hill-ciphers.ipynb

   1 {
   2  "metadata": {
   3   "name": "",
   4   "signature": "sha256:112d1c84c318592f927e18c5b0f15ed60ac8418ca15cb79596ba6212ff2d7e3f"
   5  },
   6  "nbformat": 3,
   7  "nbformat_minor": 0,
   8  "worksheets": [
   9   {
  10    "cells": [
  11     {
  12      "cell_type": "code",
  13      "collapsed": false,
  14      "input": [
  15       "import matplotlib.pyplot as plt\n",
  16       "import pandas as pd\n",
  17       "import collections\n",
  18       "import string\n",
  19       "import numpy as np\n",
  20       "from numpy import matrix\n",
  21       "from numpy import linalg\n",
  22       "%matplotlib inline\n",
  23       "\n",
  24       "from cipher import *\n",
  25       "from cipherbreak import *\n",
  26       "\n",
  27       "c6a = open('2014/6a.ciphertext').read()\n",
  28       "c6b = open('2014/6b.ciphertext').read()"
  29      ],
  30      "language": "python",
  31      "metadata": {},
  32      "outputs": [],
  33      "prompt_number": 54
  34     },
  35     {
  36      "cell_type": "code",
  37      "collapsed": false,
  38      "input": [
  39       "key_a, score = railfence_break(sanitise(c6a))\n",
  40       "key_a, score"
  41      ],
  42      "language": "python",
  43      "metadata": {},
  44      "outputs": [
  45       {
  46        "metadata": {},
  47        "output_type": "pyout",
  48        "prompt_number": 3,
  49        "text": [
  50         "(3, -2314.997881051078)"
  51        ]
  52       }
  53      ],
  54      "prompt_number": 3
  55     },
  56     {
  57      "cell_type": "code",
  58      "collapsed": false,
  59      "input": [
  60       "' '.join(segment(railfence_decipher(sanitise(c6a), key_a)))"
  61      ],
  62      "language": "python",
  63      "metadata": {},
  64      "outputs": [
  65       {
  66        "metadata": {},
  67        "output_type": "pyout",
  68        "prompt_number": 4,
  69        "text": [
  70         "'mark the last message told usa lot the scuttling equipment is designed to pump water in and out of the vessel like a submarine dive control but clearly they werent planning to turn a container ship into a sub this ship is a largescale version of something i have seen in the caribbean drug runners use a similar technique to get below radar coverage for inshore runs sinking the vessel so that the deck remains just below the wave tops the fda pirates seem more interested in staying away from shore but getting close enough to track and record electronic communications without detection i am guessing this scuttling system is what they call nautilus in their log but i am still baffled by the references to seahorse the next page of the log looks harder to crack but the cipher clerk tells me it is a hill cipher and that they must have been in a hurry or have been enciphering by hand since they just used a two by two matrix actually we have been pretty lax with our security and i think the next message is end will use avi genere cipher given that we are using secure cables i dont think we have too much to worry about so i will keep the keyword short say three characters more later harry'"
  71        ]
  72       }
  73      ],
  74      "prompt_number": 4
  75     },
  76     {
  77      "cell_type": "code",
  78      "collapsed": false,
  79      "input": [
  80       "c6bs = sanitise(c6b)\n",
  81       "c6bs"
  82      ],
  83      "language": "python",
  84      "metadata": {},
  85      "outputs": [
  86       {
  87        "metadata": {},
  88        "output_type": "pyout",
  89        "prompt_number": 7,
  90        "text": [
  91         "'hwssswxfewhhrfewpdrvttdhxbccleayphalnadhiehaoudrotwnrrvysabjlttbaytmelrkaidopthatlelrtwaamaneksvvzrvllatkcrjquicizgtoqcpnrrkttowandqehtqrvtbaydqealannohulanuzlwextlvjrvivhnohdqmgykaclmswrupdetfioftfelhzpxhaswftwprrsweiseohefpdrvttnvagdvswgoerbetnharvaeevtlltbmgaiatgelinmdawevhatterdhrznbnvoutnefoteveaehlaymhacglzeptvvdimworfisgtuzlwibeqohubtghamqornjnnrumqvjtxeltfovgawdaeevllgrtxibgtibevmpsaateoasevaeyqohameonncfuidoefafattemuimnflznbekofobrliaehhauihnnnwzaeevtlltpaalnanvtzlzuucptaelinanpaahewfthaosetaribnbnvhaevdhyytlmuxb'"
  92        ]
  93       }
  94      ],
  95      "prompt_number": 7
  96     },
  97     {
  98      "cell_type": "code",
  99      "collapsed": false,
 100      "input": [
 101       "c6b_nums = [ord(c) - ord('a') for c in c6bs]\n",
 102       "c6b_nums"
 103      ],
 104      "language": "python",
 105      "metadata": {},
 106      "outputs": [
 107       {
 108        "metadata": {},
 109        "output_type": "pyout",
 110        "prompt_number": 17,
 111        "text": [
 112         "[7,\n",
 113         " 22,\n",
 114         " 18,\n",
 115         " 18,\n",
 116         " 18,\n",
 117         " 22,\n",
 118         " 23,\n",
 119         " 5,\n",
 120         " 4,\n",
 121         " 22,\n",
 122         " 7,\n",
 123         " 7,\n",
 124         " 17,\n",
 125         " 5,\n",
 126         " 4,\n",
 127         " 22,\n",
 128         " 15,\n",
 129         " 3,\n",
 130         " 17,\n",
 131         " 21,\n",
 132         " 19,\n",
 133         " 19,\n",
 134         " 3,\n",
 135         " 7,\n",
 136         " 23,\n",
 137         " 1,\n",
 138         " 2,\n",
 139         " 2,\n",
