxyz\n"
 679      ]
 680     }
 681    ],
 682    "source": [
 683     "for b in sorted(bombe.banks):\n",
 684     "    print(b, ': ', end='')\n",
 685     "    for w in sorted(bombe.banks[b]):\n",
 686     "        if bombe.banks[b][w]:\n",
 687     "            print(w, end='')\n",
 688     "        else:\n",
 689     "            print('.', end='')\n",
 690     "    print('')"
 691    ]
 692   },
 693   {
 694    "cell_type": "code",
 695    "execution_count": 50,
 696    "metadata": {
 697     "collapsed": false
 698    },
 699    "outputs": [
 700     {
 701      "data": {
 702       "text/plain": [
 703        "('a', 'a', 'a')"
 704       ]
 705      },
 706      "execution_count": 50,
 707      "metadata": {},
 708      "output_type": "execute_result"
 709     }
 710    ],
 711    "source": [
 712     "bombe.wheel_positions_l"
 713    ]
 714   },
 715   {
 716    "cell_type": "code",
 717    "execution_count": 51,
 718    "metadata": {
 719     "collapsed": false
 720    },
 721    "outputs": [
 722     {
 723      "name": "stdout",
 724      "output_type": "stream",
 725      "text": [
 726       "['t', 'o'] pqr\n",
 727       "['h', 'p'] pqs\n",
 728       "['i', 'g'] pqt\n",
 729       "['s', 'n'] pqu\n",
 730       "['i', 'd'] pqv\n",
 731       "['s', 'x'] pqw\n",
 732       "['a', 'c'] pqx\n",
 733       "['t', 'r'] pqy\n",
 734       "['e', 'w'] pqz\n",
 735       "['s', 'o'] pqa\n",
 736       "['t', 'm'] pqb\n",
 737       "['m', 'n'] pqc\n",
 738       "['e', 'l'] pqd\n",
 739       "['s', 'n'] pqe\n",
 740       "['s', 'e'] pqf\n",
 741       "['a', 'c'] pqg\n",
 742       "['g', 'j'] pqh\n",
 743       "['e', 'z'] pqi\n"
 744      ]
 745     }
 746    ],
 747    "source": [
 748     "bombe.set_positions('p', 'q', 'r')\n",
 749     "for c in bombe.connections:\n",
 750     "    print(c.banks, cat(c.scrambler.wheel_positions_l))"
 751    ]
 752   },
 753   {
 754    "cell_type": "code",
 755    "execution_count": 52,
 756    "metadata": {
 757     "collapsed": false
 758    },
 759    "outputs": [],
 760    "source": [
 761     "# bombe.run()\n",
 762     "# print('x')"
 763    ]
 764   },
 765   {
 766    "cell_type": "code",
 767    "execution_count": 53,
 768    "metadata": {
 769     "collapsed": false
 770    },
 771    "outputs": [
 772     {
 773      "name": "stdout",
 774      "output_type": "stream",
 775      "text": [
 776       "a : .b.defghijklmnopqrstuvwxyz\n",
 777       "b : a.cde.ghij.lmnop.rst..wx.z\n",
 778       "c : .b.defghijklmnopqrstuvwxyz\n",
 779       "d : abc.e.gh.jklmnopqrstuvwxyz\n",
 780       "e : abcd.fghijklmnopqrstuvwxyz\n",
 781       "f : a.c.e.g.ij.lmno..rst..wx.z\n",
 782       "g : abcdef.h..klmnopqrstuvwxyz\n",
 783       "h : abcde.g.ij.lmno.qrst..wxyz\n",
 784       "i : abc.ef.h.jklmnopqrstuvwxyz\n",
 785       "j : abcdef.hi.klmnopqrstuvwx.z\n",
 786       "k : a.cde.g.ij.lmno..rst..wx.z\n",
 787       "l : abcdefghijk.mnopqrstuvwxyz\n",
 788       "m : abcdefghijkl.nopqrstuvwxyz\n",
 789       "n : abcdefghijklm.opqrstuvwxyz\n",
 790       "o : abcdefghijklmn.pqrstuvwxyz\n",
 791       "p : abcde.g.ij.lmno.qrst..wxyz\n",
 792       "q : a.cde.ghij.lmnop.rst..wx.z\n",
 793       "r : abcdefghijklmnopq.stuvwxyz\n",
 794       "s : abcdefghijklmnopqr.tuvwxyz\n",
 795       "t : abcdefghijklmnopqrs.uvwxyz\n",
 796       "u : a.cde.g.ij.lmno..rst..wx.z\n",
 797       "v : a.cde.g.ij.lmno..rst..wx.z\n",
 798       "w : abcdefghijklmnopqrstuv.xyz\n",
 799       "x : abcdefghijklmnopqrstuvw.yz\n",
 800       "y : a.cde.ghi..lmnop.rst..wx.z\n",
 801       "z : abcdefghijklmnopqrstuvwxy.\n"
 802      ]
 803     }
 804    ],
 805    "source": [
 806     "bombe.set_positions('a', 'a', 'b')\n",
 807     "bombe.test(Signal('s', 'a'))\n",
 808     "\n",
 809     "for b in sorted(bombe.banks):\n",
 810     "    print(b, ': ', end='')\n",
 811     "    for w in sorted(bombe.banks[b]):\n",
 812     "        if bombe.banks[b][w]:\n",
 813     "            print(w, end='')\n",
 814     "        else:\n",
 815     "            print('.', end='')\n",
 816     "    print('')"
 817    ]
 818   },
 819   {
 820    "cell_type": "code",
 821    "execution_count": 54,
 822    "metadata": {
 823     "collapsed": false
