From 3e8d2bd8cd7c623116fa3d2b77db954f51b191e4 Mon Sep 17 00:00:00 2001 From: Neil Smith Date: Thu, 6 Mar 2014 23:16:45 -0500 Subject: [PATCH] Added development files --- caesar_break_parameter_trials.csv | 93 ++ challenge6.ipynb | 1141 ++++++++++++++++++ challenge7.ipynb | 321 +++++ cipher.py | 499 ++++++++ cipher.sublime-project | 2 + cipherbreak.py | 416 +++++++ find_best_caesar_break_parameters.py | 90 ++ find_wikipedia_titles.py | 35 + language_models.py | 156 +++ lettercount.py | 21 + make-cracking-dictionary.py | 19 + norms.py | 189 +++ segment.py | 19 + unknown-word-probability-investigation.ipynb | 179 +++ 14 files changed, 3180 insertions(+) create mode 100644 caesar_break_parameter_trials.csv create mode 100644 challenge6.ipynb create mode 100644 challenge7.ipynb create mode 100644 cipher.py create mode 100644 cipher.sublime-project create mode 100644 cipherbreak.py create mode 100644 find_best_caesar_break_parameters.py create mode 100644 find_wikipedia_titles.py create mode 100644 language_models.py create mode 100644 lettercount.py create mode 100644 make-cracking-dictionary.py create mode 100644 norms.py create mode 100644 segment.py create mode 100644 unknown-word-probability-investigation.ipynb diff --git a/caesar_break_parameter_trials.csv b/caesar_break_parameter_trials.csv new file mode 100644 index 0000000..6f71f07 --- /dev/null +++ b/caesar_break_parameter_trials.csv @@ -0,0 +1,93 @@ +,message_length +scoring, 300, 100, 50, 30, 20, 10, 5 +Pletters, 0.9994, 0.9994, 0.9994, 0.9966, 0.9778, 0.8174, 0.4712 +Pletters, 0.9994, 0.9994, 0.9994, 0.9966, 0.9778, 0.8174, 0.4712 +Pletters, 0.9994, 0.9994, 0.9994, 0.9966, 0.9778, 0.8174, 0.4712 +Pletters, 0.9994, 0.9994, 0.9994, 0.9966, 0.9778, 0.8174, 0.4712 +Pletters, 0.9994, 0.9994, 0.9994, 0.9966, 0.9778, 0.8174, 0.4712 +Pletters, 0.9994, 0.9994, 0.9994, 0.9966, 0.9778, 0.8174, 0.4712 +Pletters, 0.9994, 0.9994, 0.9994, 0.9966, 0.9778, 0.8174, 0.4712 +cosine_distance + euclidean_scaled, 0.9996, 0.9996, 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"cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from cipherbreak import *\n", + "with open('2013/mona-lisa-words.txt') as f:\n", + " mlwords = [line.rstrip() for line in f]\n", + "mltrans = collections.defaultdict(list)\n", + "for word in mlwords:\n", + " mltrans[transpositions_of(word)] += [word]\n", + "c6a = open('2013/6a.ciphertext').read()\n", + "c6b = open('2013/6b.ciphertext').read()" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c1a = open('2013/1a.ciphertext').read()\n", + "c1b = open('2013/1b.ciphertext').read()\n", + "c2a = open('2013/2a.ciphertext').read()\n", + "c2b = open('2013/2b.ciphertext').read()\n", + "c3a = open('2013/3a.ciphertext').read()\n", + "c3b = open('2013/3b.ciphertext').read()\n", + "c4a = open('2013/4a.ciphertext').read()\n", + "c4b = open('2013/4b.ciphertext').read()\n", + "c5a = open('2013/5a.ciphertext').read()\n", + "c5b = open('2013/5b.ciphertext').read()\n", + "\n", + "p1a = caesar_decipher(c1a, 8)\n", + "p1b = caesar_decipher(c1b, 14)\n", + "p2a = affine_decipher(c2a, 3, 3, True)\n", + "p2b = caesar_decipher(c2b, 6)\n", + "p3a = affine_decipher(c3a, 7, 8, True)\n", + "p3b = keyword_decipher(c3b, 'louvigny', 2)\n", + "p4a = keyword_decipher(c4a, 'montal', 2)\n", + "p4b = keyword_decipher(c4b, 'salvation', 2)\n", + "p5a = keyword_decipher(c5a, 'alfredo', 2)\n", + "p5b = vigenere_decipher(sanitise(c5b), 'florence')" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 3 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plot_frequency_histogram(frequencies(sanitise(c6a)))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stderr", + "text": [ + "/usr/local/lib/python3.3/dist-packages/matplotlib/figure.py:372: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n", + " \"matplotlib is currently using a non-GUI backend, \"\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c6af = frequencies(sanitise(c6a))\n", + "plot_frequency_histogram(c6af, sort_key=lambda l: c6af[l])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c6a" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 10, + "text": [ + "'CPYYL GVVIR PDDVU BCSUP QOWPW SYBYP ODBCS PBBPR CSIOZ PTSTV HYVTW PYOZC OGCRV TTPUI BVGVS YOUGZ ZSRYS BPYLY SHSYY OUGBV BCSWP OUBOU GPUIR DSPYD LTSUB OVUOU GZPYP ZSSTZ DONSB CSLNU SJPAV EBBCS ZRPTV EYHYO SUIDL ZZVHH ORSYJ PZWDP UUOUG BVWED DBCSL WORNS IEWCS YBYPO DBCSU OGCBP HBSYZ CSJSU BTOZZ OUGAE BLVER PUYSP IPAVE BBCPB OUBCS OYYSW VYBZB ODDUV MVLVU GSBBO UGPRR SZZBV BCSVY OGOUP DTOZZ TVUPO UBCSG PDDSY LPUIO PTASG OUUOU GBVBC OUNJS TOGCB USSIB VYVDD VEBPA DPRNA PGMVA LVEJP UBBVI VOBVY ZCPDD OALBC SJPLO JPZZE YWYOZ SIALB COZYS WVYBB CSVBC SYWPW SYZJS CPFSH YVTBC SUPQO ZPBBC OZDSF SDPYS SURYL WBSIE ZOUGA OHOIV YWDPL HPOYZ BLDSR OWCSY ZBCOZ VUSOZ UBTPL ASBCS ROWCS YRDSY NJPZV HHIEB LBCPB IPLJS GVBDE RNL\\n'" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "len(sanitise(c6b))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 11, + "text": [ + "1573" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c6as = sanitise(c6a)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 12 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "frequencies(ngrams(c6as, 2))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 13, + "text": [ + "Counter({'bc': 21, 'cs': 20, 'ou': 15, 'sy': 12, 'oz': 10, 'ug': 10, 'ub': 8, 'bv': 8, 'su': 7, 'bb': 7, 'zz': 6, 'yo': 6, 'dd': 6, 'ys': 6, 'py': 6, 'pu': 6, 'jp': 6, 've': 6, 'vy': 6, 'cp': 5, 'co': 5, 'si': 5, 'yz': 5, 'ds': 5, 'po': 5, 'bo': 5, 'eb': 5, 'vb': 5, 'vu': 5, 'sb': 4, 'zb': 4, 'yb': 4, 'dp': 4, 'pl': 4, 'pd': 4, 'pb': 4, 'pz': 4, 'bp': 4, 'js': 4, 'wp': 4, 'og': 4, 'up': 4, 'uo': 4, 'ui': 4, 'yl': 4, 'tv': 3, 'to': 3, 'lv': 3, 'lb': 3, 'yv': 3, 'sj': 3, 'sg': 3, 'sp': 3, 'sr': 3, 'ss': 3, 'sw': 3, 'zs': 3, 'zv': 3, 'zc': 3, 'al': 3, 'yw': 3, 'rn': 3, 'rp': 3, 'db': 3, 'us': 3, 'yy': 3, 'yp': 3, 'st': 3, 'ie': 3, 'gv': 3, 'gp': 3, 'zp': 3, 'gb': 3, 'gc': 3, 'pa': 3, 'pt': 3, 'pr': 3, 'bl': 3, 'wc': 3, 'ow': 3, 'od': 3, 'vh': 3, 'vt': 3, 'hy': 3, 'tp': 2, 'ts': 2, 'cb': 2, 'lw': 2, 'fs': 2, 'sh': 2, 'sl': 2, 'so': 2, 'sz': 2, 'sv': 2, 'zo': 2, 'ro': 2, 'wv': 2, 'rd': 2, 'ry': 2, 'rs': 2, 'dl': 2, 'do': 2, 'dv': 2, 'ir': 2, 'ip': 2, 'qo': 2, 'io': 2, 'ib': 2, 'gz': 2, 'ga': 2, 'av': 2, 'go': 2, 'pw': 2, 'pq': 2, 'by': 2, 'bs': 2, 'bt': 2, 'wd': 2, 'oy': 2, 'or': 2, 'ws': 2, 'iv': 2, 'zd': 2, 'ey': 2, 'er': 2, 'ns': 2, 'vi': 2, 'nj': 2, 'ho': 2, 'uu': 2, 'hh': 2, 'mv': 2, 'as': 2, 'tz': 1, 'tt': 1, 'tw': 1, 'ta': 1, 'tb': 1, 'lp': 1, 'lt': 1, 'ly': 1, 'lz': 1, 'la': 1, 'ld': 1, 'lg': 1, 'lh': 1, 'lj': 1, 'cr': 1, 'lo': 1, 'ln': 1, 'wb': 1, 'sc': 1, 'sd': 1, 'sf': 1, 'na': 1, 'zr': 1, 'ap': 1, 'wo': 1, 'zw': 1, 'zu': 1, 'zt': 1, 'zy': 1, 'ad': 1, 'ae': 1, 'zj': 1, 'ao': 1, 'rc': 1, 'hb': 1, 'rr': 1, 'rv': 1, 'yj': 1, 'yh': 1, 'yn': 1, 'hi': 1, 'de': 1, 'yd': 1, 'yr': 1, 'du': 1, 'dt': 1, 'nl': 1, 'gm': 1, 'wy': 1, 'ia': 1, 'id': 1, 'gs': 1, 'pi': 1, 'ph': 1, 'pg': 1, 'pf': 1, 'bz': 1, 'bu': 1, 'bi': 1, 'bd': 1, 'we': 1, 'ov': 1, 'op': 1, 'os': 1, 'on': 1, 'oi': 1, 'oj': 1, 'oa': 1, 'ob': 1, 'ej': 1, 'ze': 1, 'ed': 1, 'ez': 1, 'ew': 1, 'vg': 1, 'vd': 1, 'va': 1, 'vo': 1, 'oh': 1, 'nu': 1, 'vl': 1, 'vw': 1, 'vv': 1, 'vs': 1, 'uy': 1, 'uv': 1, 'ur': 1, 'un': 1, 'hp': 1, 'hs': 1, 'vm': 1})" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "' '.join(segment(letters(c6a).translate(''.maketrans({'B':'t', 'C':'h', 'S':'e', 'O':'i', 'U':'n', 'G':'g', 'A':'b', 'V':'o', 'N':'k', 'J':'w', 'T':'m', 'I':'d', 'P':'a', 'W':'p', 'R':'c', 'Y':'r', 'L':'y', 'D':'l', 'H':'f', 'Z':'s', 'Q':'z', 'E':'u', 'F':'v', 'M':'j'}))))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 14, + "text": [ + "'harry good call on the nazi paper trail the attached is a memo from paris high command to goering s secretary referring to the painting and clearly mentioning sara seems like they knew about the scam our friendly ss officer was planning to pull they picked up her trail the night after she went missing but you can read about that in their report still no joy on getting access to the original miss mona in the gallery and i am beginning to think we might need to rollout a black bag job you want to do it or shall i by the way i was surprised by this report the other papers we have from the nazis at this level are encrypted using bifid or playfair style ciphers this one isnt maybe the cipher clerk was off duty that day we got lucky'" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "trans={'B':'t', 'C':'h', 'S':'e', 'O':'i', 'U':'n', 'G':'g', 'A':'b', 'V':'o', 'N':'k', 'J':'w', 'T':'m', 'I':'d', 'P':'a', 'W':'p', 'R':'c', 'Y':'r', 'L':'y', 'D':'l', 'H':'f', 'Z':'s', 'Q':'z', 'E':'u', 'F':'v', 'M':'j'}" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "''.join(sorted(trans.keys(), key=lambda k: trans[k]))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 16, + "text": [ + "'PARISHGCOMNDTUVWYZBEFJLQ'" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "' '.join(segment(keyword_decipher(c6as, 'parishighcommand', 