 140         " 11,\n",
 141         " 4,\n",
 142         " 0,\n",
 143         " 24,\n",
 144         " 15,\n",
 145         " 7,\n",
 146         " 0,\n",
 147         " 11,\n",
 148         " 13,\n",
 149         " 0,\n",
 150         " 3,\n",
 151         " 7,\n",
 152         " 8,\n",
 153         " 4,\n",
 154         " 7,\n",
 155         " 0,\n",
 156         " 14,\n",
 157         " 20,\n",
 158         " 3,\n",
 159         " 17,\n",
 160         " 14,\n",
 161         " 19,\n",
 162         " 22,\n",
 163         " 13,\n",
 164         " 17,\n",
 165         " 17,\n",
 166         " 21,\n",
 167         " 24,\n",
 168         " 18,\n",
 169         " 0,\n",
 170         " 1,\n",
 171         " 9,\n",
 172         " 11,\n",
 173         " 19,\n",
 174         " 19,\n",
 175         " 1,\n",
 176         " 0,\n",
 177         " 24,\n",
 178         " 19,\n",
 179         " 12,\n",
 180         " 4,\n",
 181         " 11,\n",
 182         " 17,\n",
 183         " 10,\n",
 184         " 0,\n",
 185         " 8,\n",
 186         " 3,\n",
 187         " 14,\n",
 188         " 15,\n",
 189         " 19,\n",
 190         " 7,\n",
 191         " 0,\n",
 192         " 19,\n",
 193         " 11,\n",
 194         " 4,\n",
 195         " 11,\n",
 196         " 17,\n",
 197         " 19,\n",
 198         " 22,\n",
 199         " 0,\n",
 200         " 0,\n",
 201         " 12,\n",
 202         " 0,\n",
 203         " 13,\n",
 204         " 4,\n",
 205         " 10,\n",
 206         " 18,\n",
 207         " 21,\n",
 208         " 21,\n",
 209         " 25,\n",
 210         " 17,\n",
 211         " 21,\n",
 212         " 11,\n",
 213         " 11,\n",
 214         " 0,\n",
 215         " 19,\n",
 216         " 10,\n",
 217         " 2,\n",
 218         " 17,\n",
 219         " 9,\n",
 220         " 16,\n",
 221         " 20,\n",
 222         " 8,\n",
 223         " 2,\n",
 224         " 8,\n",
 225         " 25,\n",
 226         " 6,\n",
 227         " 19,\n",
 228         " 14,\n",
 229         " 16,\n",
 230         " 2,\n",
 231         " 15,\n",
 232         " 13,\n",
 233         " 17,\n",
 234         " 17,\n",
 235         " 10,\n",
 236         " 19,\n",
 237         " 19,\n",
 238         " 14,\n",
 239         " 22,\n",
 240         " 0,\n",
 241         " 13,\n",
 242         " 3,\n",
 243         " 16,\n",
 244         " 4,\n",
 245         " 7,\n",
 246         " 19,\n",
 247         " 16,\n",
 248         " 17,\n",
 249         " 21,\n",
 250         " 19,\n",
 251         " 1,\n",
 252         " 0,\n",
 253         " 24,\n",
 254         " 3,\n",
 255         " 16,\n",
 256         " 4,\n",
 257         " 0,\n",
 258         " 11,\n",
 259         " 0,\n",
 260         " 13,\n",
 261         " 13,\n",
 262         " 14,\n",
 263         " 7,\n",
 264         " 20,\n",
 265         " 11,\n",
 266         " 0,\n",
 267         " 13,\n",
 268         " 20,\n",
 269         " 25,\n",
 270         " 11,\n",
 271         " 22,\n",
 272         " 4,\n",
 273         " 23,\n",
 274         " 19,\n",
 275         " 11,\n",
 276         " 21,\n",
 277         " 9,\n",
 278         " 17,\n",
 279         " 21,\n",
 280         " 8,\n",
 281         " 21,\n",
 282         " 7,\n",
 283         " 13,\n",
 284         " 14,\n",
 285         " 7,\n",
 286         " 3,\n",
 287         " 16,\n",
 288         " 12,\n",
 289         " 6,\n",
 290         " 24,\n",
 291         " 10,\n",
 292         " 0,\n",
 293         " 2,\n",
 294         " 11,\n",
 295         " 12,\n",
 296         " 18,\n",
 297         " 22,\n",
 298         " 17,\n",
 299         " 20,\n",
 300         " 15,\n",
 301         " 3,\n",
 302         " 4,\n",
 303         " 19,\n",
 304         " 5,\n",
 305         " 8,\n",
 306         " 14,\n",
 307         " 5,\n",
 308         " 19,\n",
 309         " 5,\n",
 310         " 4,\n",
 311         " 11,\n",
 312         " 7,\n",
 313         " 25,\n",
 314         " 15,\n",
 315         " 23,\n",
 316         " 7,\n",
 317         " 0,\n",
 318         " 18,\n",
 319         " 22,\n",
 320         " 5,\n",
 321         " 19,\n",
 322         " 22,\n",
 323         " 15,\n",
 324         " 17,\n",
 325         " 17,\n",
 326         " 18,\n",
 327         " 22,\n",
 328         " 4,\n",
 329         " 8,\n",
 330         " 18,\n",
 331         " 4,\n",
 332         " 14,\n",
 333         " 7,\n",
 334         " 4,\n",
 335         " 5,\n",
 336         " 15,\n",
 337         " 3,\n",
 338         " 17,\n",
 339         " 21,\n",
 340         " 19,\n",
 341         " 19,\n",
 342         " 13,\n",
 343         " 21,\n",
 344         " 0,\n",
 345         " 6,\n",
 346         " 3,\n",
 347         " 21,\n",
 348         " 18,\n",
 349         " 22,\n",
 350         " 6,\n",
 351         " 14,\n",
 352         " 4,\n",
 353         " 17,\n",
 354         " 1,\n",
 355         " 4,\n",
 356         " 19,\n",
 357         " 13,\n",
 358         " 7,\n",
 359         " 0,\n",
 360         " 17,\n",
 361         " 21,\n",
 362         " 0,\n",
 363         " 4,\n",
 364         " 4,\n",
 365         " 21,\n",
 366         " 19,\n",
 367         " 11,\n",
 368         " 11,\n",
 369         " 19,\n",
 370         " 1,\n",
 371         " 12,\n",
 372         " 6,\n",
 373         " 0,\n",