 824    },
 825    "outputs": [
 826     {
 827      "name": "stdout",
 828      "output_type": "stream",
 829      "text": [
 830       "a : ..........................\n",
 831       "b : ..........................\n",
 832       "c : ..........................\n",
 833       "d : ..........................\n",
 834       "e : ....e.....................\n",
 835       "f : ..........................\n",
 836       "g : ..........................\n",
 837       "h : ..........................\n",
 838       "i : ..........................\n",
 839       "j : ..........................\n",
 840       "k : ..........................\n",
 841       "l : ...........l..............\n",
 842       "m : ............m.............\n",
 843       "n : .............n............\n",
 844       "o : ..............o...........\n",
 845       "p : ..........................\n",
 846       "q : ..........................\n",
 847       "r : .................r........\n",
 848       "s : ..................s.......\n",
 849       "t : ...................t......\n",
 850       "u : ..........................\n",
 851       "v : ..........................\n",
 852       "w : ......................w...\n",
 853       "x : .......................x..\n",
 854       "y : ..........................\n",
 855       "z : .........................z\n"
 856      ]
 857     }
 858    ],
 859    "source": [
 860     "bombe.set_positions('a', 'a', 'b')\n",
 861     "bombe.test()\n",
 862     "\n",
 863     "for b in sorted(bombe.banks):\n",
 864     "    print(b, ': ', end='')\n",
 865     "    for w in sorted(bombe.banks[b]):\n",
 866     "        if bombe.banks[b][w]:\n",
 867     "            print(w, end='')\n",
 868     "        else:\n",
 869     "            print('.', end='')\n",
 870     "    print('')"
 871    ]
 872   },
 873   {
 874    "cell_type": "code",
 875    "execution_count": 55,
 876    "metadata": {
 877     "collapsed": false
 878    },
 879    "outputs": [
 880     {
 881      "data": {
 882       "text/plain": [
 883        "1"
 884       ]
 885      },
 886      "execution_count": 55,
 887      "metadata": {},
 888      "output_type": "execute_result"
 889     }
 890    ],
 891    "source": [
 892     "len([bombe.banks['t'][w] for w in bombe.banks['t'] if bombe.banks['t'][w]])"
 893    ]
 894   },
 895   {
 896    "cell_type": "code",
 897    "execution_count": 25,
 898    "metadata": {
 899     "collapsed": false
 900    },
 901    "outputs": [],
 902    "source": [
 903     "# %%timeit\n",
 904     "# results = bombe.run()\n",
 905     "# print(len(results), ('a', 'a', 'b') in results)"
 906    ]
 907   },
 908   {
 909    "cell_type": "code",
 910    "execution_count": 26,
 911    "metadata": {
 912     "collapsed": false
 913    },
 914    "outputs": [],
 915    "source": [
 916     "# %%timeit\n",
 917     "# results = bombe.run(use_diagonal_board=False)\n",
 918     "# print(len(results), ('a', 'a', 'b') in results)"
 919    ]
 920   },
 921   {
 922    "cell_type": "code",
 923    "execution_count": 27,
 924    "metadata": {
 925     "collapsed": false
 926    },
 927    "outputs": [
 928     {
 929      "data": {
 930       "text/plain": [
 931        "('a', 'a', 'b')"
 932       ]
 933      },
 934      "execution_count": 27,
 935      "metadata": {},
 936      "output_type": "execute_result"
 937     }
 938    ],
 939    "source": [
 940     "bombe.wheel_positions_l"
 941    ]
 942   },
 943   {
 944    "cell_type": "code",
 945    "execution_count": 28,
 946    "metadata": {
 947     "collapsed": false
 948    },
 949    "outputs": [
 950     {
 951      "data": {
 952       "text/plain": [
 953        "False"
 954       ]
 955      },
 956      "execution_count": 28,
 957      "metadata": {},
 958      "output_type": "execute_result"
 959     }
 960    ],
 961    "source": [
 962     "bombe.test(Signal('t', 't'), ('p', 'p', 'p'))"
 963    ]
 964   },
 965   {
 966    "cell_type": "code",
 967    "execution_count": 29,
 968    "metadata": {
 969     "collapsed": false
 970    },
 971    "outputs": [
 972     {
 973      "data": {
 974       "text/plain": [
 975        "('p', 'p', 'p')"
 976       ]
 977      },
 978      "execution_count": 29,