2)))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 17, + "text": [ + "'harry good call on the nazi paper trail the attached is a memo from paris high command to goering s secretary referring to the painting and clearly mentioning sara seems like they knew about the scam our friendly ss officer was planning to pull they picked up her trail the night after she went missing but you can read about that in their report still no joy on getting access to the original miss mona in the gallery and i am beginning to think we might need to rollout a black bag job you want to do it or shall i by the way i was surprised by this report the other papers we have from the nazis at this level are encrypted using bifid or playfair style ciphers this one isnt maybe the cipher clerk was off duty that day we got lucky'" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c6bs = sanitise(c6b)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 18 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "len(c6bs)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 19, + "text": [ + "1573" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from itertools import permutations" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 20 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "list(permutations(range(4)))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 21, + "text": [ + "[(0, 1, 2, 3),\n", + " (0, 1, 3, 2),\n", + " (0, 2, 1, 3),\n", + " (0, 2, 3, 1),\n", + " (0, 3, 1, 2),\n", + " (0, 3, 2, 1),\n", + " (1, 0, 2, 3),\n", + " (1, 0, 3, 2),\n", + " (1, 2, 0, 3),\n", + " (1, 2, 3, 0),\n", + " (1, 3, 0, 2),\n", + " (1, 3, 2, 0),\n", + " (2, 0, 1, 3),\n", + " (2, 0, 3, 1),\n", + " (2, 1, 0, 3),\n", + " (2, 1, 3, 0),\n", + " (2, 3, 0, 1),\n", + " (2, 3, 1, 0),\n", + " (3, 0, 1, 2),\n", + " (3, 0, 2, 1),\n", + " (3, 1, 0, 2),\n", + " (3, 1, 2, 0),\n", + " (3, 2, 0, 1),\n", + " (3, 2, 1, 0)]" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "[column_transposition_decipher(c6bs, p, fillvalue=' ') for p in permutations(range(4))]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 22, + "text": [ + 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"text": [ + "[29, 503, 985]" + ] + } + ], + "prompt_number": 42 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "''.join([c[0] for c in every_nth(c6bs, 11)])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 32, + "text": [ + "'hithhnfrfer'" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "''.join([c[0] for c in every_nth(c6bs, 13)])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 33, + "text": [ + "'hithhnfrferte'" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "''.join([c[0] for c in chunks(c6bs, 121)])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 34, + "text": [ + "'hhrnrnumeodti'" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "''.join([c[0] for c in chunks(c6bs, 13)])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 35, + "text": [ + "'harrseehthoexttnsneitetghuydoihuouocttiuedeeerrsohiaeefhifsiitiohtreiehseiiszomhhihtdtoeentencsllilrdieodhpbrlakhntnsdwon'" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'l' in ''.join([c[0] for c in chunks(c6bs, 13)])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 36, + "text": [ + "True" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "every_nth(c6bs, 11)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 38, + "text": [ + 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'mahthiqrsef',\n", + " 'ndiauedhimi',\n", + " 'osatuiboikg',\n", + " 'oeoeftzelln',\n", + " 'tuneadoshag',\n", + " 'avganmtitgr',\n", + " 'hetnbttndrt',\n", + " 'aaweeanrsee',\n", + " 'seisuarrrtb',\n", + " 'hoseiefanml',\n", + " 'ttwrtgaodrt',\n", + " 'iasthrnfedl',\n", + " 'jeagrhtrscl',\n", + " 'euidayderwg',\n", + " 'attleaitfsf',\n", + " 'nabursgfhno']" + ] + } + ], + "prompt_number": 64 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "[(q, u) for q in [i for i in range(len(c6bs)) if c6bs[i] == 'q'] for u in [i for i in range(len(c6bs)) if c6bs[i] == 'u'] if abs(q-u) < 13]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 44, + "text": [ + "[(29, 37), (503, 507), (985, 973)]" + ] + } + ], + "prompt_number": 44 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "every_nth(c6bs, 13)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 54, + "text": [ + "['harrseehthoexttnsneitetghuydoihuouocttiuedeeerrsohiaeefhifsiitiohtreiehseiiszomhhihtdtoeentencsllilrdieodhpbrlakhntnsdwon',\n", + " 'iorhiniterttuehfeywehueagrieaaernltvanmalddeoptwukuongaiwpuldsrsedrheseenlfoonnavsoenwtsnhelbdetnwhnotsgoarieayuvalanetog',\n", + " 'tfefhiroseaorphlaufbtvetaenehudagtoaelnreeeasarsorrhetneghrveapoamcvrocsotmftttankinonfiphawiclegwttycyctxaengntnenovtpar',\n", + " 'hfqsbrchpdhftprdkniaoeflahnitoaetatiortnttnnrhricnehdibeaimdopltitfeofnooolltahlaaehrtwnoataisviildltntmersltrwniannnpogt',\n", + " 'httenhiooharttioutaplaeisruaielrwoopaprdpdnebehatnmneiehdlretotygaehibbetirenllpicaeygyryyuheootnwsgaaoufshsaesnetrmfsaoe',\n", + " 'nnhtrmtrshsnorsgnnpchehaieehenuaimnndfooeessunnnytnoeiuustoonfaoealixmthngorrapladdgydmraeaaarstohrrsmtddoilttvoiubirwwab',\n", + " 'faiarralochewanhtnamwolcelgsaaatsxalupwtnwneryfieaiuooiaiwmefgneaervlrttwdewfeseeogereiaiuposeefetnsaeolsncnomnulihfesfel',\n", + " 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"language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 61, + "text": [ + "['hthithnfrfere',\n", + " 'foaoftnasltyr',\n", + " 'qurrethimserl',\n", + " 'sirhfetaeeiuw',\n", + " 'bisihnrrtsioi',\n", + " 'rtenihmrpytdo',\n", + " 'cpeiritalnbrn',\n", + " 'hshtoorliewth',\n", + " 'putesosotoynw',\n", + " 'dnhrehhcpicmo',\n", + " 'haotaashtijen',\n", + " 'fgetorneusram',\n", + " 'tbxurtowleatr',\n", + " 'pnteptraaesee',\n", + " 'rtthhisnrstsr',\n", + " 'dsnfloghaumge',\n", + " 'ktseauntiahyt',\n", + " 'nwnyutnnvhigl',\n", + " 'ifewfapasrela',\n", + " 'ahiebpcmcplae',\n", + " 'odthtlhwsulas',\n", + " 'eteuvaeotaeua',\n", + " 'fsteeehlbhtrh',\n", + " 'lrgatiaceehtn',\n", + " 'anhgasietufnp',\n", + " 'huurerelittmd',\n", + " 'neyinuegicoun',\n", + " 'itdeeahsuelhn',\n", + " 'tdoahieainyfn',\n", + " 'ofiauenatiyeo',\n", + " 'ayhedluaroerh',\n", + " 'eiurarateraha',\n", + " 'ttongwiswsaib',\n", + " 'arultomxletoe',\n", + " 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'luifmroeffdte',\n", + " 'ldsoferwiiyqb',\n", + " 'tizotnrfantdg',\n", + " 'aeontlaepdsha',\n", + " 'homntlpsnbtua',\n", + " 'lrhaaplemnpds',\n", + " 'aahvniaelnhcl',\n", + " 'ajiskcdoaedtg',\n", + " 'edhoiadgwayne',\n", + " 'hetenegeeueoe',\n", + " 'rmdnoyyrfctet',\n", + " 'totwngdetasuo',\n", + " 'whotfymihrgro',\n", + " 'ntesirraofref',\n", + " 'osenpyaissest',\n", + " 'apnhhyeulhiwc',\n", + " 'tuteauapeanle',\n", + " 'aeelwhaoelurs',\n", + " 'ianbieasaeteg',\n", + " 'secdcorepsron',\n", + " 'viselosedudst',\n", + " 'isltettfseoen',\n", + " 'iilngnoerntee',\n", + " 'liiwwwhteirsi',\n", + " 'dflhtsrndesrh',\n", + " 'ldrntgrsuasea',\n", + " 'tndoyasadutew',\n", + " 'npitcameterto',\n", + " 'ttesyotocnyus',\n", + " 'meogcudlpadla',\n", + " 'eedotfdsbfela',\n", + " 'rehaxsonidtii',\n", + " 'siprahicdcshp',\n", + " 'lrbieslnalhof',\n", + " 'tmrenatoraiek',\n", + " 'rslagetmrdcwn',\n", + " 'wraynsvnuldoe',\n", + " 'nnkutnoutiiun',\n", + " 'iehvneilohltf',\n", + " 'acnaetuifttae',\n", + " 'notlnrbhbegls',\n", + " 'nonaomifkoarn',\n", + " 'ntsnvfretrcfh',\n", + " 'prdetswsucpec',\n", + " 'oiwtpawfhdays',\n", + " 'giooaoaelndfg',\n", + " 'tfngrebltllgo']" + ] + } + ], + "prompt_number": 61 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/challenge7.ipynb b/challenge7.ipynb new file mode 100644 index 0000000..d7d18f4 --- /dev/null +++ b/challenge7.ipynb @@ -0,0 +1,321 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from cipherbreak import *\n", + "with open('2013/mona-lisa-words.txt') as f:\n", + " mlwords = [line.rstrip() for line in f]\n", + "mltrans = collections.defaultdict(list)\n", + "for word in mlwords:\n", + " mltrans[transpositions_of(word)] += [word]\n", + "c7a = open('2013/7a.ciphertext').read()\n", + "c7b = open('2013/7b.ciphertext').read()" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c1a = open('2013/1a.ciphertext').read()\n", + "c1b = open('2013/1b.ciphertext').read()\n", + "c2a = open('2013/2a.ciphertext').read()\n", + "c2b = open('2013/2b.ciphertext').read()\n", + "c3a = open('2013/3a.ciphertext').read()\n", + "c3b = open('2013/3b.ciphertext').read()\n", + "c4a = open('2013/4a.ciphertext').read()\n", + "c4b = open('2013/4b.ciphertext').read()\n", + "c5a = open('2013/5a.ciphertext').read()\n", + "c5b = open('2013/5b.ciphertext').read()\n", + "\n", + "p1a = caesar_decipher(c1a, 8)\n", + "p1b = caesar_decipher(c1b, 14)\n", + "p2a = affine_decipher(c2a, 3, 3, True)\n", + "p2b = caesar_decipher(c2b, 6)\n", + "p3a = affine_decipher(c3a, 7, 8, True)\n", + "p3b = keyword_decipher(c3b, 'louvigny', 2)\n", + "p4a = keyword_decipher(c4a, 'montal', 2)\n", + "p4b = keyword_decipher(c4b, 'salvation', 2)\n", + "p5a = keyword_decipher(c5a, 'alfredo', 2)\n", + "p5b = vigenere_decipher(sanitise(c5b), 