 374         " 8,\n",
 375         " 0,\n",
 376         " 19,\n",
 377         " 6,\n",
 378         " 4,\n",
 379         " 11,\n",
 380         " 8,\n",
 381         " 13,\n",
 382         " 12,\n",
 383         " 3,\n",
 384         " 0,\n",
 385         " 22,\n",
 386         " 4,\n",
 387         " 21,\n",
 388         " 7,\n",
 389         " 0,\n",
 390         " 19,\n",
 391         " 19,\n",
 392         " 4,\n",
 393         " 17,\n",
 394         " 3,\n",
 395         " 7,\n",
 396         " 17,\n",
 397         " 25,\n",
 398         " 13,\n",
 399         " 1,\n",
 400         " 13,\n",
 401         " 21,\n",
 402         " 14,\n",
 403         " 20,\n",
 404         " 19,\n",
 405         " 13,\n",
 406         " 4,\n",
 407         " 5,\n",
 408         " 14,\n",
 409         " 19,\n",
 410         " 4,\n",
 411         " 21,\n",
 412         " 4,\n",
 413         " 0,\n",
 414         " 4,\n",
 415         " 7,\n",
 416         " 11,\n",
 417         " 0,\n",
 418         " 24,\n",
 419         " 12,\n",
 420         " 7,\n",
 421         " 0,\n",
 422         " 2,\n",
 423         " 6,\n",
 424         " 11,\n",
 425         " 25,\n",
 426         " 4,\n",
 427         " 15,\n",
 428         " 19,\n",
 429         " 21,\n",
 430         " 21,\n",
 431         " 3,\n",
 432         " 8,\n",
 433         " 12,\n",
 434         " 22,\n",
 435         " 14,\n",
 436         " 17,\n",
 437         " 5,\n",
 438         " 8,\n",
 439         " 18,\n",
 440         " 6,\n",
 441         " 19,\n",
 442         " 20,\n",
 443         " 25,\n",
 444         " 11,\n",
 445         " 22,\n",
 446         " 8,\n",
 447         " 1,\n",
 448         " 4,\n",
 449         " 16,\n",
 450         " 14,\n",
 451         " 7,\n",
 452         " 20,\n",
 453         " 1,\n",
 454         " 19,\n",
 455         " 6,\n",
 456         " 7,\n",
 457         " 0,\n",
 458         " 12,\n",
 459         " 16,\n",
 460         " 14,\n",
 461         " 17,\n",
 462         " 13,\n",
 463         " 9,\n",
 464         " 13,\n",
 465         " 13,\n",
 466         " 17,\n",
 467         " 20,\n",
 468         " 12,\n",
 469         " 16,\n",
 470         " 21,\n",
 471         " 9,\n",
 472         " 19,\n",
 473         " 23,\n",
 474         " 4,\n",
 475         " 11,\n",
 476         " 19,\n",
 477         " 5,\n",
 478         " 14,\n",
 479         " 21,\n",
 480         " 6,\n",
 481         " 0,\n",
 482         " 22,\n",
 483         " 3,\n",
 484         " 0,\n",
 485         " 4,\n",
 486         " 4,\n",
 487         " 21,\n",
 488         " 11,\n",
 489         " 11,\n",
 490         " 6,\n",
 491         " 17,\n",
 492         " 19,\n",
 493         " 23,\n",
 494         " 8,\n",
 495         " 1,\n",
 496         " 6,\n",
 497         " 19,\n",
 498         " 8,\n",
 499         " 1,\n",
 500         " 4,\n",
 501         " 21,\n",
 502         " 12,\n",
 503         " 15,\n",
 504         " 18,\n",
 505         " 0,\n",
 506         " 0,\n",
 507         " 19,\n",
 508         " 4,\n",
 509         " 14,\n",
 510         " 0,\n",
 511         " 18,\n",
 512         " 4,\n",
 513         " 21,\n",
 514         " 0,\n",
 515         " 4,\n",
 516         " 24,\n",
 517         " 16,\n",
 518         " 14,\n",
 519         " 7,\n",
 520         " 0,\n",
 521         " 12,\n",
 522         " 4,\n",
 523         " 14,\n",
 524         " 13,\n",
 525         " 13,\n",
 526         " 2,\n",
 527         " 5,\n",
 528         " 20,\n",
 529         " 8,\n",
 530         " 3,\n",
 531         " 14,\n",
 532         " 4,\n",
 533         " 5,\n",
 534         " 0,\n",
 535         " 5,\n",
 536         " 0,\n",
 537         " 19,\n",
 538         " 19,\n",
 539         " 4,\n",
 540         " 12,\n",
 541         " 20,\n",
 542         " 8,\n",
 543         " 12,\n",
 544         " 13,\n",
 545         " 5,\n",
 546         " 11,\n",
 547         " 25,\n",
 548         " 13,\n",
 549         " 1,\n",
 550         " 4,\n",
 551         " 10,\n",
 552         " 14,\n",
 553         " 5,\n",
 554         " 14,\n",
 555         " 1,\n",
 556         " 17,\n",
 557         " 11,\n",
 558         " 8,\n",
 559         " 0,\n",
 560         " 4,\n",
 561         " 7,\n",
 562         " 7,\n",
 563         " 0,\n",
 564         " 20,\n",
 565         " 8,\n",
 566         " 7,\n",
 567         " 13,\n",
 568         " 13,\n",
 569         " 13,\n",
 570         " 22,\n",
 571         " 25,\n",
 572         " 0,\n",
 573         " 4,\n",
 574         " 4,\n",
 575         " 21,\n",
 576         " 19,\n",
 577         " 11,\n",
 578         " 11,\n",
 579         " 19,\n",
 580         " 15,\n",
 581         " 0,\n",
 582         " 0,\n",
 583         " 11,\n",
 584         " 13,\n",
 585         " 0,\n",
 586         " 13,\n",
 587         " 21,\n",
 588         " 19,\n",
 589         " 25,\n",
 590         " 11,\n",
 591         " 25,\n",
 592         " 20,\n",
 593         " 20,\n",
 594         " 2,\n",
 595         " 15,\n",
 596         " 19,\n",
 597         " 0,\n",
 598         " 4,\n",
 599         " 11,\n",
 600         " 8,\n",
 601         " 13,\n",
 602         " 0,\n",
 603         " 13,\n",
 604         " 15,\n",
 605         " 0,\n",
 606         " 0,\n",