 979      "metadata": {},
 980      "output_type": "execute_result"
 981     }
 982    ],
 983    "source": [
 984     "bombe.wheel_positions_l"
 985    ]
 986   },
 987   {
 988    "cell_type": "code",
 989    "execution_count": 30,
 990    "metadata": {
 991     "collapsed": false
 992    },
 993    "outputs": [
 994     {
 995      "name": "stdout",
 996      "output_type": "stream",
 997      "text": [
 998       "a : abcdefghijklmnop.rst.vwxyz\n",
 999       "b : a.cde.g.ij.lmno..rst..wx.z\n",
1000       "c : abcdefghijklmnop.rst.vwxyz\n",
1001       "d : abcdefghijklmnopqrstuvwxyz\n",
1002       "e : abcdefghijklmnopqrstuvwxyz\n",
1003       "f : a.cde.g.ij.lmno..rst..wx.z\n",
1004       "g : abcdefghijklmnopqrstuvwxyz\n",
1005       "h : a.cde.ghijklmnop.rst.vwxyz\n",
1006       "i : abcdefghijklmnopqrstuvwxyz\n",
1007       "j : abcdefghijklmnopqrstuvwxyz\n",
1008       "k : a.cde.ghij.lmnop.rst..wx.z\n",
1009       "l : abcdefghijklmnopqrstuvwxyz\n",
1010       "m : abcdefghijklmnopqrstuvwxyz\n",
1011       "n : abcdefghijklmnopqrstuvwxyz\n",
1012       "o : abcdefghijklmnopqrstuvwxyz\n",
1013       "p : a.cde.ghijklmnop.rst.vwxyz\n",
1014       "q : ...de.g.ij.lmno..rst..wx.z\n",
1015       "r : abcdefghijklmnopqrstuvwxyz\n",
1016       "s : abcdefghijklmnopqrstuvwxyz\n",
1017       "t : abcdefghijklmnopqrstuvwxyz\n",
1018       "u : ...de.g.ij.lmno..rst..wx.z\n",
1019       "v : a.cde.ghij.lmnop.rst..wx.z\n",
1020       "w : abcdefghijklmnopqrstuvwxyz\n",
1021       "x : abcdefghijklmnopqrstuvwxyz\n",
1022       "y : a.cde.ghij.lmnop.rst..wx.z\n",
1023       "z : abcdefghijklmnopqrstuvwxyz\n"
1024      ]
1025     }
1026    ],
1027    "source": [
1028     "for b in sorted(bombe.banks):\n",
1029     "    print(b, ': ', end='')\n",
1030     "    for w in sorted(bombe.banks[b]):\n",
1031     "        if bombe.banks[b][w]:\n",
1032     "            print(w, end='')\n",
1033     "        else:\n",
1034     "            print('.', end='')\n",
1035     "    print('')"
1036    ]
1037   },
1038   {
1039    "cell_type": "code",
1040    "execution_count": 31,
1041    "metadata": {
1042     "collapsed": false
1043    },
1044    "outputs": [
1045     {
1046      "data": {
1047       "text/plain": [
1048        "17576"
1049       ]
1050      },
1051      "execution_count": 31,
1052      "metadata": {},
1053      "output_type": "execute_result"
1054     }
1055    ],
1056    "source": [
1057     "allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1058     "len(list(allwheels))"
1059    ]
1060   },
1061   {
1062    "cell_type": "code",
1063    "execution_count": 32,
1064    "metadata": {
1065     "collapsed": false
1066    },
1067    "outputs": [
1068     {
1069      "data": {
1070       "text/plain": [
1071        "(('a', 'a', 'b'), True)"
1072       ]
1073      },
1074      "execution_count": 32,
1075      "metadata": {},
1076      "output_type": "execute_result"
1077     }
1078    ],
1079    "source": [
1080     "b = Bombe(wheel_i_spec, wheel_ii_spec, wheel_iii_spec, reflector_b_spec, menu=menu)\n",
1081     "b(('a', 'a', 'b'))"
1082    ]
1083   },
1084   {
1085    "cell_type": "code",
1086    "execution_count": 33,
1087    "metadata": {
1088     "collapsed": false
1089    },
1090    "outputs": [],
1091    "source": [
1092     "b = Bombe(wheel_i_spec, wheel_ii_spec, wheel_iii_spec, reflector_b_spec, menu=menu)(('a', 'a', 'b'))"
1093    ]
1094   },
1095   {
1096    "cell_type": "code",
1097    "execution_count": 34,
1098    "metadata": {
1099     "collapsed": false
1100    },
1101    "outputs": [
1102     {
1103      "data": {
1104       "text/plain": [
1105        "[('a', 'a', 'b')]"
1106       ]
1107      },
1108      "execution_count": 34,
1109      "metadata": {},
1110      "output_type": "execute_result"
1111     }
1112    ],
1113    "source": [
1114     "allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1115     "\n",
1116     "with multiprocessing.Pool() as pool:\n",
1117     "    res = pool.map(Bombe(wheel_i_spec, wheel_ii_spec, wheel_iii_spec, reflector_b_spec, menu=menu),\n",
1118     "                  allwheels)\n",
1119     "[r[0] for r in res if r[1]]"
1120    ]
1121   },
1122   {
1123    "cell_type": "code",