'florence')" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plot_frequency_histogram(frequencies(sanitise(c7a)))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stderr", + "text": [ + "/usr/local/lib/python3.3/dist-packages/matplotlib/figure.py:372: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n", + " \"matplotlib is currently using a non-GUI backend, \"\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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w+O3J4XDoyJEjSktLk91u91lXWFioxYsXa+LEiTrnnHN0zjnn+Az2FStW6Oyz\nz9a1116rzs5OTZo0SR6PR06n02fPl1xyiRITE7t9/h5//HEdPHhQF198sSTpwgsv1FNPPeV3mr6E\nD+oi7I4ePaqBAweqra1NU6ZM0dNPP628vLxe6eXzzz/v1WNbva22tlbTp0/Xrl27gp520aJFGjRo\nkO64444IdBa7Ojs7NW7cOK1evVrnn39+b7djNHbxIexuueUW5efna9y4cbr66qt7LZwOHDigSZMm\n6a677uqV5ZuiJ7vpomH3bDSpqalRRkaGpk6dSjgFgBEUAMBIjKAAAEYioAAARiKgAABGIqAAAEYi\noAAARiKgAABG+j/og6x5jaDpPwAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c7af = frequencies(sanitise(c7a))\n", + "plot_frequency_histogram(c7af, sort_key=lambda l: c7af[l])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c7bf = frequencies(sanitise(c7b))\n", + "plot_frequency_histogram(c7bf, sort_key=lambda l: c7bf[l])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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to make the painting look like part of the box by the way no one was going to turn it over to look if they didnt know it was there and they were pretty unlikely to be looking for someone to smuggle a painting in anyway access to the gallery was straightforward and it took around twenty minutes to switch the copy with the original i hid the painting among a bunch of reproductions in the museum shop and camped out for the night in the guards bathroom turns out they prefer to use the directors facilities upon the top floor with the new exhibition opening on saturday the place was busy enough to slip out first thing and as arranged i made sure i was first into the shop i now have the honour of having bought the cheapest ever work by davinci or not the xray results came back this morning and as you suspected this is one of saras fake siam told it is close to perfect but hidden under the layers of paint she scribbled a picture of the nazi eagle emblem in leads he signed its too the tech guys think she may have used abit of old pipe like a crayon to deface the board before she started work on it anyway that leaves the question of where the hell the real painting might be its hard to believe that she left it with the ss and icant see her going on the run with it stuck under her coat its not like she could roll it up i worked through some more of the nazi papers and found this note atleast it tells us where she went looks like the cipher clerk was back by the way i have moved on to venice to try to find any trace of sara there but i have a feeling the solution to this mystery is back in paris where it all began i left the painting at the paris office maybe you could arrange to return it it should be easier to get it in than it was to extract it all the best harry'" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "vigenere_frequency_break(sanitise(c7b))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 16, + "text": [ + "('aattuualptaaauaaaa', 0.10312795085805967)" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "' '.join(segment(vigenere_decipher(sanitise(c7b),'aattuualptaaauaaaa' )))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 17, + "text": [ + "'ttmaqoehqveytelettkf vfantitlnhhttprnmews qrfwquefetnntmmohpun kit a murvsoegeomjsemwelpo yotkcoytmamvgijtrhtk pcrnydlmautreryrciti man rtxrnmzeatctythrycyb obmmisfdefehefyfnvws note neetztxkrqcavlennemh tmeemnnfvulnntneyfrt a ohtmohynxzxnzontunrg hubfooznoirdgkiztyqh eodatncnenpgyccwfmai masxprjmmtoktyiheouf jnteemaetxhkyutyaatk ausmmfuccthuyotxmltn tythhtootmnrnusztdsm mkoiyftfhharuianbwha eixyetfoatnboksfiheu ywcrthbfulmrsaetmlpu ymhtryamodjafttteaff ttnwmqtfzwbhntypttmt are dldnrkyhsacctyerfamm tgomtxzumtmtmtanskid jfpoxhothtoaixvidebb 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+ "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 18, + "text": [ + "1304" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/cipher.py b/cipher.py new file mode 100644 index 0000000..c5d542b --- /dev/null +++ b/cipher.py @@ -0,0 +1,499 @@ +import string +import collections +import logging +import math +from itertools import zip_longest, cycle, chain +from language_models import * + +logger = logging.getLogger(__name__) +logger.addHandler(logging.FileHandler('cipher.log')) +logger.setLevel(logging.WARNING) +#logger.setLevel(logging.INFO) +#logger.setLevel(logging.DEBUG) + + +modular_division_table = [[0]*26 for _ in range(26)] +for a in range(26): + for b in range(26): + c = (a * b) % 26 + modular_division_table[b][c] = a + + +def every_nth(text, n, fillvalue=''): + """Returns n strings, each of which consists of every nth character, + starting with the 0th, 1st, 2nd, ... (n-1)th character + + >>> every_nth(string.ascii_lowercase, 5) + ['afkpuz', 'bglqv', 'chmrw', 'dinsx', 'ejoty'] + >>> every_nth(string.ascii_lowercase, 1) + ['abcdefghijklmnopqrstuvwxyz'] + >>> every_nth(string.ascii_lowercase, 26) # doctest: +NORMALIZE_WHITESPACE + ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', + 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z'] + >>> every_nth(string.ascii_lowercase, 5, fillvalue='!') + ['afkpuz', 'bglqv!', 'chmrw!', 'dinsx!', 'ejoty!'] + """ + split_text = [text[i:i+n] for i in range(0, len(text), n)] + return [''.join(l) for l in zip_longest(*split_text, fillvalue=fillvalue)] + +def combine_every_nth(split_text): + """Reforms a text split into every_nth strings + + >>> combine_every_nth(every_nth(string.ascii_lowercase, 5)) + 'abcdefghijklmnopqrstuvwxyz' + >>> combine_every_nth(every_nth(string.ascii_lowercase, 1)) + 'abcdefghijklmnopqrstuvwxyz' + >>> combine_every_nth(every_nth(string.ascii_lowercase, 26)) + 'abcdefghijklmnopqrstuvwxyz' + """ + return ''.join([''.join(l) + for l in zip_longest(*split_text, fillvalue='')]) + +def chunks(text, n, fillvalue=None): + """Split a text into chunks of n characters + + >>> chunks('abcdefghi', 3) + ['abc', 'def', 'ghi'] + >>> chunks('abcdefghi', 4) + ['abcd', 'efgh', 'i'] + >>> chunks('abcdefghi', 4, fillvalue='!') + ['abcd', 'efgh', 'i!!!'] + """ + if fillvalue: + padding = fillvalue[0] * (n - len(text) % n) + else: + padding = '' + return [(text+padding)[i:i+n] for i in range(0, len(text), n)] + +def transpose(items, transposition): + """Moves items around according to the given transposition + + >>> transpose(['a', 'b', 'c', 'd'], (0,1,2,3)) + ['a', 'b', 'c', 'd'] + >>> transpose(['a', 'b', 'c', 'd'], (3,1,2,0)) + ['d', 'b', 'c', 'a'] + >>> transpose([10,11,12,13,14,15], (3,2,4,1,5,0)) + [13, 12, 14, 11, 15, 10] + """ + transposed = [''] * len(transposition) + for p, t in enumerate(transposition): + transposed[p] = items[t] + return transposed + +def untranspose(items, transposition): + """Undoes a transpose + + >>> untranspose(['a', 'b', 'c', 'd'], [0,1,2,3]) + ['a', 'b', 'c', 'd'] + >>> untranspose(['d', 'b', 'c', 'a'], [3,1,2,0]) + ['a', 'b', 'c', 'd'] + >>> untranspose([13, 12, 14, 11, 15, 10], [3,2,4,1,5,0]) + [10, 11, 12, 13, 14, 15] + """ + transposed = [''] * len(transposition) + for p, t in enumerate(transposition): + transposed[t] = items[p] + return transposed + +def deduplicate(text): + return list(collections.OrderedDict.fromkeys(text)) + + +def caesar_encipher_letter(letter, shift): + """Encipher a letter, given a shift amount + + >>> caesar_encipher_letter('a', 1) + 'b' + >>> caesar_encipher_letter('a', 2) + 'c' + >>> caesar_encipher_letter('b', 2) + 'd' + >>> caesar_encipher_letter('x', 2) + 'z' + >>> caesar_encipher_letter('y', 2) + 'a' + >>> caesar_encipher_letter('z', 2) + 'b' + >>> caesar_encipher_letter('z', -1) + 'y' + >>> caesar_encipher_letter('a', -1) + 'z' + """ + if letter in string.ascii_letters: + if letter in string.ascii_uppercase: + alphabet_start = ord('A') + else: + alphabet_start = ord('a') + return chr(((ord(letter) - alphabet_start + shift) % 26) + + alphabet_start) + else: + return letter + +def caesar_decipher_letter(letter, shift): + """Decipher a letter, given a shift amount + + >>> caesar_decipher_letter('b', 1) + 'a' + >>> caesar_decipher_letter('b', 2) + 'z' + """ + return caesar_encipher_letter(letter, -shift) + +def caesar_encipher(message, shift): + """Encipher a message with the Caesar cipher of given shift + + >>> caesar_encipher('abc', 1) + 'bcd' + >>> caesar_encipher('abc', 2) + 'cde' + >>> caesar_encipher('abcxyz', 2) + 'cdezab' + >>> caesar_encipher('ab cx yz', 2) + 'cd ez ab' + """ + enciphered = [caesar_encipher_letter(l, shift) for l in message] + return ''.join(enciphered) + +def caesar_decipher(message, shift): + """Encipher a message with the Caesar cipher of given shift + + >>> caesar_decipher('bcd', 1) + 'abc' + >>> caesar_decipher('cde', 2) + 'abc' + >>> caesar_decipher('cd ez ab', 2) + 'ab cx yz' + """ + return