 607         " 7,\n",
 608         " 4,\n",
 609         " 22,\n",
 610         " 5,\n",
 611         " 19,\n",
 612         " 7,\n",
 613         " 0,\n",
 614         " 14,\n",
 615         " 18,\n",
 616         " 4,\n",
 617         " 19,\n",
 618         " 0,\n",
 619         " 17,\n",
 620         " 8,\n",
 621         " 1,\n",
 622         " 13,\n",
 623         " 1,\n",
 624         " 13,\n",
 625         " 21,\n",
 626         " 7,\n",
 627         " 0,\n",
 628         " 4,\n",
 629         " 21,\n",
 630         " 3,\n",
 631         " 7,\n",
 632         " 24,\n",
 633         " 24,\n",
 634         " 19,\n",
 635         " 11,\n",
 636         " 12,\n",
 637         " 20,\n",
 638         " 23,\n",
 639         " 1]"
 640        ]
 641       }
 642      ],
 643      "prompt_number": 17
 644     },
 645     {
 646      "cell_type": "code",
 647      "collapsed": false,
 648      "input": [
 649       "m = np.matrix([[7,8], [11,11]])\n",
 650       "m"
 651      ],
 652      "language": "python",
 653      "metadata": {},
 654      "outputs": [
 655       {
 656        "metadata": {},
 657        "output_type": "pyout",
 658        "prompt_number": 106,
 659        "text": [
 660         "matrix([[ 7,  8],\n",
 661         "        [11, 11]])"
 662        ]
 663       }
 664      ],
 665      "prompt_number": 106
 666     },
 667     {
 668      "cell_type": "code",
 669      "collapsed": false,
 670      "input": [
 671       "np.linalg.det(m)"
 672      ],
 673      "language": "python",
 674      "metadata": {},
 675      "outputs": [
 676       {
 677        "metadata": {},
 678        "output_type": "pyout",
 679        "prompt_number": 107,
 680        "text": [
 681         "-11.000000000000002"
 682        ]
 683       }
 684      ],
 685      "prompt_number": 107
 686     },
 687     {
 688      "cell_type": "code",
 689      "collapsed": false,
 690      "input": [
 691       "m.I"
 692      ],
 693      "language": "python",
 694      "metadata": {},
 695      "outputs": [
 696       {
 697        "metadata": {},
 698        "output_type": "pyout",
 699        "prompt_number": 108,
 700        "text": [
 701         "matrix([[-1.        ,  0.72727273],\n",
 702         "        [ 1.        , -0.63636364]])"
 703        ]
 704       }
 705      ],
 706      "prompt_number": 108
 707     },
 708     {
 709      "cell_type": "code",
 710      "collapsed": false,
 711      "input": [
 712       "v = np.matrix([[7], [22]])\n",
 713       "v"
 714      ],
 715      "language": "python",
 716      "metadata": {},
 717      "outputs": [
 718       {
 719        "metadata": {},
 720        "output_type": "pyout",
 721        "prompt_number": 37,
 722        "text": [
 723         "matrix([[ 7],\n",
 724         "        [22]])"
 725        ]
 726       }
 727      ],
 728      "prompt_number": 37
 729     },
 730     {
 731      "cell_type": "code",
 732      "collapsed": false,
 733      "input": [
 734       "c = (m*v) % 26\n",
 735       "c"
 736      ],
 737      "language": "python",
 738      "metadata": {},
 739      "outputs": [
 740       {
 741        "metadata": {},
 742        "output_type": "pyout",
 743        "prompt_number": 46,
 744        "text": [
 745         "matrix([[9],\n",
 746         "        [5]])"
 747        ]
 748       }
 749      ],
 750      "prompt_number": 46
 751     },
 752     {
 753      "cell_type": "code",
 754      "collapsed": false,
 755      "input": [
 756       "np.linalg.solve(m, c) % 26"
 757      ],
 758      "language": "python",
 759      "metadata": {},
 760      "outputs": [
 761       {
 762        "metadata": {},
 763        "output_type": "pyout",
 764        "prompt_number": 48,
 765        "text": [
 766         "matrix([[  7.],\n",
 767         "        [ 22.]])"
 768        ]
 769       }
 770      ],
 771      "prompt_number": 48
 772     },
 773     {
 774      "cell_type": "code",
 775      "collapsed": false,
 776      "input": [
 777       "m*v"
 778      ],
 779      "language": "python",
 780      "metadata": {},
 781      "outputs": [
 782       {
 783        "metadata": {},
 784        "output_type": "pyout",
 785        "prompt_number": 40,
 786        "text": [
 787         "matrix([[ 87],\n",
 788         "        [109]])"
 789        ]
 790       }
 791      ],
 792      "prompt_number": 40
 793     },
 794     {
 795      "cell_type": "code",
 796      "collapsed": false,
 797      "input": [
 798       "(m*v)%26"
 799      ],
 800      "language": "python",
 801      "metadata": {},
 802      "outputs": [
 803       {
 804        "metadata": {},
 805        "output_type": "pyout",
 806        "prompt_number": 41,
 807        "text": [
 808         "matrix([[9],\n",
 809         "        [5]])"
 810        ]
 811       }
 812      ],
 813      "prompt_number": 41
 814     },
 815     {
 816      "cell_type": "code",
 817      "collapsed": false,
 818      "input": [
 819       "np.linalg.solve(m, (m*v)%26)%26"
 820      ],
 821      "language": "python",
 822      "metadata": {},
 823      "outputs": [
 824       {
 825        "metadata": {},
 826        "output_type": "pyout",
 827        "prompt_number": 42,
 828        "text": [
 829         "matrix([[  7.],\n",
 830         "        [ 22.]])"