1124    "execution_count": 35,
1125    "metadata": {
1126     "collapsed": true
1127    },
1128    "outputs": [],
1129    "source": [
1130     "def run_multi_bombe(wheel1_spec, wheel2_spec, wheel3_spec, reflector_spec, menu,\n",
1131     "                    start_signal=None, use_diagonal_board=True, \n",
1132     "                    verify_plugboard=True):\n",
1133     "    allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1134     "\n",
1135     "    with multiprocessing.Pool() as pool:\n",
1136     "        res = pool.map(Bombe(wheel1_spec, wheel2_spec, wheel3_spec, \n",
1137     "            reflector_spec, menu=menu, start_signal=start_signal, \n",
1138     "            use_diagonal_board=use_diagonal_board, \n",
1139     "            verify_plugboard=verify_plugboard),\n",
1140     "                  allwheels)\n",
1141     "    return [r[0] for r in res if r[1]]"
1142    ]
1143   },
1144   {
1145    "cell_type": "code",
1146    "execution_count": 36,
1147    "metadata": {
1148     "collapsed": false
1149    },
1150    "outputs": [
1151     {
1152      "data": {
1153       "text/plain": [
1154        "[('a', 'a', 'b')]"
1155       ]
1156      },
1157      "execution_count": 36,
1158      "metadata": {},
1159      "output_type": "execute_result"
1160     }
1161    ],
1162    "source": [
1163     "[r[0] for r in res if r[1]]"
1164    ]
1165   },
1166   {
1167    "cell_type": "code",
1168    "execution_count": 58,
1169    "metadata": {
1170     "collapsed": false
1171    },
1172    "outputs": [],
1173    "source": [
1174     "# Setting sheet line 31 from http://www.codesandciphers.org.uk/enigma/enigma3.htm\n",
1175     "# Enigma simulation settings are \n",
1176     "# http://enigma.louisedade.co.uk/enigma.html?m3;b;b153;AFTX;AJFE;AU-BG-EY-FP-HL-IN-JZ-OS-QR-TX\n",
1177     "w_enigma = Enigma(reflector_b_spec, \n",
1178     "                wheel_i_spec, wheel_i_pegs,\n",
1179     "                wheel_v_spec, wheel_v_pegs,\n",
1180     "                wheel_iii_spec, wheel_iii_pegs,\n",
1181     "                6, 20, 24,\n",
1182     "                'ua pf rq so ni ey bg hl tx zj')"
1183    ]
1184   },
1185   {
1186    "cell_type": "code",
1187    "execution_count": 59,
1188    "metadata": {
1189     "collapsed": false
1190    },
1191    "outputs": [
1192     {
1193      "data": {
1194       "text/plain": [
1195        "('e', 'l', 'e')"
1196       ]
1197      },
1198      "execution_count": 59,
1199      "metadata": {},
1200      "output_type": "execute_result"
1201     }
1202    ],
1203    "source": [
1204     "w_enigma.set_wheels('j', 'e', 'b')\n",
1205     "tuple(unpos(p) for p in w_enigma.wheel_positions)"
1206    ]
1207   },
1208   {
1209    "cell_type": "code",
1210    "execution_count": 39,
1211    "metadata": {
1212     "collapsed": false
1213    },
1214    "outputs": [
1215     {
1216      "data": {
1217       "text/plain": [
1218        "'dhnpforeeimgg'"
1219       ]
1220      },
1221      "execution_count": 39,
1222      "metadata": {},
1223      "output_type": "execute_result"
1224     }
1225    ],
1226    "source": [
1227     "w_enigma.set_wheels('j', 'e', 'b')\n",
1228     "pt = 'someplaintext'\n",
1229     "ct = w_enigma.encipher(pt)\n",
1230     "ct"
1231    ]
1232   },
1233   {
1234    "cell_type": "code",
1235    "execution_count": 40,
1236    "metadata": {
1237     "collapsed": false
1238    },
1239    "outputs": [
1240     {
1241      "data": {
1242       "text/plain": [
1243        "('j', 'e', 'o')"
1244       ]
1245      },
1246      "execution_count": 40,
1247      "metadata": {},
1248      "output_type": "execute_result"
1249     }
1250    ],
1251    "source": [
1252     "w_enigma.wheel_positions_l"
1253    ]
1254   },
1255   {
1256    "cell_type": "code",
1257    "execution_count": 41,
1258    "metadata": {
1259     "collapsed": false
1260    },
1261    "outputs": [
1262     {
1263      "data": {
1264       "text/plain": [
1265        "[MenuIem(before='s', after='d', number=1),\n",
1266        " MenuIem(before='o', after='h', number=2),\n",
1267        " MenuIem(before='m', after='n', number=3),\n",
1268        " MenuIem(before='e', after='p', number=4),\n",
1269        " MenuIem(before='p', after='f', number=5),\n",