caesar_encipher(message, -shift) + +def affine_encipher_letter(letter, multiplier=1, adder=0, one_based=True): + """Encipher a letter, given a multiplier and adder + + >>> ''.join([affine_encipher_letter(l, 3, 5, True) \ + for l in string.ascii_uppercase]) + 'HKNQTWZCFILORUXADGJMPSVYBE' + >>> ''.join([affine_encipher_letter(l, 3, 5, False) \ + for l in string.ascii_uppercase]) + 'FILORUXADGJMPSVYBEHKNQTWZC' + """ + if letter in string.ascii_letters: + if letter in string.ascii_uppercase: + alphabet_start = ord('A') + else: + alphabet_start = ord('a') + letter_number = ord(letter) - alphabet_start + if one_based: letter_number += 1 + cipher_number = (letter_number * multiplier + adder) % 26 + if one_based: cipher_number -= 1 + return chr(cipher_number % 26 + alphabet_start) + else: + return letter + +def affine_decipher_letter(letter, multiplier=1, adder=0, one_based=True): + """Encipher a letter, given a multiplier and adder + + >>> ''.join([affine_decipher_letter(l, 3, 5, True) \ + for l in 'HKNQTWZCFILORUXADGJMPSVYBE']) + 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' + >>> ''.join([affine_decipher_letter(l, 3, 5, False) \ + for l in 'FILORUXADGJMPSVYBEHKNQTWZC']) + 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' + """ + if letter in string.ascii_letters: + if letter in string.ascii_uppercase: + alphabet_start = ord('A') + else: + alphabet_start = ord('a') + cipher_number = ord(letter) - alphabet_start + if one_based: cipher_number += 1 + plaintext_number = ( + modular_division_table[multiplier] + [(cipher_number - adder) % 26] ) + if one_based: plaintext_number -= 1 + return chr(plaintext_number % 26 + alphabet_start) + else: + return letter + +def affine_encipher(message, multiplier=1, adder=0, one_based=True): + """Encipher a message + + >>> affine_encipher('hours passed during which jerico tried every ' \ + 'trick he could think of', 15, 22, True) + 'lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls omytd jlaxe mh' + """ + enciphered = [affine_encipher_letter(l, multiplier, adder, one_based) + for l in message] + return ''.join(enciphered) + +def affine_decipher(message, multiplier=1, adder=0, one_based=True): + """Decipher a message + + >>> affine_decipher('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg ' \ + 'jfaoe ls omytd jlaxe mh', 15, 22, True) + 'hours passed during which jerico tried every trick he could think of' + """ + enciphered = [affine_decipher_letter(l, multiplier, adder, one_based) + for l in message] + return ''.join(enciphered) + + +def keyword_cipher_alphabet_of(keyword, wrap_alphabet=0): + """Find the cipher alphabet given a keyword. + wrap_alphabet controls how the rest of the alphabet is added + after the keyword. + 0 : from 'a' + 1 : from the last letter in the sanitised keyword + 2 : from the largest letter in the sanitised keyword + + >>> keyword_cipher_alphabet_of('bayes') + 'bayescdfghijklmnopqrtuvwxz' + >>> keyword_cipher_alphabet_of('bayes', 0) + 'bayescdfghijklmnopqrtuvwxz' + >>> keyword_cipher_alphabet_of('bayes', 1) + 'bayestuvwxzcdfghijklmnopqr' + >>> keyword_cipher_alphabet_of('bayes', 2) + 'bayeszcdfghijklmnopqrtuvwx' + """ + if wrap_alphabet == 0: + cipher_alphabet = ''.join(deduplicate(sanitise(keyword) + + string.ascii_lowercase)) + else: + if wrap_alphabet == 1: + last_keyword_letter = deduplicate(sanitise(keyword))[-1] + else: + last_keyword_letter = sorted(sanitise(keyword))[-1] + last_keyword_position = string.ascii_lowercase.find( + last_keyword_letter) + 1 + cipher_alphabet = ''.join( + deduplicate(sanitise(keyword) + + string.ascii_lowercase[last_keyword_position:] + + string.ascii_lowercase)) + return cipher_alphabet + + +def keyword_encipher(message, keyword, wrap_alphabet=0): + """Enciphers a message with a keyword substitution cipher. + wrap_alphabet controls how the rest of the alphabet is added + after the keyword. + 0 : from 'a' + 1 : from the last letter in the sanitised keyword + 2 : from the largest letter in the sanitised keyword + + >>> keyword_encipher('test message', 'bayes') + 'rsqr ksqqbds' + >>> keyword_encipher('test message', 'bayes', 0) + 'rsqr ksqqbds' + >>> keyword_encipher('test message', 'bayes', 1) + 'lskl dskkbus' + >>> keyword_encipher('test message', 'bayes', 2) + 'qspq jsppbcs' + """ + cipher_alphabet = keyword_cipher_alphabet_of(keyword, wrap_alphabet) + cipher_translation = ''.maketrans(string.ascii_lowercase, cipher_alphabet) + return message.lower().translate(cipher_translation) + +def keyword_decipher(message, keyword, wrap_alphabet=0): + """Deciphers a message with a keyword substitution cipher. + wrap_alphabet controls how the rest of the alphabet is added + after the keyword. + 0 : from 'a' + 1 : from the last letter in the sanitised keyword + 2 : from the largest letter in the sanitised keyword + + >>> keyword_decipher('rsqr ksqqbds', 'bayes') + 'test message' + >>> keyword_decipher('rsqr ksqqbds', 'bayes', 0) + 'test message' + >>> keyword_decipher('lskl dskkbus', 'bayes', 1) + 'test message' + >>> keyword_decipher('qspq jsppbcs', 'bayes', 2) + 'test message' + """ + cipher_alphabet = keyword_cipher_alphabet_of(keyword, wrap_alphabet) + cipher_translation = ''.maketrans(cipher_alphabet, string.ascii_lowercase) + return message.lower().translate(cipher_translation) + + +def vigenere_encipher(message, keyword): + """Vigenere encipher + + >>> vigenere_encipher('hello', 'abc') + 'hfnlp' + """ + shifts = [ord(l) - ord('a') for l in sanitise(keyword)] + pairs = zip(message, cycle(shifts)) + return ''.join([caesar_encipher_letter(l, k) for l, k in pairs]) + +def vigenere_decipher(message, keyword): + """Vigenere decipher + + >>> vigenere_decipher('hfnlp', 'abc') + 'hello' + """ + shifts = [ord(l) - ord('a') for l in sanitise(keyword)] + pairs = zip(message, cycle(shifts)) + return ''.join([caesar_decipher_letter(l, k) for l, k in pairs]) + +beaufort_encipher=vigenere_decipher +beaufort_decipher=vigenere_encipher + + +def transpositions_of(keyword): + """Finds the transpostions given by a keyword. For instance, the keyword + 'clever' rearranges to 'celrv', so the first column (0) stays first, the + second column (1) moves to third, the third column (2) moves to second, + and so on. + + If passed a tuple, assume it's already a transposition and just return it. + + >>> transpositions_of('clever') + (0, 2, 1, 4, 3) + >>> transpositions_of('fred') + (3, 2, 0, 1) + >>> transpositions_of((3, 2, 0, 1)) + (3, 2, 0, 1) + """ + if isinstance(keyword, tuple): + return keyword + else: + key = deduplicate(keyword) + transpositions = tuple(key.index(l) for l in sorted(key)) + return transpositions + +def pad(message_len, group_len, fillvalue): + padding_length = group_len - message_len % group_len + if padding_length == group_len: padding_length = 0 + padding = '' + for i in range(padding_length): + if callable(fillvalue): + padding += fillvalue() + else: + padding += fillvalue + return padding + +def column_transposition_encipher(message, keyword, fillvalue=' ', + fillcolumnwise=False, + emptycolumnwise=False): + """Enciphers using the column transposition cipher. + Message is padded to allow all rows to be the same length. + + >>> column_transposition_encipher('hellothere', 'abcdef', fillcolumnwise=True) + 'hlohr eltee ' + >>> column_transposition_encipher('hellothere', 'abcdef', fillcolumnwise=True, emptycolumnwise=True) + 'hellothere ' + >>> column_transposition_encipher('hellothere', 'abcdef') + 'hellothere ' + >>> column_transposition_encipher('hellothere', 'abcde') + 'hellothere' + >>> column_transposition_encipher('hellothere', 'abcde', fillcolumnwise=True, emptycolumnwise=True) + 'hellothere' + >>> column_transposition_encipher('hellothere', 'abcde', fillcolumnwise=True, emptycolumnwise=False) + 'hlohreltee' + >>> column_transposition_encipher('hellothere', 'abcde', fillcolumnwise=False, emptycolumnwise=True) + 'htehlelroe' + >>> column_transposition_encipher('hellothere', 'abcde', fillcolumnwise=False, emptycolumnwise=False) + 'hellothere' + >>> column_transposition_encipher('hellothere', 'clever', fillcolumnwise=True, emptycolumnwise=True) + 'heotllrehe' + >>> column_transposition_encipher('hellothere', 'clever', fillcolumnwise=True, emptycolumnwise=False) + 'holrhetlee' + >>> column_transposition_encipher('hellothere', 'clever', fillcolumnwise=False, emptycolumnwise=True) + 'htleehoelr' + >>> column_transposition_encipher('hellothere', 'clever', fillcolumnwise=False, emptycolumnwise=False) + 'hleolteher' + >>> column_transposition_encipher('hellothere', 'cleverly') + 'hleolthre e ' + >>> column_transposition_encipher('hellothere', 'cleverly', fillvalue='!') + 'hleolthre!e!' + >>> column_transposition_encipher('hellothere', 'cleverly', fillvalue=lambda: '*') + 'hleolthre*e*' + """ + transpositions = transpositions_of(keyword) + message += pad(len(message), len(transpositions), fillvalue) + if fillcolumnwise: + rows = every_nth(message, len(message) // len(transpositions)) + else: + rows = chunks(message, len(transpositions)) + transposed = [transpose(r, transpositions) for r in rows] + if