 831        ]
 832       }
 833      ],
 834      "prompt_number": 42
 835     },
 836     {
 837      "cell_type": "code",
 838      "collapsed": false,
 839      "input": [
 840       "len(m)"
 841      ],
 842      "language": "python",
 843      "metadata": {},
 844      "outputs": [
 845       {
 846        "metadata": {},
 847        "output_type": "pyout",
 848        "prompt_number": 51,
 849        "text": [
 850         "2"
 851        ]
 852       }
 853      ],
 854      "prompt_number": 51
 855     },
 856     {
 857      "cell_type": "code",
 858      "collapsed": false,
 859      "input": [
 860       "def hill_encipher(matrix, message_letters, fillvalue='a'):\n",
 861       "    n = len(matrix)\n",
 862       "    sanitised_message = sanitise(message_letters)\n",
 863       "    if len(sanitised_message) % n != 0:\n",
 864       "        padding = fillvalue[0] * (n - len(sanitised_message) % n)\n",
 865       "    else:\n",
 866       "        padding = ''\n",
 867       "    message = [ord(c) - ord('a') for c in sanitised_message + padding]\n",
 868       "    message_chunks = [message[i:i+n] for i in range(0, len(message), n)]\n",
 869       "    # message_chunks = chunks(message, len(matrix), fillvalue=None)\n",
 870       "    enciphered_chunks = [((matrix * np.matrix(c).T).T).tolist()[0] for c in message_chunks]\n",
 871       "    return ''.join([chr(int(round(l)) % 26 + ord('a')) for l in sum(enciphered_chunks, [])])"
 872      ],
 873      "language": "python",
 874      "metadata": {},
 875      "outputs": [],
 876      "prompt_number": 181
 877     },
 878     {
 879      "cell_type": "code",
 880      "collapsed": false,
 881      "input": [
 882       "hill_encipher(m, 'hellothere')"
 883      ],
 884      "language": "python",
 885      "metadata": {},
 886      "outputs": [
 887       {
 888        "metadata": {},
 889        "output_type": "pyout",
 890        "prompt_number": 156,
 891        "text": [
 892         "'drjiqzdrvx'"
 893        ]
 894       }
 895      ],
 896      "prompt_number": 156
 897     },
 898     {
 899      "cell_type": "code",
 900      "collapsed": false,
 901      "input": [
 902       "msg = [ord(c) - ord('a') for c in 'hellothere']\n",
 903       "msg"
 904      ],
 905      "language": "python",
 906      "metadata": {},
 907      "outputs": [
 908       {
 909        "metadata": {},
 910        "output_type": "pyout",
 911        "prompt_number": 68,
 912        "text": [
 913         "[7, 4, 11, 11, 14, 19, 7, 4, 17, 4]"
 914        ]
 915       }
 916      ],
 917      "prompt_number": 68
 918     },
 919     {
 920      "cell_type": "code",
 921      "collapsed": false,
 922      "input": [
 923       "msgc = [msg[i:i+len(m)] for i in range(0, len(msg), len(m))]\n",
 924       "msgc"
 925      ],
 926      "language": "python",
 927      "metadata": {},
 928      "outputs": [
 929       {
 930        "metadata": {},
 931        "output_type": "pyout",
 932        "prompt_number": 112,
 933        "text": [
 934         "[[7, 11], [14, 25], [21, 14], [7, 11], [11, 15], [0, 0]]"
 935        ]
 936       }
 937      ],
 938      "prompt_number": 112
 939     },
 940     {
 941      "cell_type": "code",
 942      "collapsed": false,
 943      "input": [
 944       "((m*np.matrix(msgc[0]).T).T % 26).tolist()[0]"
 945      ],
 946      "language": "python",
 947      "metadata": {},
 948      "outputs": [
 949       {
 950        "metadata": {},
 951        "output_type": "pyout",
 952        "prompt_number": 87,
 953        "text": [
 954         "[7, 11]"
 955        ]
 956       }
 957      ],
 958      "prompt_number": 87
 959     },
 960     {
 961      "cell_type": "code",
 962      "collapsed": false,
 963      "input": [
 964       "def hill_decipher(matrix, message, fillvalue='a'):\n",
 965       "    adjugate = linalg.det(matrix)*linalg.inv(matrix)\n",
 966       "    inverse_determinant = modular_division_table[int(round(linalg.det(matrix))) % 26][1]\n",
 967       "    inverse_matrix = (inverse_determinant * adjugate) % 26\n",
 968       "    return hill_encipher(inverse_matrix, message, fillvalue)                                                 "
 969      ],
 970      "language": "python",
 971      "metadata": {},
 972      "outputs": [],
 973      "prompt_number": 195
 974     },
 975     {
 976      "cell_type": "code",
 977      "collapsed": false,
 978      "input": [
 979       "hill_decipher(m, 'drjiqzdrvx')"
 980      ],
 981      "language": "python",
 982      "metadata": {},
 983      "outputs": [
 984       {
 985        "metadata": {},
 986        "output_type": "pyout",
 987        "prompt_number": 161,
 988        "text": [
 989         "'hellothere'"
 990        ]
 991       }
 992      ],
 993      "prompt_number": 161
 994     },
 995     {
 996      "cell_type": "code",
 997      "collapsed": false,
 998      "input": [
 999       "msg = [ord(c) - ord('a') for c in 'drjiqzdrvxaa']\n",
1000       "msg"
1001      ],
1002      "language": "python",
1003      "metadata": {},
1004      "outputs": [
1005       {
1006        "metadata": {},
1007        "output_type": "pyout",
1008        "prompt_number": 114,
1009        "text": [
1010         "[3, 17, 9, 8, 16, 25, 3, 17, 21, 23, 0, 0]"
1011        ]
1012       }
1013      ],
1014      "prompt_number": 114
1015     },
1016     {
1017      "cell_type": "code",
1018      "collapsed": false,
1019      "input": [
1020       "msgc = [msg[i:i+len(m)] for i in range(0, len(msg), len(m))]\n",
1021       "msgc"
1022      ],
1023      "language": "python",
1024      "metadata": {},
1025      "outputs": [
1026       {
1027        "metadata": {},
1028        "output_type": "pyout",
1029        "prompt_number": 115,
1030        "text": [
1031         "[[3, 17], [9, 8], [16, 25], [3, 17], [21, 23], [0, 0]]"
1032        ]
1033       }
1034      ],
1035      "prompt_number": 115
1036     },
1037     {
1038      "cell_type": "code",
1039      "collapsed": false,
1040      "input": [
1041       "(np.linalg.solve(m, np.matrix(msgc[0]).T).T % 26)"
1042      ],
1043      "language": "python",
1044      "metadata": {},
1045      "outputs": [
1046       {
1047        "metadata": {},
1048        "output_type": "pyout",
1049        "prompt_number": 116,
1050        "text": [
1051         "matrix([[  9.36363636,  18.18181818]])"
1052        ]
1053       }
1054      ],
1055      "prompt_number": 116
1056     },
1057     {
1058      "cell_type": "code",
1059      "collapsed": false,
1060      "input": [
1061       "m_adj = linalg.det(m)*linalg.inv(m)\n",
1062       "m_adj"
1063      ],
1064      "language": "python",
1065      "metadata": {},
1066      "outputs": [
1067       {
1068        "metadata": {},
1069        "output_type": "pyout",
1070        "prompt_number": 142,
1071        "text": [
1072         "matrix([[ 11.,  -8.],\n",
1073         "        [-11.,   7.]])"