1270        " MenuIem(before='l', after='o', number=6),\n",
1271        " MenuIem(before='a', after='r', number=7),\n",
1272        " MenuIem(before='i', after='e', number=8),\n",
1273        " MenuIem(before='n', after='e', number=9),\n",
1274        " MenuIem(before='t', after='i', number=10),\n",
1275        " MenuIem(before='e', after='m', number=11),\n",
1276        " MenuIem(before='x', after='g', number=12),\n",
1277        " MenuIem(before='t', after='g', number=13)]"
1278       ]
1279      },
1280      "execution_count": 41,
1281      "metadata": {},
1282      "output_type": "execute_result"
1283     }
1284    ],
1285    "source": [
1286     "w_menu = [MenuItem(p, c, i+1) for i, (p, c) in enumerate(zip(pt, ct))]\n",
1287     "w_menu"
1288    ]
1289   },
1290   {
1291    "cell_type": "code",
1292    "execution_count": 42,
1293    "metadata": {
1294     "collapsed": false,
1295     "scrolled": true
1296    },
1297    "outputs": [
1298     {
1299      "data": {
1300       "text/plain": [
1301        "[('a', 'y', 'm'),\n",
1302        " ('c', 'p', 'v'),\n",
1303        " ('c', 's', 'f'),\n",
1304        " ('c', 'w', 'j'),\n",
1305        " ('d', 'r', 'k'),\n",
1306        " ('e', 'l', 'f'),\n",
1307        " ('e', 's', 'v'),\n",
1308        " ('e', 'y', 'd'),\n",
1309        " ('e', 'y', 'o'),\n",
1310        " ('f', 'z', 'x'),\n",
1311        " ('g', 'b', 'l'),\n",
1312        " ('g', 'c', 'd'),\n",
1313        " ('g', 'c', 'f'),\n",
1314        " ('g', 'j', 'p'),\n",
1315        " ('h', 'c', 'i'),\n",
1316        " ('h', 'm', 'w'),\n",
1317        " ('h', 'o', 'd'),\n",
1318        " ('h', 'p', 'b'),\n",
1319        " ('h', 's', 't'),\n",
1320        " ('i', 'b', 's'),\n",
1321        " ('i', 'v', 'b'),\n",
1322        " ('j', 'y', 'u'),\n",
1323        " ('k', 'b', 'x'),\n",
1324        " ('k', 'f', 't'),\n",
1325        " ('k', 'l', 'e'),\n",
1326        " ('k', 'l', 'm'),\n",
1327        " ('k', 'r', 'z'),\n",
1328        " ('k', 's', 'p'),\n",
1329        " ('l', 'd', 'z'),\n",
1330        " ('l', 'i', 'y'),\n",
1331        " ('l', 'y', 'f'),\n",
1332        " ('m', 'b', 'h'),\n",
1333        " ('m', 'p', 'l'),\n",
1334        " ('n', 'l', 'r'),\n",
1335        " ('o', 'k', 'x'),\n",
1336        " ('p', 'a', 'g'),\n",
1337        " ('p', 'c', 'v'),\n",
1338        " ('p', 'f', 'o'),\n",
1339        " ('p', 'm', 'i'),\n",
1340        " ('p', 'x', 'n'),\n",
1341        " ('p', 'x', 'p'),\n",
1342        " ('q', 'q', 'n'),\n",
1343        " ('q', 'r', 'w'),\n",
1344        " ('q', 'v', 'l'),\n",
1345        " ('q', 'x', 't'),\n",
1346        " ('s', 'a', 'h'),\n",
1347        " ('s', 'h', 'v'),\n",
1348        " ('s', 'l', 'p'),\n",
1349        " ('s', 'l', 's'),\n",
1350        " ('u', 'r', 'h'),\n",
1351        " ('v', 'v', 'v'),\n",
1352        " ('v', 'x', 'a'),\n",
1353        " ('w', 'j', 'z'),\n",
1354        " ('w', 'k', 'u'),\n",
1355        " ('x', 'f', 'p'),\n",
1356        " ('x', 'j', 'n'),\n",
1357        " ('x', 'o', 'q'),\n",
1358        " ('x', 'x', 'x'),\n",
1359        " ('y', 'n', 'c'),\n",
1360        " ('y', 'r', 'f'),\n",
1361        " ('z', 't', 'y'),\n",
1362        " ('z', 'z', 'k')]"
1363       ]
1364      },
1365      "execution_count": 42,
1366      "metadata": {},
1367      "output_type": "execute_result"
1368     }
1369    ],
1370    "source": [
1371     "allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1372     "\n",
1373     "with multiprocessing.Pool() as pool:\n",
1374     "    res = pool.map(Bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, \n",
1375     "                         menu=w_menu, verify_plugboard=False),\n",
1376     "                  allwheels)\n",
1377     "[r[0] for r in res if r[1]]"
1378    ]
1379   },
1380   {
1381    "cell_type": "code",
1382    "execution_count": 43,
1383    "metadata": {
1384     "collapsed": false
1385    },
1386    "outputs": [
1387     {
1388      "data": {
1389       "text/plain": [
1390        "62"
1391       ]
1392      },
1393      "execution_count": 43,
1394      "metadata": {},
1395      "output_type": "execute_result"
1396     }
1397    ],
1398    "source": [
1399     "len([r[0] for r in res if r[1]])"
1400    ]
1401   },
1402   {