emptycolumnwise: + return combine_every_nth(transposed) + else: + return ''.join(chain(*transposed)) + +def column_transposition_decipher(message, keyword, fillvalue=' ', + fillcolumnwise=False, + emptycolumnwise=False): + """Deciphers using the column transposition cipher. + Message is padded to allow all rows to be the same length. + + >>> column_transposition_decipher('hellothere', 'abcde', fillcolumnwise=True, emptycolumnwise=True) + 'hellothere' + >>> column_transposition_decipher('hlohreltee', 'abcde', fillcolumnwise=True, emptycolumnwise=False) + 'hellothere' + >>> column_transposition_decipher('htehlelroe', 'abcde', fillcolumnwise=False, emptycolumnwise=True) + 'hellothere' + >>> column_transposition_decipher('hellothere', 'abcde', fillcolumnwise=False, emptycolumnwise=False) + 'hellothere' + >>> column_transposition_decipher('heotllrehe', 'clever', fillcolumnwise=True, emptycolumnwise=True) + 'hellothere' + >>> column_transposition_decipher('holrhetlee', 'clever', fillcolumnwise=True, emptycolumnwise=False) + 'hellothere' + >>> column_transposition_decipher('htleehoelr', 'clever', fillcolumnwise=False, emptycolumnwise=True) + 'hellothere' + >>> column_transposition_decipher('hleolteher', 'clever', fillcolumnwise=False, emptycolumnwise=False) + 'hellothere' + """ + transpositions = transpositions_of(keyword) + message += pad(len(message), len(transpositions), '*') + if emptycolumnwise: + rows = every_nth(message, len(message) // len(transpositions)) + else: + rows = chunks(message, len(transpositions)) + untransposed = [untranspose(r, transpositions) for r in rows] + if fillcolumnwise: + return combine_every_nth(untransposed) + else: + return ''.join(chain(*untransposed)) + +def scytale_encipher(message, rows, fillvalue=' '): + """Enciphers using the scytale transposition cipher. + Message is padded with spaces to allow all rows to be the same length. + + >>> scytale_encipher('thequickbrownfox', 3) + 'tcnhkfeboqrxuo iw ' + >>> scytale_encipher('thequickbrownfox', 4) + 'tubnhirfecooqkwx' + >>> scytale_encipher('thequickbrownfox', 5) + 'tubnhirfecooqkwx' + >>> scytale_encipher('thequickbrownfox', 6) + 'tqcrnxhukof eibwo ' + >>> scytale_encipher('thequickbrownfox', 7) + 'tqcrnxhukof eibwo ' + """ + transpositions = [i for i in range(math.ceil(len(message) / rows))] + return column_transposition_encipher(message, transpositions, + fillcolumnwise=False, emptycolumnwise=True) + +def scytale_decipher(message, rows): + """Deciphers using the scytale transposition cipher. + Assumes the message is padded so that all rows are the same length. + + >>> scytale_decipher('tcnhkfeboqrxuo iw ', 3) + 'thequickbrownfox ' + >>> scytale_decipher('tubnhirfecooqkwx', 4) + 'thequickbrownfox' + >>> scytale_decipher('tubnhirfecooqkwx', 5) + 'thequickbrownfox' + >>> scytale_decipher('tqcrnxhukof eibwo ', 6) + 'thequickbrownfox ' + >>> scytale_decipher('tqcrnxhukof eibwo ', 7) + 'thequickbrownfox ' + """ + transpositions = [i for i in range(math.ceil(len(message) / rows))] + return column_transposition_decipher(message, transpositions, + fillcolumnwise=False, emptycolumnwise=True) + + +if __name__ == "__main__": + import doctest + doctest.testmod() diff --git a/cipher.sublime-project b/cipher.sublime-project new file mode 100644 index 0000000..2c63c08 --- /dev/null +++ b/cipher.sublime-project @@ -0,0 +1,2 @@ +{ +} diff --git a/cipherbreak.py b/cipherbreak.py new file mode 100644 index 0000000..d2c35c9 --- /dev/null +++ b/cipherbreak.py @@ -0,0 +1,416 @@ +import string +import collections +import norms +import logging +from itertools import zip_longest, cycle, permutations +from segment import segment +from multiprocessing import Pool +from math import log10 + +import matplotlib.pyplot as plt + +from cipher import * +from language_models import * + +# To time a run: +# +# import timeit +# c5a = open('2012/5a.ciphertext', 'r').read() +# timeit.timeit('keyword_break(c5a)', setup='gc.enable() ; from __main__ import c5a ; from cipher import keyword_break', number=1) +# timeit.repeat('keyword_break_mp(c5a, chunksize=500)', setup='gc.enable() ; from __main__ import c5a ; from cipher import keyword_break_mp', repeat=5, number=1) + +transpositions = collections.defaultdict(list) +for word in keywords: + transpositions[transpositions_of(word)] += [word] + +def frequencies(text): + """Count the number of occurrences of each character in text + + >>> sorted(frequencies('abcdefabc').items()) + [('a', 2), ('b', 2), ('c', 2), ('d', 1), ('e', 1), ('f', 1)] + >>> sorted(frequencies('the quick brown fox jumped over the lazy ' \ + 'dog').items()) # doctest: +NORMALIZE_WHITESPACE + [(' ', 8), ('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1), + ('g', 1), ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), + ('n', 1), ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2), + ('v', 1), ('w', 1), ('x', 1), ('y', 1), ('z', 1)] + >>> sorted(frequencies('The Quick BROWN fox jumped! over... the ' \ + '(9lazy) DOG').items()) # doctest: +NORMALIZE_WHITESPACE + [(' ', 8), ('!', 1), ('(', 1), (')', 1), ('.', 3), ('9', 1), ('B', 1), + ('D', 1), ('G', 1), ('N', 1), ('O', 2), ('Q', 1), ('R', 1), ('T', 1), + ('W', 1), ('a', 1), ('c', 1), ('d', 1), ('e', 4), ('f', 1), ('h', 2), + ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('o', 2), ('p', 1), + ('r', 1), ('t', 1), ('u', 2), ('v', 1), ('x', 1), ('y', 1), ('z', 1)] + >>> sorted(frequencies(sanitise('The Quick BROWN fox jumped! over... ' \ + 'the (9lazy) DOG')).items()) # doctest: +NORMALIZE_WHITESPACE + [('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1), ('g', 1), + ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('n', 1), + ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2), ('v', 1), + ('w', 1), ('x', 1), ('y', 1), ('z', 1)] + >>> frequencies('abcdefabcdef')['x'] + 0 + """ + #counts = collections.defaultdict(int) + #for c in text: + # counts[c] += 1 + #return counts + return collections.Counter(c for c in text) + + +def caesar_break(message, fitness=Pletters): + """Breaks a Caesar cipher using frequency analysis + + >>> caesar_break('ibxcsyorsaqcheyklxivoexlevmrimwxsfiqevvmihrsasrxliwyrh' \ + 'ecjsppsamrkwleppfmergefifvmhixscsymjcsyqeoixlm') # doctest: +ELLIPSIS + (4, -130.849890899...) + >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgtee' \ + 'raxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') # doctest: +ELLIPSIS + (19, -128.82516920...) + >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurer' \ + 'svaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') # doctest: +ELLIPSIS + (13, -126.25233502...) + """ + sanitised_message = sanitise(message) + best_shift = 0 + best_fit = float('-inf') + for shift in range(26): + plaintext = caesar_decipher(sanitised_message, shift) + fit = fitness(plaintext) + logger.debug('Caesar break attempt using key {0} gives fit of {1} ' + 'and decrypt starting: {2}'.format(shift, fit, plaintext[:50])) + if fit > best_fit: + best_fit = fit + best_shift = shift + logger.info('Caesar break best fit: key {0} gives fit of {1} and ' + 'decrypt starting: {2}'.format(best_shift, best_fit, + caesar_decipher(sanitised_message, best_shift)[:50])) + return best_shift, best_fit + +def affine_break(message, fitness=Pletters): + """Breaks an affine cipher using frequency analysis + + >>> affine_break('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls ' \ + 'omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls ' \ + 'ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx ' \ + 'ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls ' \ + 'bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai ' \ + 'kxd clm ckuxj.') # doctest: +ELLIPSIS + ((15, 22, True), -340.611412245...) + """ + sanitised_message = sanitise(message) + best_multiplier = 0 + best_adder = 0 + best_one_based = True + best_fit = float("-inf") + for one_based in [True, False]: + for multiplier in [x for x in range(1, 26, 2) if x != 13]: + for adder in range(26): + plaintext = affine_decipher(sanitised_message, + multiplier, adder, one_based) + fit = fitness(plaintext) + logger.debug('Affine break attempt using key {0}x+{1} ({2}) ' + 'gives fit of {3} and decrypt starting: {4}'. + format(multiplier, adder, one_based, fit, + plaintext[:50])) + if fit > best_fit: + best_fit = fit + best_multiplier = multiplier + best_adder = adder + best_one_based = one_based + logger.info('Affine break best fit with key {0}x+{1} ({2}) gives fit of {3} ' + 'and decrypt starting: {4}'.format( + best_multiplier, best_adder, best_one_based, best_fit, + affine_decipher(sanitised_message, best_multiplier, + best_adder, best_one_based)[:50])) + return (best_multiplier, best_adder, best_one_based), best_fit + +def keyword_break(message, wordlist=keywords, fitness=Pletters): + """Breaks a keyword substitution cipher using a dictionary and + frequency analysis + + >>> keyword_break(keyword_encipher('this is a test message for the ' \ + 'keyword decipherment', 'elephant', 1), \ + wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS + (('elephant', 1), -52.8345642265...) + """ + best_keyword = '' + best_wrap_alphabet = True + best_fit = float("-inf") + for wrap_alphabet in range(3): + for keyword in wordlist: + plaintext = keyword_decipher(message, keyword, wrap_alphabet) + fit = fitness(plaintext) + logger.debug('Keyword break attempt using key {0} (wrap={1}) ' + 'gives fit of {2} and decrypt starting: {3}'.format( + keyword, wrap_alphabet, fit, + sanitise(plaintext)[:50])) + if fit > best_fit: + best_fit = fit + best_keyword = keyword + best_wrap_alphabet = wrap_alphabet + logger.info('Keyword break best fit with key {0} (wrap={1}) gives fit of ' + '{2} and decrypt starting: {3}'.format(best_keyword, + best_wrap_alphabet, best_fit, sanitise( + keyword_decipher(message, best_keyword, + best_wrap_alphabet))[:50])) + return (best_keyword, best_wrap_alphabet), best_fit + +def keyword_break_mp(message, wordlist=keywords, fitness=Pletters, chunksize=500): + """Breaks a keyword substitution cipher using a dictionary and + frequency analysis + + >>> keyword_break_mp(keyword_encipher('this is a test message for the ' \ + 'keyword decipherment', 'elephant', 1), \ + wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS + (('elephant', 1), -52.834564226507...) + """ + with Pool() as pool: + helper_args = [(message, word, wrap, fitness) + for word in wordlist for wrap in range(3)] + # Gotcha: the helper function here needs to be defined at the top level + # (limitation of Pool.starmap) + breaks = pool.starmap(keyword_break_worker, helper_args, chunksize) + return max(breaks, key=lambda k: k[1]) + +def keyword_break_worker(message, keyword, wrap_alphabet, fitness): + plaintext = keyword_decipher(message, keyword, wrap_alphabet) + fit = fitness(plaintext) + logger.debug('Keyword break attempt using key {0} (wrap={1}) gives fit of ' + '{2} and decrypt starting: {3}'.format(keyword, + wrap_alphabet, fit, sanitise(plaintext)[:50])) + return (keyword, wrap_alphabet), fit + +def scytale_break(message, fitness=Pbigrams): + """Breaks a Scytale cipher + + >>> scytale_break('tfeulchtrtteehwahsdehneoifeayfsondmwpltmaoalhikotoere' \ + 'dcweatehiplwxsnhooacgorrcrcraotohsgullasenylrendaianeplscdriioto' \ + 'aek') # doctest: +ELLIPSIS + (6, -281.276219108...) + """ + best_key = 0 + best_fit = float("-inf") + for key in range(1, 20): + if len(message) % key == 0: + plaintext = scytale_decipher(message, key) + fit = fitness(sanitise(plaintext)) + logger.debug('Scytale break attempt using key {0} gives fit of ' + '{1} and decrypt starting: {2}'.format(key, + fit, sanitise(plaintext)[:50])) + if fit > best_fit: + best_fit = fit + best_key = key + logger.info('Scytale break best fit with key {0} gives fit of {1} and ' + 'decrypt starting: {2}'.format(best_key, best_fit, + sanitise(scytale_decipher(message, best_key))[:50])) + return best_key, best_fit + + +def column_transposition_break_mp(message, translist=transpositions, + fitness=Pbigrams, chunksize=500): + """Breaks a column transposition cipher using a dictionary and + n-gram frequency analysis + """ + # >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \ + # "It is a truth universally acknowledged, that a single man in \ + # possession of a good fortune, must be in want of a wife. However \ + # little known the feelings or views of such a man may be on his \ + # first entering a neighbourhood, this truth is so well fixed in the \ + # minds of the surrounding families, that he is considered the \ + # rightful property of some one or other of their daughters."), \ + # 'encipher'), \ + # translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \ + # (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \ + # (6, 1, 0, 4, 5, 3, 2): ['keyword']}) # doctest: +ELLIPSIS + # (((2, 0, 5, 3, 1, 4, 6), False), 0.0628106372...) + # >>> column_transposition_break_mp(column_transposition_encipher(sanitise( \ + # "It is a truth universally acknowledged, that a single man in \ + # possession of a good fortune, must be in want of a wife. However \ + # little known the feelings or views of such a man may be on his \ + # first entering a neighbourhood, this truth is so well fixed in the \ + # minds of the surrounding families, that he is considered the \ + # rightful property of some one or other of their daughters."), \ + # 'encipher'), \ + # translist={(2, 0, 5, 3, 1, 4, 6): ['encipher'], \ + # (5, 0, 6, 1, 3, 4, 2): ['fourteen'], \ + # (6, 1, 0, 4, 5, 3, 2): ['keyword']}, \ + # target_counts=normalised_english_trigram_counts) # doctest: +ELLIPSIS + # (((2, 0, 5, 3, 1, 4, 6), False), 0.0592259560...) + # """ + with Pool() as pool: + helper_args = [(message, trans, columnwise, fitness) + for trans in translist.keys() + for columnwise in [True, False]] + # Gotcha: the helper function here needs to be defined at the top level + # (limitation of Pool.starmap) + breaks = pool.starmap(column_transposition_break_worker, + helper_args, chunksize) + return max(breaks, key=lambda k: k[1]) +column_transposition_break = column_transposition_break_mp + +def column_transposition_break_worker(message, transposition, columnwise, + fitness): + plaintext = column_transposition_decipher(message, transposition, columnwise=columnwise) + fit = fitness(sanitise(plaintext)) + logger.debug('Column transposition break attempt using key {0} ' + 'gives fit of {1} and decrypt starting: {2}'.format( + transposition, fit, + sanitise(plaintext)[:50])) + return (transposition, columnwise), fit + + +def transposition_break_exhaustive(message, fitness=Pbigrams): + best_transposition = '' + best_pw = float('-inf') + for keylength in range(1, 21): + if len(message) % keylength == 0: + for transposition in permutations(range(keylength)): + for columnwise in [True, False]: + plaintext = column_transposition_decipher(message, + transposition, columnwise=columnwise) + fit=fitness(plaintext) + logger.debug('Column transposition break attempt using key {0} {1} ' + 'gives fit of {2} and decrypt starting: {3}'.format( + transposition, columnwise, pw, + sanitise(plaintext)[:50])) + if fit > best_fit: + best_transposition = transposition + best_columnwise = columnwise + best_fit = fit + return (best_transposition, best_columnwise), best_pw + + +def vigenere_keyword_break(message, wordlist=keywords, fitness=Pletters): + """Breaks a vigenere cipher using a dictionary and + frequency analysis + + >>> vigenere_keyword_break(vigenere_encipher(sanitise('this is a test ' \ + 'message for the vigenere decipherment'), 'cat'), \ + wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS + ('cat', -52.9479167030...) + """ + best_keyword = '' + best_fit = float("-inf") + for keyword in wordlist: + plaintext = vigenere_decipher(message, keyword) + fit = fitness(plaintext) + logger.debug('Vigenere break attempt using key {0} ' + 'gives fit of {1} and decrypt starting: {2}'.format( + keyword, fit, + sanitise(plaintext)[:50])) + if fit > best_fit: + best_fit = fit + best_keyword = keyword + logger.info('Vigenere break best fit with key {0} gives fit ' + 'of {1} and decrypt starting: {2}'.format(best_keyword, + best_fit, sanitise( + vigenere_decipher(message, best_keyword))[:50])) + return best_keyword, best_fit + +def vigenere_keyword_break_mp(message, wordlist=keywords, fitness=Pletters, + chunksize=500): + """Breaks a vigenere cipher using a dictionary and + frequency analysis + + >>> vigenere_keyword_break_mp(vigenere_encipher(sanitise('this is a test ' \ + 'message for the vigenere decipherment'), 'cat'), \ + wordlist=['cat', 'elephant', 'kangaroo']) # doctest: +ELLIPSIS + ('cat', -52.9479167030...) + """ + with Pool() as pool: + helper_args = [(message, word, fitness) + for word in wordlist] + # Gotcha: the helper function here needs to be defined at the top level + # (limitation of Pool.starmap) + breaks = pool.starmap(vigenere_keyword_break_worker, helper_args, chunksize) + return max(breaks, key=lambda k: k[1]) + +def vigenere_keyword_break_worker(message, keyword, fitness): + plaintext = vigenere_decipher(message, keyword) + fit = fitness(plaintext) + logger.debug('Vigenere keyword break attempt using key {0} gives fit of ' + '{1} and decrypt starting: {2}'.format(keyword, + fit, sanitise(plaintext)[:50])) + return keyword, fit + + + +def vigenere_frequency_break(message, fitness=Pletters): + """Breaks a Vigenere cipher with frequency analysis + + >>> vigenere_frequency_break(vigenere_encipher(sanitise("It is time to " \ + "run. She is ready and so am I. I stole Daniel's pocketbook this " \ + "afternoon when he left his jacket hanging on the easel in the " \ + "attic. I jump every time I hear a footstep on the stairs, " \ + "certain that the theft has been discovered and that I will " \ + "be caught. The SS officer visits less often now that he is " \ + "sure"), 'florence')) # doctest: +ELLIPSIS + ('florence', -307.5549865898...) + """ + best_fit = float("-inf") + best_key = '' + sanitised_message = sanitise(message) + for trial_length in range(1, 20): + splits = every_nth(sanitised_message, trial_length) + key = ''.join([chr(caesar_break(s)[0] + ord('a')) for s in splits]) + plaintext = vigenere_decipher(sanitised_message, key) + fit = fitness(plaintext) + logger.debug('Vigenere key length of {0} ({1}) gives fit of {2}'. + format(trial_length, key, fit)) + if fit > best_fit: + best_fit = fit + best_key = key + logger.info('Vigenere break best fit with key {0} gives fit ' + 'of {1} and decrypt starting: {2}'.format(best_key, + best_fit, sanitise( + vigenere_decipher(message, best_key))[:50])) + return best_key, best_fit + +def beaufort_frequency_break(message, fitness=Pletters): + """Breaks a Beaufort cipher with frequency analysis + + >>> beaufort_frequency_break(beaufort_encipher(sanitise("It is time to " \ + "run. She is ready and so am I. I stole Daniel's pocketbook this " \ + "afternoon when he left his jacket hanging on the easel in the " \ + "attic. I jump every time I hear a footstep on the stairs, " \ + "certain that the theft has been discovered and that I will " \ + "be caught. The SS officer visits less often now " \ + "that he is sure"), 'florence')) # doctest: +ELLIPSIS + ('florence', -307.5549865898...) + """ + best_fit = float("-inf") + best_key = '' + sanitised_message = sanitise(message) + for trial_length in range(1, 20): + splits = every_nth(sanitised_message, trial_length) + key = ''.join([chr(-caesar_break(s)[0] % 26 + ord('a')) for s in splits]) + plaintext = beaufort_decipher(sanitised_message, key) + fit = fitness(plaintext) + logger.debug('Beaufort key length of {0} ({1}) gives fit of {2}'. + format(trial_length, key, fit)) + if fit > best_fit: + best_fit = fit + best_key = key + logger.info('Beaufort break best fit with key {0} gives fit ' + 'of {1} and decrypt starting: {2}'.format(best_key, + best_fit, sanitise( + beaufort_decipher(message, best_key))[:50])) + return best_key, best_fit + + + +def plot_frequency_histogram(freqs, sort_key=None): + x = range(len(freqs.keys())) + y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)] + f = plt.figure() + ax = f.add_axes([0.1, 0.1, 0.9, 0.9]) + ax.bar(x, y, align='center') + ax.set_xticks(x) + ax.set_xticklabels(sorted(freqs.keys(), key=sort_key)) + f.show() + + +if __name__ == "__main__": + import doctest + doctest.testmod() + diff --git a/find_best_caesar_break_parameters.py b/find_best_caesar_break_parameters.py new file mode 100644 index 0000000..9ed5348 --- /dev/null +++ b/find_best_caesar_break_parameters.py @@ -0,0 +1,90 @@ +import random +import collections +from cipher import * +from cipherbreak import * +import itertools + +corpus = sanitise(''.join([open('shakespeare.txt', 'r').read(), + open('sherlock-holmes.txt', 'r').read(), + open('war-and-peace.txt', 'r').read()])) +corpus_length = len(corpus) + +euclidean_scaled_english_counts = norms.euclidean_scale(english_counts) + +# def frequency_compare(text, target_frequency, frequency_scaling, metric): +# counts = frequency_scaling(frequencies(text)) +# return -1 * metric(target_frequency, counts) + +# def euclidean_compare(text): +# return frequency_compare(text, norms.euclidean_scale(english_counts), +# norms.euclidean_scale, norms.euclidean_distance) + +metrics = [{'func': norms.l1, 'invert': True, 'name': 'l1'}, + {'func': norms.l2, 'invert': True, 'name': 'l2'}, + {'func': norms.l3, 'invert': True, 'name': 'l3'}, + {'func': norms.cosine_distance, 'invert': False, 'name': 'cosine_distance'}, + {'func': norms.harmonic_mean, 'invert': True, 'name': 'harmonic_mean'}, + {'func': norms.geometric_mean, 'invert': True, 'name': 'geometric_mean'}] +scalings = [{'corpus_frequency': normalised_english_counts, + 'scaling': norms.normalise, + 'name': 'normalised'}, + {'corpus_frequency': euclidean_scaled_english_counts, + 'scaling': norms.euclidean_scale, + 'name': 'euclidean_scaled'}] +message_lengths = [300, 100, 50, 30, 20, 10, 5] + +trials = 5000 + +scores = {} + + +def make_frequency_compare_function(target_frequency, frequency_scaling, metric, invert): + def frequency_compare(text): + counts = frequency_scaling(frequencies(text)) + if invert: + score = -1 * metric(target_frequency, counts) + else: + score = metric(target_frequency, counts) + return score + return frequency_compare + + +def scoring_functions(): + return [{'func': make_frequency_compare_function(s['corpus_frequency'], + s['scaling'], m['func'], m['invert']), + 'name': '{} + {}'.format(m['name'], s['name'])} + for m in metrics + for s in scalings] + [{'func': Pletters, 'name': 'Pletters'}] + +def eval_scores(): + [eval_one_score(f, l) + for f in scoring_functions() + for l in message_lengths] + +def eval_one_score(scoring_function, message_length): + print(scoring_function['name'], message_length) + if scoring_function['name'] not in scores: + scores[scoring_function['name']] = collections.defaultdict(int) + for _ in range(trials): + sample_start = random.randint(0, corpus_length - message_length) + sample = corpus[sample_start:(sample_start + message_length)] + key = random.randint(1, 25) + ciphertext = caesar_encipher(sample, key) + found_key, _ = caesar_break(ciphertext, scoring_function['func']) + if found_key == key: + scores[scoring_function['name']][message_length] += 1 + return scores[scoring_function['name']][message_length] + +def show_results(): + with open('caesar_break_parameter_trials.csv', 'w') as f: + print(',message_length', file = f) + print('scoring,', ', '.join([str(l) for l in message_lengths]), file = f) + for scoring in sorted(scores.keys()): + for length in message_lengths: + print(scoring, end='', sep='', file=f) + for l in message_lengths: + print(',', scores[scoring][l] / trials, end='', file=f) + print('', file = f) + +eval_scores() +show_results() diff --git a/find_wikipedia_titles.py b/find_wikipedia_titles.py new file mode 100644 index 0000000..8d56124 --- /dev/null +++ b/find_wikipedia_titles.py @@ -0,0 +1,35 @@ +import urllib.request +import urllib.parse +import json +import time + +initial_request_url = "http://en.wikipedia.org/w/api.php?action=query&list=allpages&format=json&aplimit=10&apminsize=5000" +request_url = "http://en.wikipedia.org/w/api.php?action=query&list=allpages&format=json&aplimit=10&apminsize=5000&apcontinue={}" +titles_file = '/opt/sources/wp-titles.txt' + +def titles_of(result): + return [p['title'] for p in result['query']['allpages'] ] + +def next_title(result): + return result['query-continue']['allpages']['apcontinue'] + +def write_titles(titles): + with open(titles_file, 'a') as f: + print('\n'.join(titles), file=f) + +def request_again(start_title): + request = urllib.request.Request(request_url.format(urllib.parse.quote(start_title))) + request.add_header('User-Agent','neil.wpspider@njae.me.uk') + result = json.loads(urllib.request.urlopen(request).read().decode()) + return titles_of(result), next_title(result) + +f = open(titles_file, 'w') +f.close() + +result = json.loads(urllib.request.urlopen(initial_request_url).read().decode()) +n_title = next_title(result) +titles = titles_of(result) +while titles != []: + write_titles(titles) + time.sleep(0.5) + titles, n_title = request_again(n_title) diff --git a/language_models.py b/language_models.py new file mode 100644 index 0000000..9297468 --- /dev/null +++ b/language_models.py @@ -0,0 +1,156 @@ +import string +import norms +import random +import collections +import unicodedata +import itertools +from math import log10 + +def letters(text): + """Remove all non-alphabetic characters from a text + >>> letters('The Quick') + 'TheQuick' + >>> letters('The Quick BROWN fox jumped! over... the (9lazy) DOG') + 'TheQuickBROWNfoxjumpedoverthelazyDOG' + """ + return ''.join([c for c in text if c in string.ascii_letters]) + +def unaccent(text): + """Remove all accents from letters. + It does this by converting the unicode string to decomposed compatability + form, dropping all the combining accents, then re-encoding the bytes. + + >>> unaccent('hello') + 'hello' + >>> unaccent('HELLO') + 'HELLO' + >>> unaccent('héllo') + 'hello' + >>> unaccent('héllö') + 'hello' + >>> unaccent('HÉLLÖ') + 'HELLO' + """ + return unicodedata.normalize('NFKD', text).\ + encode('ascii', 'ignore').