1074        ]
1075       }
1076      ],
1077      "prompt_number": 142
1078     },
1079     {
1080      "cell_type": "code",
1081      "collapsed": false,
1082      "input": [
1083       "modular_division_table[int(round(linalg.det(m))) % 26][1]"
1084      ],
1085      "language": "python",
1086      "metadata": {},
1087      "outputs": [
1088       {
1089        "metadata": {},
1090        "output_type": "pyout",
1091        "prompt_number": 148,
1092        "text": [
1093         "7"
1094        ]
1095       }
1096      ],
1097      "prompt_number": 148
1098     },
1099     {
1100      "cell_type": "code",
1101      "collapsed": false,
1102      "input": [
1103       "m_inv = (modular_division_table[int(round(linalg.det(m))) % 26][1] * m_adj) % 26\n",
1104       "m_inv"
1105      ],
1106      "language": "python",
1107      "metadata": {},
1108      "outputs": [
1109       {
1110        "metadata": {},
1111        "output_type": "pyout",
1112        "prompt_number": 150,
1113        "text": [
1114         "matrix([[ 25.,  22.],\n",
1115         "        [  1.,  23.]])"
1116        ]
1117       }
1118      ],
1119      "prompt_number": 150
1120     },
1121     {
1122      "cell_type": "code",
1123      "collapsed": false,
1124      "input": [
1125       "hill_encipher(m_inv, 'drjiqzdrvx')"
1126      ],
1127      "language": "python",
1128      "metadata": {},
1129      "outputs": [
1130       {
1131        "metadata": {},
1132        "output_type": "pyout",
1133        "prompt_number": 157,
1134        "text": [
1135         "'hellothere'"
1136        ]
1137       }
1138      ],
1139      "prompt_number": 157
1140     },
1141     {
1142      "cell_type": "code",
1143      "collapsed": false,
1144      "input": [
1145       "np.dot(m , 1/linalg.det(m) * mc)"
1146      ],
1147      "language": "python",
1148      "metadata": {},
1149      "outputs": [
1150       {
1151        "metadata": {},
1152        "output_type": "pyout",
1153        "prompt_number": 120,
1154        "text": [
1155         "matrix([[ 1.,  0.],\n",
1156         "        [ 0.,  1.]])"
1157        ]
1158       }
1159      ],
1160      "prompt_number": 120
1161     },
1162     {
1163      "cell_type": "code",
1164      "collapsed": false,
1165      "input": [
1166       "ml = np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]])\n",
1167       "ml"
1168      ],
1169      "language": "python",
1170      "metadata": {},
1171      "outputs": [
1172       {
1173        "metadata": {},
1174        "output_type": "pyout",
1175        "prompt_number": 122,
1176        "text": [
1177         "matrix([[ 6, 24,  1],\n",
1178         "        [13, 16, 10],\n",
1179         "        [20, 17, 15]])"
1180        ]
1181       }
1182      ],
1183      "prompt_number": 122
1184     },
1185     {
1186      "cell_type": "code",
1187      "collapsed": false,
1188      "input": [
1189       "ml_adj = linalg.det(ml)*linalg.inv(ml) % 26\n",
1190       "ml_adj"
1191      ],
1192      "language": "python",
1193      "metadata": {},
1194      "outputs": [
1195       {
1196        "metadata": {},
1197        "output_type": "pyout",
1198        "prompt_number": 137,
1199        "text": [
1200         "matrix([[ 18.,  21.,  16.],\n",
1201         "        [  5.,  18.,   5.],\n",
1202         "        [  5.,  14.,  18.]])"
1203        ]
1204       }
1205      ],
1206      "prompt_number": 137
1207     },
1208     {
1209      "cell_type": "code",
1210      "collapsed": false,
1211      "input": [
1212       "modular_division_table[int(linalg.det(ml) % 26)][1]"
1213      ],
1214      "language": "python",
1215      "metadata": {},
1216      "outputs": [
1217       {
1218        "metadata": {},
1219        "output_type": "pyout",
1220        "prompt_number": 138,
1221        "text": [
1222         "25"
1223        ]
1224       }
1225      ],
1226      "prompt_number": 138
1227     },
1228     {
1229      "cell_type": "code",
1230      "collapsed": false,
1231      "input": [
1232       "ml_inv = (modular_division_table[int(linalg.det(ml) % 26)][1] * ml_adj) % 26\n",
1233       "ml_inv"
1234      ],
1235      "language": "python",
1236      "metadata": {},
1237      "outputs": [
1238       {
1239        "metadata": {},
1240        "output_type": "pyout",
1241        "prompt_number": 139,
1242        "text": [
1243         "matrix([[  8.,   5.,  10.],\n",
1244         "        [ 21.,   8.,  21.],\n",
1245         "        [ 21.,  12.,   8.]])"