1403    "cell_type": "code",
1404    "execution_count": 44,
1405    "metadata": {
1406     "collapsed": false,
1407     "scrolled": true
1408    },
1409    "outputs": [
1410     {
1411      "data": {
1412       "text/plain": [
1413        "[('c', 'p', 'v'),\n",
1414        " ('c', 's', 'f'),\n",
1415        " ('e', 'l', 'f'),\n",
1416        " ('g', 'c', 'f'),\n",
1417        " ('j', 'y', 'u'),\n",
1418        " ('o', 'k', 'x'),\n",
1419        " ('p', 'a', 'g'),\n",
1420        " ('q', 'q', 'n'),\n",
1421        " ('q', 'v', 'l'),\n",
1422        " ('q', 'x', 't'),\n",
1423        " ('s', 'l', 'p'),\n",
1424        " ('u', 'r', 'h'),\n",
1425        " ('y', 'n', 'c')]"
1426       ]
1427      },
1428      "execution_count": 44,
1429      "metadata": {},
1430      "output_type": "execute_result"
1431     }
1432    ],
1433    "source": [
1434     "allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1435     "\n",
1436     "with multiprocessing.Pool() as pool:\n",
1437     "    res = pool.map(Bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, \n",
1438     "                         menu=w_menu, verify_plugboard=True),\n",
1439     "                  allwheels)\n",
1440     "[r[0] for r in res if r[1]]"
1441    ]
1442   },
1443   {
1444    "cell_type": "code",
1445    "execution_count": 45,
1446    "metadata": {
1447     "collapsed": false
1448    },
1449    "outputs": [
1450     {
1451      "data": {
1452       "text/plain": [
1453        "[('c', 'p', 'v'),\n",
1454        " ('c', 's', 'f'),\n",
1455        " ('e', 'l', 'f'),\n",
1456        " ('g', 'c', 'f'),\n",
1457        " ('j', 'y', 'u'),\n",
1458        " ('o', 'k', 'x'),\n",
1459        " ('p', 'a', 'g'),\n",
1460        " ('q', 'q', 'n'),\n",
1461        " ('q', 'v', 'l'),\n",
1462        " ('q', 'x', 't'),\n",
1463        " ('s', 'l', 'p'),\n",
1464        " ('u', 'r', 'h'),\n",
1465        " ('y', 'n', 'c')]"
1466       ]
1467      },
1468      "execution_count": 45,
1469      "metadata": {},
1470      "output_type": "execute_result"
1471     }
1472    ],
1473    "source": [
1474     "run_multi_bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, w_menu)"
1475    ]
1476   },
1477   {
1478    "cell_type": "code",
1479    "execution_count": 46,
1480    "metadata": {
1481     "collapsed": false
1482    },
1483    "outputs": [],
1484    "source": [
1485     "# allwheels = itertools.product(string.ascii_lowercase, repeat=3)\n",
1486     "\n",
1487     "# with multiprocessing.Pool() as pool:\n",
1488     "#     res = pool.map(Bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, \n",
1489     "#                          menu=w_menu, start_signal=Signal('t', 'x')),\n",
1490     "#                   allwheels)\n",
1491     "# [r[0] for r in res if r[1]]"
1492    ]
1493   },
1494   {
1495    "cell_type": "code",
1496    "execution_count": 47,
1497    "metadata": {
1498     "collapsed": false
1499    },
1500    "outputs": [
1501     {
1502      "data": {
1503       "text/plain": [
1504        "13"
1505       ]
1506      },
1507      "execution_count": 47,
1508      "metadata": {},
1509      "output_type": "execute_result"
1510     }
1511    ],
1512    "source": [
1513     "len([r[0] for r in res if r[1]])"
1514    ]
1515   },
1516   {
1517    "cell_type": "code",
1518    "execution_count": 48,
1519    "metadata": {
1520     "collapsed": false
1521    },
1522    "outputs": [],
1523    "source": [
1524     "w_bombe = Bombe(wheel_i_spec, wheel_v_spec, wheel_iii_spec, reflector_b_spec, \n",
1525     "                         menu=w_menu)"
1526    ]
1527   },
1528   {
1529    "cell_type": "code",
1530    "execution_count": 49,
1531    "metadata": {
1532     "collapsed": false
1533    },
1534    "outputs": [
1535     {
1536      "data": {
1537       "text/plain": [
1538        "Signal(bank='e', wire='e')"
1539       ]
1540      },
1541      "execution_count": 49,
1542      "metadata": {},
1543      "output_type": "execute_result"
1544     }
1545    ],
1546    "source": [
1547     "w_bombe.test_start"
1548    ]
1549   },
1550   {
1551    "cell_type": "code",
1552    "execution_count": 50,
1553    "metadata": {
1554     "collapsed": false
1555    },
1556    "outputs": [
1557     {
1558      "data": {