1246        ]
1247       }
1248      ],
1249      "prompt_number": 139
1250     },
1251     {
1252      "cell_type": "code",
1253      "collapsed": false,
1254      "input": [
1255       "hill_encipher(ml, 'hello there')"
1256      ],
1257      "language": "python",
1258      "metadata": {},
1259      "outputs": [
1260       {
1261        "metadata": {},
1262        "output_type": "pyout",
1263        "prompt_number": 193,
1264        "text": [
1265         "'tfjflpznvyac'"
1266        ]
1267       }
1268      ],
1269      "prompt_number": 193
1270     },
1271     {
1272      "cell_type": "code",
1273      "collapsed": false,
1274      "input": [
1275       "hill_decipher(ml, 'tfjflpznvyac')"
1276      ],
1277      "language": "python",
1278      "metadata": {},
1279      "outputs": [
1280       {
1281        "metadata": {},
1282        "output_type": "pyout",
1283        "prompt_number": 196,
1284        "text": [
1285         "'hellothereaa'"
1286        ]
1287       }
1288      ],
1289      "prompt_number": 196
1290     },
1291     {
1292      "cell_type": "code",
1293      "collapsed": false,
1294      "input": [
1295       "hill_encipher(ml, 'act')"
1296      ],
1297      "language": "python",
1298      "metadata": {},
1299      "outputs": [
1300       {
1301        "metadata": {},
1302        "output_type": "pyout",
1303        "prompt_number": 182,
1304        "text": [
1305         "'poh'"
1306        ]
1307       }
1308      ],
1309      "prompt_number": 182
1310     },
1311     {
1312      "cell_type": "code",
1313      "collapsed": false,
1314      "input": [
1315       "hill_decipher(ml, 'poh')"
1316      ],
1317      "language": "python",
1318      "metadata": {},
1319      "outputs": [
1320       {
1321        "output_type": "stream",
1322        "stream": "stdout",
1323        "text": [
1324         "[[  8.   5.  10.]\n",
1325         " [ 21.   8.  21.]\n",
1326         " [ 21.  12.   8.]]\n"
1327        ]
1328       },
1329       {
1330        "metadata": {},
1331        "output_type": "pyout",
1332        "prompt_number": 192,
1333        "text": [
1334         "'act'"
1335        ]
1336       }
1337      ],
1338      "prompt_number": 192
1339     },
1340     {
1341      "cell_type": "code",
1342      "collapsed": false,
1343      "input": [
1344       "[chr(int(round(i)) % 26 + ord('a')) for i in (ml_inv * np.matrix([ord(c) - ord('a') for c in 'poh']).T).T.tolist()[0]]"
1345      ],
1346      "language": "python",
1347      "metadata": {},
1348      "outputs": [
1349       {
1350        "metadata": {},
1351        "output_type": "pyout",
1352        "prompt_number": 180,
1353        "text": [
1354         "['a', 'c', 't']"
1355        ]
1356       }
1357      ],
1358      "prompt_number": 180
1359     },
1360     {
1361      "cell_type": "code",
1362      "collapsed": false,
1363      "input": [
1364       "hill_encipher(ml_inv, 'poh')"
1365      ],
1366      "language": "python",
1367      "metadata": {},
1368      "outputs": [
1369       {
1370        "metadata": {},
1371        "output_type": "pyout",
1372        "prompt_number": 184,
1373        "text": [
1374         "'act'"
1375        ]
1376       }
1377      ],
1378      "prompt_number": 184
1379     },
1380     {
1381      "cell_type": "code",
1382      "collapsed": false,
1383      "input": [
1384       "len([list(m) for m in itertools.product([list(r) for r in itertools.product(range(26), repeat=3)], repeat=3)])"
1385      ],
1386      "language": "python",
1387      "metadata": {},
1388      "outputs": [
1389       {
1390        "ename": "KeyboardInterrupt",
1391        "evalue": "",
1392        "output_type": "pyerr",
1393        "traceback": [
1394         "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
1395         "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
1396        ]
1397       }
1398      ],
1399      "prompt_number": 203
1400     },
1401     {
1402      "cell_type": "code",
1403      "collapsed": false,
1404      "input": [
1405       "(3**3)**3"
1406      ],
1407      "language": "python",
1408      "metadata": {},
1409      "outputs": [
1410       {
1411        "metadata": {},
1412        "output_type": "pyout",
1413        "prompt_number": 202,
1414        "text": [
1415         "19683"
1416        ]
1417       }
1418      ],
1419      "prompt_number": 202
1420     },
1421     {
1422      "cell_type": "code",
1423      "collapsed": false,
1424      "input": [
1425       "[np.matrix(list(m)) for m in itertools.product([list(r) for r in itertools.product(range(3), repeat=2)], repeat=2)]"
1426      ],
1427      "language": "python",
1428      "metadata": {},
1429      "outputs": [
1430       {
1431        "metadata": {},
1432        "output_type": "pyout",
1433        "prompt_number": 206,
1434        "text": [
1435         "[matrix([[0, 0],\n",
1436         "         [0, 0]]), matrix([[0, 0],\n",
1437         "         [0, 1]]), matrix([[0, 0],\n",
1438         "         [0, 2]]), matrix([[0, 0],\n",
1439         "         [1, 0]]), matrix([[0, 0],\n",
1440         "         [1, 1]]), matrix([[0, 0],\n",
1441         "         [1, 2]]), matrix([[0, 0],\n",
1442         "         [2, 0]]), matrix([[0, 0],\n",
1443         "         [2, 1]]), matrix([[0, 0],\n",
1444         "         [2, 2]]), matrix([[0, 1],\n",
1445         "         [0, 0]]), matrix([[0, 1],\n",
1446         "         [0, 1]]), matrix([[0, 1],\n",
1447         "         [0, 2]]), matrix([[0, 1],\n",
1448         "         [1, 0]]), matrix([[0, 1],\n",
1449         "         [1, 1]]), matrix([[0, 1],\n",
1450         "         [1, 2]]), matrix([[0, 1],\n",
1451         "         [2, 0]]), matrix([[0, 1],\n",
1452         "         [2, 1]]), matrix([[0, 1],\n",
1453         "         [2, 2]]), matrix([[0, 2],\n",
1454         "         [0, 0]]), matrix([[0, 2],\n",
1455         "         [0, 1]]), matrix([[0, 2],\n",
1456         "         [0, 2]]), matrix([[0, 2],\n",
1457         "         [1, 0]]), matrix([[0, 2],\n",
1458         "         [1, 1]]), matrix([[0, 2],\n",
1459         "         [1, 2]]), matrix([[0, 2],\n",
1460         "         [2, 0]]), matrix([[0, 2],\n",
1461         "         [2, 1]]), matrix([[0, 2],\n",
1462         "         [2, 2]]), matrix([[1, 0],\n",
1463         "         [0, 0]]), matrix([[1, 0],\n",
1464         "         [0, 1]]), matrix([[1, 0],\n",
1465         "         [0, 2]]), matrix([[1, 0],\n",