1559       "text/plain": [
1560        "True"
1561       ]
1562      },
1563      "execution_count": 50,
1564      "metadata": {},
1565      "output_type": "execute_result"
1566     }
1567    ],
1568    "source": [
1569     "w_bombe.test(start_positions=('e', 'l', 'f'))"
1570    ]
1571   },
1572   {
1573    "cell_type": "code",
1574    "execution_count": 51,
1575    "metadata": {
1576     "collapsed": false
1577    },
1578    "outputs": [
1579     {
1580      "data": {
1581       "text/plain": [
1582        "True"
1583       ]
1584      },
1585      "execution_count": 51,
1586      "metadata": {},
1587      "output_type": "execute_result"
1588     }
1589    ],
1590    "source": [
1591     "w_bombe.test(Signal('t', 'x'), ('e', 'l', 'f'))"
1592    ]
1593   },
1594   {
1595    "cell_type": "code",
1596    "execution_count": 52,
1597    "metadata": {
1598     "collapsed": false
1599    },
1600    "outputs": [
1601     {
1602      "name": "stdout",
1603      "output_type": "stream",
1604      "text": [
1605       "True\n",
1606       "a : a.cdefghi..l.nopqrst.vwx..\n",
1607       "b : ....efghi...mnop.......x..\n",
1608       "c : a....fg.i..lmn.p.r.t...x..\n",
1609       "d : a...efghij.lmn...rstu..xyz\n",
1610       "e : ab.defghijklmnopqrstuvwxyz\n",
1611       "f : abcde.ghijklmnopqrstuvwxyz\n",
1612       "g : abcdef.hijklmnopqrstuvwxyz\n",
1613       "h : ab.defghi...mnopq.stuvwx..\n",
1614       "i : abcdefgh.jklmnopqrstuvwxyz\n",
1615       "j : ...defg.i...mn.p...t...x..\n",
1616       "k : ....efg.i..lmnop.r.t...x..\n",
1617       "l : a.cdefg.i.k.mnopqr.t..wxyz\n",
1618       "m : .bcdefghijklmnopqrstuvwxyz\n",
1619       "n : abcdefghijklmnopqr.tuvwxyz\n",
1620       "o : ab..efghi.klmnopqr.t...xyz\n",
1621       "p : abc.efghijklmnopqrstuvwxyz\n",
1622       "q : a...efghi..lmnop.r.t...x..\n",
1623       "r : a.cdefg.i.klmnopqrst..w..z\n",
1624       "s : a..defghi...m..p.rstuv.xyz\n",
1625       "t : a.cdefghijklmnopqrstuvwxyz\n",
1626       "u : ...defghi...mn.p..st...x..\n",
1627       "v : a...efghi...mn.p..st...x..\n",
1628       "w : a...efghi..lmn.p.r.t...x..\n",
1629       "x : abcdefghijklmnopq.stuvwxyz\n",
1630       "y : ...defg.i..lmnop..st...x..\n",
1631       "z : ...defg.i..lmnop.rst...x..\n"
1632      ]
1633     }
1634    ],
1635    "source": [
1636     "r = w_bombe.test(start_positions=('c', 'p', 'v'))\n",
1637     "print(r)\n",
1638     "for b in sorted(w_bombe.banks):\n",
1639     "    print(b, ': ', end='')\n",
1640     "    for w in sorted(w_bombe.banks[b]):\n",
1641     "        if w_bombe.banks[b][w]:\n",
1642     "            print(w, end='')\n",
1643     "        else:\n",
1644     "            print('.', end='')\n",
1645     "    print('')"
1646    ]
1647   },
1648   {
1649    "cell_type": "code",
1650    "execution_count": 53,
1651    "metadata": {
1652     "collapsed": false
1653    },
1654    "outputs": [
1655     {
1656      "name": "stdout",
1657      "output_type": "stream",
1658      "text": [
1659       "True\n",
1660       "a : abcdefghi..lmnop.rst.v.x.z\n",
1661       "b : a...ef.hi..lmnop.r.t...x..\n",
1662       "c : a..defg.i..lmn.p.rst...x..\n",
1663       "d : a.c.efghi.klmnopqrstu.wxyz\n",
1664       "e : abcdefghijklmnopqrstuvwx.z\n",
1665       "f : abcdefghijklmno.qrstuvwxyz\n",
1666       "g : a.cdefghijklmnopqrstuvwxyz\n",
1667       "h : ab.defghi...mnopqrstuvwxyz\n",
1668       "i : abcdefghijklm.opqrstuvwxyz\n",
1669       "j : ....efg.i..lmnop...t...x..\n",
1670       "k : ...defg.i..lmn.p..st...x..\n",
1671       "l : abcdefg.ijklmnopqrstuv.x..\n",
1672       "m : abcdefghijkl.nopqrstuvwxyz\n",
1673       "n : abcdefgh.jklmnopqrstuvwxyz\n",
1674       "o : ab.defghij.lmnop.r.tuvwxyz\n",
1675       "p : abcde.ghijklmnopqrstuvwxyz\n",
1676       "q : ...defghi..lmn.p..st...x..\n",
1677       "r : abcdefghi..lmnop.rst.v.x.z\n",
1678       "s : a.cdefghi.klmn.pqr.tuvwxyz\n",
1679       "t : abcdefghijklmnopqrstuvw.yz\n",
1680       "u : ...defghi..lmnop..st...x..\n",
1681       "v : a...efghi..lmnop.rst...x..\n",
1682       "w : ...defghi...mnop..st...x..\n",
1683       "x : abcdefghijklmnopqrs.uvwxyz\n",
1684       "y : ...d.fghi...mnop..st...x..\n",
1685       "z : a..defghi...mnop.rst...x..\n"
1686      ]
1687     }
1688    ],
1689    "source": [
1690     "r = w_bombe.test(start_positions=('e', 'l', 'f'))\n",
1691     "print(r)\n",
1692     "for b in sorted(w_bombe.banks):\n",
1693     "    print(b, ': ', end='')\n",
1694     "    for w in sorted(w_bombe.banks[b]):\n",
1695     "        if w_bombe.banks[b][w]:\n",
1696     "            print(w, end='')\n",
1697     "        else:\n",
1698     "            print('.', end='')\n",
1699     "    print('')"
1700    ]
1701   },
1702   {
1703    "cell_type": "code",
1704    "execution_count": 54,
1705    "metadata": {
1706     "collapsed": false
1707    },
1708    "outputs": [
1709     {
1710      "data": {
1711       "text/plain": [
1712        "{frozenset({'m'}),\n",
1713        " frozenset({'i', 'n'}),\n",
1714        " frozenset({'f', 'p'}),\n",
1715        " frozenset({'t', 'x'}),\n",
1716        " frozenset({'e', 'y'}),\n",
1717        " frozenset({'b', 'g'})}"
1718       ]
1719      },
1720      "execution_count": 54,
1721      "metadata": {},
1722      "output_type": "execute_result"
1723     }
1724    ],
1725    "source": [
1726     "ps = w_bombe.possible_plugboards()\n",
1727     "ps"
1728    ]
1729   },
1730   {
1731    "cell_type": "code",
1732    "execution_count": 55,
1733    "metadata": {
1734     "collapsed": false
1735    },
1736    "outputs": [
1737     {
1738      "data": {
1739       "text/plain": [
1740        "True"
1741       ]
1742      },
1743      "execution_count": 55,
1744      "metadata": {},
1745      "output_type": "execute_result"
1746     }
1747    ],
1748    "source": [
1749     "all(s0.isdisjoint(s1) for s0 in ps for s1 in ps if s0 != s1)"
1750    ]
1751   },
1752   {
1753    "cell_type": "code",
1754    "execution_count": 56,
1755    "metadata": {
1756     "collapsed": false
1757    },
1758    "outputs": [
1759     {
1760      "data": {
1761       "text/plain": [
1762        "({frozenset({1, 2}), frozenset({3, 4}), frozenset({2, 3})},\n",
1763        " frozenset({1, 2}),\n",
1764        " frozenset({3, 4}),\n",
1765        " frozenset({2, 3}))"
1766       ]
1767      },
1768      "execution_count": 56,
1769      "metadata": {},
1770      "output_type": "execute_result"
1771     }
1772    ],
1773    "source": [
1774     "s = set()\n",
1775     "f1 = frozenset((1, 2))\n",
1776     "f2 = frozenset((3, 4))\n",
1777     "f3 = frozenset((2, 3))\n",
1778     "s = s.union({f1})\n",
1779     "s = s.union({f2})\n",
1780     "s = s.union({f1})\n",
1781     "s = s.union({f3})\n",
1782     "s, f1, f2, f3"
1783    ]
1784   },
1785   {
1786    "cell_type": "code",
1787    "execution_count": 57,
1788    "metadata": {
1789     "collapsed": false
1790    },
1791    "outputs": [
1792     {
1793      "data": {
1794       "text/plain": [
1795        "False"
1796       ]
1797      },
1798      "execution_count": 57,
1799      "metadata": {},
1800      "output_type": "execute_result"
1801     }
1802    ],
1803    "source": [
1804     "all(s0.isdisjoint(s1) for s0 in s for s1 in s if s0 != s1)"
1805    ]
1806   },
1807   {
1808    "cell_type": "code",
1809    "execution_count": 58,
1810    "metadata": {
1811     "collapsed": false
1812    },
1813    "outputs": [
1814     {
1815      "data": {
1816       "text/plain": [
1817        "False"
1818       ]
1819      },
1820      "execution_count": 58,
1821      "metadata": {},
1822      "output_type": "execute_result"
1823     }
1824    ],
1825    "source": [
1826     "{1, 2}.isdisjoint({1, 6})"
1827    ]
1828   },
1829   {
1830    "cell_type": "code",
1831    "execution_count": null,
1832    "metadata": {
1833     "collapsed": true
1834    },
1835    "outputs": [],
1836    "source": []
1837   }
1838  ],
1839  "metadata": {
1840   "kernelspec": {
1841    "display_name": "Python 3",
1842    "language": "python",
1843    "name": "python3"
1844   },
1845   "language_info": {
1846    "codemirror_mode": {
1847     "name": "ipython",
1848     "version": 3
1849    },
1850    "file_extension": ".py",
1851    "mimetype": "text/x-python",
1852    "name": "python",
1853    "nbconvert_exporter": "python",
1854    "pygments_lexer": "ipython3",
1855    "version": "3.5.1+"
1856   }
1857  },
1858  "nbformat": 4,
1859  "nbformat_minor": 0
1860 }