1466         "         [1, 0]]), matrix([[1, 0],\n",
1467         "         [1, 1]]), matrix([[1, 0],\n",
1468         "         [1, 2]]), matrix([[1, 0],\n",
1469         "         [2, 0]]), matrix([[1, 0],\n",
1470         "         [2, 1]]), matrix([[1, 0],\n",
1471         "         [2, 2]]), matrix([[1, 1],\n",
1472         "         [0, 0]]), matrix([[1, 1],\n",
1473         "         [0, 1]]), matrix([[1, 1],\n",
1474         "         [0, 2]]), matrix([[1, 1],\n",
1475         "         [1, 0]]), matrix([[1, 1],\n",
1476         "         [1, 1]]), matrix([[1, 1],\n",
1477         "         [1, 2]]), matrix([[1, 1],\n",
1478         "         [2, 0]]), matrix([[1, 1],\n",
1479         "         [2, 1]]), matrix([[1, 1],\n",
1480         "         [2, 2]]), matrix([[1, 2],\n",
1481         "         [0, 0]]), matrix([[1, 2],\n",
1482         "         [0, 1]]), matrix([[1, 2],\n",
1483         "         [0, 2]]), matrix([[1, 2],\n",
1484         "         [1, 0]]), matrix([[1, 2],\n",
1485         "         [1, 1]]), matrix([[1, 2],\n",
1486         "         [1, 2]]), matrix([[1, 2],\n",
1487         "         [2, 0]]), matrix([[1, 2],\n",
1488         "         [2, 1]]), matrix([[1, 2],\n",
1489         "         [2, 2]]), matrix([[2, 0],\n",
1490         "         [0, 0]]), matrix([[2, 0],\n",
1491         "         [0, 1]]), matrix([[2, 0],\n",
1492         "         [0, 2]]), matrix([[2, 0],\n",
1493         "         [1, 0]]), matrix([[2, 0],\n",
1494         "         [1, 1]]), matrix([[2, 0],\n",
1495         "         [1, 2]]), matrix([[2, 0],\n",
1496         "         [2, 0]]), matrix([[2, 0],\n",
1497         "         [2, 1]]), matrix([[2, 0],\n",
1498         "         [2, 2]]), matrix([[2, 1],\n",
1499         "         [0, 0]]), matrix([[2, 1],\n",
1500         "         [0, 1]]), matrix([[2, 1],\n",
1501         "         [0, 2]]), matrix([[2, 1],\n",
1502         "         [1, 0]]), matrix([[2, 1],\n",
1503         "         [1, 1]]), matrix([[2, 1],\n",
1504         "         [1, 2]]), matrix([[2, 1],\n",
1505         "         [2, 0]]), matrix([[2, 1],\n",
1506         "         [2, 1]]), matrix([[2, 1],\n",
1507         "         [2, 2]]), matrix([[2, 2],\n",
1508         "         [0, 0]]), matrix([[2, 2],\n",
1509         "         [0, 1]]), matrix([[2, 2],\n",
1510         "         [0, 2]]), matrix([[2, 2],\n",
1511         "         [1, 0]]), matrix([[2, 2],\n",
1512         "         [1, 1]]), matrix([[2, 2],\n",
1513         "         [1, 2]]), matrix([[2, 2],\n",
1514         "         [2, 0]]), matrix([[2, 2],\n",
1515         "         [2, 1]]), matrix([[2, 2],\n",
1516         "         [2, 2]])]"
1517        ]
1518       }
1519      ],
1520      "prompt_number": 206
1521     },
1522     {
1523      "cell_type": "code",
1524      "collapsed": false,
1525      "input": [
1526       "all_matrices = [np.matrix(list(m)) for m in itertools.product([list(r) for r in itertools.product(range(26), repeat=2)], repeat=2)]\n",
1527       "valid_matrices = [m for m, d in zip(all_matrices, (int(round(linalg.det(m))) for m in all_matrices))\n",
1528       "                  if d != 0\n",
1529       "                  if d % 2 != 0\n",
1530       "                  if d % 13 != 0 ]\n",
1531       "len(valid_matrices)"
1532      ],
1533      "language": "python",
1534      "metadata": {},
1535      "outputs": [
1536       {
1537        "metadata": {},
1538        "output_type": "pyout",
1539        "prompt_number": 215,
1540        "text": [
1541         "157248"
1542        ]
1543       }
1544      ],
1545      "prompt_number": 215
1546     },
1547     {
1548      "cell_type": "code",
1549      "collapsed": false,
1550      "input": [
1551       "%%timeit\n",
1552       "[m for m, d in zip(all_matrices, (int(round(linalg.det(m))) for m in all_matrices))\n",
1553       "                  if d != 0\n",
1554       "                  if d % 2 != 0\n",
1555       "                  if d % 13 != 0 ]\n",
1556       "print('done')"
1557      ],
1558      "language": "python",
1559      "metadata": {},
1560      "outputs": [
1561       {
1562        "output_type": "stream",
1563        "stream": "stdout",
1564        "text": [
1565         "done\n",
1566         "done"
1567        ]
1568       },
1569       {
1570        "output_type": "stream",
1571        "stream": "stdout",
1572        "text": [
1573         "\n",
1574         "done"
1575        ]
1576       },
1577       {
1578        "output_type": "stream",
1579        "stream": "stdout",
1580        "text": [
1581         "\n",
1582         "done"
1583        ]
1584       },
1585       {
1586        "output_type": "stream",
1587        "stream": "stdout",
1588        "text": [
1589         "\n",
1590         "1 loops, best of 3: 10 s per loop\n"
1591        ]
1592       }
1593      ],
1594      "prompt_number": 216
1595     },
1596     {
1597      "cell_type": "code",
1598      "collapsed": false,
1599      "input": [
1600       "%%timeit\n",
1601       "[m for m in all_matrices\n",
1602       "                  if int(round(linalg.det(m))) != 0\n",
1603       "                  if int(round(linalg.det(m))) % 2 != 0\n",
1604       "                  if int(round(linalg.det(m))) % 13 != 0 ]\n",
1605       "print('done')"
1606      ],
1607      "language": "python",
1608      "metadata": {},
1609      "outputs": [
1610       {
1611        "output_type": "stream",
1612        "stream": "stdout",
1613        "text": [
1614         "done\n",
1615         "done"
1616        ]
1617       },
1618       {
1619        "output_type": "stream",
1620        "stream": "stdout",
1621        "text": [
1622         "\n",
1623         "done"
1624        ]
1625       },
1626       {
1627        "output_type": "stream",
1628        "stream": "stdout",
1629        "text": [
1630         "\n",
1631         "done"
1632        ]
1633       },
1634       {
1635        "output_type": "stream",
1636        "stream": "stdout",
1637        "text": [
1638         "\n",
1639         "1 loops, best of 3: 20.4 s per loop\n"
1640        ]
1641       }
1642      ],
1643      "prompt_number": 217
1644     },
1645     {
1646      "cell_type": "code",
1647      "collapsed": false,
1648      "input": [],
1649      "language": "python",
1650      "metadata": {},
1651      "outputs": []
1652     }
1653    ],
1654    "metadata": {}
1655   }
1656  ]
1657 }