\ + decode('utf-8') + +def sanitise(text): + """Remove all non-alphabetic characters and convert the text to lowercase + + >>> sanitise('The Quick') + 'thequick' + >>> sanitise('The Quick BROWN fox jumped! over... the (9lazy) DOG') + 'thequickbrownfoxjumpedoverthelazydog' + >>> sanitise('HÉLLÖ') + 'hello' + """ + # sanitised = [c.lower() for c in text if c in string.ascii_letters] + # return ''.join(sanitised) + return letters(unaccent(text)).lower() + + +def datafile(name, sep='\t'): + """Read key,value pairs from file. + """ + with open(name, 'r') as f: + for line in f: + splits = line.split(sep) + yield [splits[0], int(splits[1])] + +english_counts = collections.Counter(dict(datafile('count_1l.txt'))) +normalised_english_counts = norms.normalise(english_counts) + +english_bigram_counts = collections.Counter(dict(datafile('count_2l.txt'))) +normalised_english_bigram_counts = norms.normalise(english_bigram_counts) + +english_trigram_counts = collections.Counter(dict(datafile('count_3l.txt'))) +normalised_english_trigram_counts = norms.normalise(english_trigram_counts) + +with open('words.txt', 'r') as f: + keywords = [line.rstrip() for line in f] + + +def weighted_choice(d): + """Generate random item from a dictionary of item counts + """ + target = random.uniform(0, sum(d.values())) + cuml = 0.0 + for (l, p) in d.items(): + cuml += p + if cuml > target: + return l + return None + +def random_english_letter(): + """Generate a random letter based on English letter counts + """ + return weighted_choice(normalised_english_counts) + + +def ngrams(text, n): + """Returns all n-grams of a text + + >>> ngrams(sanitise('the quick brown fox'), 2) # doctest: +NORMALIZE_WHITESPACE + ['th', 'he', 'eq', 'qu', 'ui', 'ic', 'ck', 'kb', 'br', 'ro', 'ow', 'wn', + 'nf', 'fo', 'ox'] + >>> ngrams(sanitise('the quick brown fox'), 4) # doctest: +NORMALIZE_WHITESPACE + ['theq', 'hequ', 'equi', 'quic', 'uick', 'ickb', 'ckbr', 'kbro', 'brow', + 'rown', 'ownf', 'wnfo', 'nfox'] + """ + return [text[i:i+n] for i in range(len(text)-n+1)] + + +class Pdist(dict): + """A probability distribution estimated from counts in datafile. + Values are stored and returned as log probabilities. + """ + def __init__(self, data=[], estimate_of_missing=None): + data1, data2 = itertools.tee(data) + self.total = sum([d[1] for d in data1]) + for key, count in data2: + self[key] = log10(count / self.total) + self.estimate_of_missing = estimate_of_missing or (lambda k, N: 1./N) + def __missing__(self, key): + return self.estimate_of_missing(key, self.total) + +def log_probability_of_unknown_word(key, N): + """Estimate the probability of an unknown word. + """ + return -log10(N * 10**((len(key) - 2) * 1.4)) + +Pw = Pdist(datafile('count_1w.txt'), log_probability_of_unknown_word) +Pl = Pdist(datafile('count_1l.txt'), lambda _k, _N: 0) +P2l = Pdist(datafile('count_2l.txt'), lambda _k, _N: 0) + +def Pwords(words): + """The Naive Bayes log probability of a sequence of words. + """ + return sum(Pw[w.lower()] for w in words) + +def Pletters(letters): + """The Naive Bayes log probability of a sequence of letters. + """ + return sum(Pl[l.lower()] for l in letters) + +def Pbigrams(letters): + """The Naive Bayes log probability of the bigrams formed from a sequence + of letters. + """ + return sum(P2l[p] for p in ngrams(letters, 2)) + + +def cosine_distance_score(text): + """Finds the dissimilarity of a text to English, using the cosine distance + of the frequency distribution. + + >>> cosine_distance_score('abcabc') # doctest: +ELLIPSIS + 0.370847405... + """ + return norms.cosine_distance(english_counts, + collections.Counter(sanitise(text))) + + +if __name__ == "__main__": + import doctest + doctest.testmod() diff --git a/lettercount.py b/lettercount.py new file mode 100644 index 0000000..4a7082d --- /dev/null +++ b/lettercount.py @@ -0,0 +1,21 @@ +import collections +import string + +def sanitise(text): + return [l.lower() for l in text if l in string.ascii_letters] + +corpora = ['shakespeare.txt', 'sherlock-holmes.txt', 'war-and-peace.txt'] +counts = collections.defaultdict(int) + +for corpus in corpora: + text = sanitise(open(corpus, 'r').read()) + for letter in text: + counts[letter] += 1 + +sorted_letters = sorted(counts, key=counts.get, reverse=True) + +with open('count_1l.txt', 'w') as f: + for l in sorted_letters: + f.write("{0}\t{1}\n".format(l, counts[l])) + + \ No newline at end of file diff --git a/make-cracking-dictionary.py b/make-cracking-dictionary.py new file mode 100644 index 0000000..37de917 --- /dev/null +++ b/make-cracking-dictionary.py @@ -0,0 +1,19 @@ +import language_models + +american = set(open('/usr/share/dict/american-english', 'r').readlines()) +british = set(open('/usr/share/dict/british-english', 'r').readlines()) +cracklib = set(open('/usr/share/dict/cracklib-small', 'r').readlines()) + +words = american | british | cracklib + +# sanitised_words = set() + +# for w in words: + # sanitised_words.add(language_models.sanitise(w)) + +sanitised_words = set(language_models.sanitise(w) for w in words) + +sanitised_words.discard('') + +with open('words.txt', 'w') as f: + f.write('\n'.join(sorted(sanitised_words, key=lambda w: (len(w), w)))) diff --git a/norms.py b/norms.py new file mode 100644 index 0000000..3d6d37d --- /dev/null +++ b/norms.py @@ -0,0 +1,189 @@ +import collections +from math import log10 + +def normalise(frequencies): + """Scale a set of frequencies so they sum to one + + >>> sorted(normalise({1: 1, 2: 0}).items()) + [(1, 1.0), (2, 0.0)] + >>> sorted(normalise({1: 1, 2: 1}).items()) + [(1, 0.5), (2, 0.5)] + >>> sorted(normalise({1: 1, 2: 1, 3: 1}).items()) # doctest: +ELLIPSIS + [(1, 0.333...), (2, 0.333...), (3, 0.333...)] + >>> sorted(normalise({1: 1, 2: 2, 3: 1}).items()) + [(1, 0.25), (2, 0.5), (3, 0.25)] + """ + length = sum([f for f in frequencies.values()]) + return collections.defaultdict(int, ((k, v / length) + for (k, v) in frequencies.items())) + +def euclidean_scale(frequencies): + """Scale a set of frequencies so they have a unit euclidean length + + >>> sorted(euclidean_scale({1: 1, 2: 0}).items()) + [(1, 1.0), (2, 0.0)] + >>> sorted(euclidean_scale({1: 1, 2: 1}).items()) # doctest: +ELLIPSIS + [(1, 0.7071067...), (2, 0.7071067...)] + >>> sorted(euclidean_scale({1: 1, 2: 1, 3: 1}).items()) # doctest: +ELLIPSIS + [(1, 0.577350...), (2, 0.577350...), (3, 0.577350...)] + >>> sorted(euclidean_scale({1: 1, 2: 2, 3: 1}).items()) # doctest: +ELLIPSIS + [(1, 0.408248...), (2, 0.81649658...), (3, 0.408248...)] + """ + length = sum([f ** 2 for f in frequencies.values()]) ** 0.5 + return collections.defaultdict(int, ((k, v / length) + for (k, v) in frequencies.items())) + +def identity_scale(frequencies): + return frequencies + + +def l2(frequencies1, frequencies2): + """Finds the distances between two frequency profiles, expressed as dictionaries. + Assumes every key in frequencies1 is also in frequencies2 + + >>> l2({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1}) + 0.0 + >>> l2({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS + 1.73205080... + >>> l2(normalise({'a':2, 'b':2, 'c':2}), normalise({'a':1, 'b':1, 'c':1})) + 0.0 + >>> l2({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS + 1.732050807... + >>> l2(normalise({'a':0, 'b':2, 'c':0}), \ + normalise({'a':1, 'b':1, 'c':1})) # doctest: +ELLIPSIS + 0.81649658... + >>> l2({'a':0, 'b':1}, {'a':1, 'b':1}) + 1.0 + """ + total = 0 + for k in frequencies1: + total += (frequencies1[k] - frequencies2[k]) ** 2 + return total ** 0.5 +euclidean_distance = l2 + +def l1(frequencies1, frequencies2): + """Finds the distances between two frequency profiles, expressed as + dictionaries. Assumes every key in frequencies1 is also in frequencies2 + + >>> l1({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1}) + 0 + >>> l1({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) + 3 + >>> l1(normalise({'a':2, 'b':2, 'c':2}), normalise({'a':1, 'b':1, 'c':1})) + 0.0 + >>> l1({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) + 3 + >>> l1({'a':0, 'b':1}, {'a':1, 'b':1}) + 1 + """ + total = 0 + for k in frequencies1: + total += abs(frequencies1[k] - frequencies2[k]) + return total + +def l3(frequencies1, frequencies2): + """Finds the distances between two frequency profiles, expressed as + dictionaries. Assumes every key in frequencies1 is also in frequencies2 + + >>> l3({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1}) + 0.0 + >>> l3({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS + 1.44224957... + >>> l3({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS + 1.4422495703... + >>> l3(normalise({'a':0, 'b':2, 'c':0}), \ + normalise({'a':1, 'b':1, 'c':1})) # doctest: +ELLIPSIS + 0.718144896... + >>> l3({'a':0, 'b':1}, {'a':1, 'b':1}) + 1.0 + >>> l3(normalise({'a':0, 'b':1}), normalise({'a':1, 'b':1})) # doctest: +ELLIPSIS + 0.6299605249... + """ + total = 0 + for k in frequencies1: + total += abs(frequencies1[k] - frequencies2[k]) ** 3 + return total ** (1/3) + +def geometric_mean(frequencies1, frequencies2): + """Finds the geometric mean of the absolute differences between two frequency profiles, + expressed as dictionaries. + Assumes every key in frequencies1 is also in frequencies2 + + >>> geometric_mean({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) + 1 + >>> geometric_mean({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) + 1 + >>> geometric_mean({'a':2, 'b':2, 'c':2}, {'a':1, 'b':5, 'c':1}) + 3 + >>> geometric_mean(normalise({'a':2, 'b':2, 'c':2}), \ + normalise({'a':1, 'b':5, 'c':1})) # doctest: +ELLIPSIS + 0.01382140... + >>> geometric_mean(normalise({'a':2, 'b':2, 'c':2}), \ + normalise({'a':1, 'b':1, 'c':1})) # doctest: +ELLIPSIS + 0.0 + >>> geometric_mean(normalise({'a':2, 'b':2, 'c':2}), \ + normalise({'a':1, 'b':1, 'c':0})) # doctest: +ELLIPSIS + 0.009259259... + """ + total = 1 + for k in frequencies1: + total *= abs(frequencies1[k] - frequencies2[k]) + return total + +def harmonic_mean(frequencies1, frequencies2): + """Finds the harmonic mean of the absolute differences between two frequency profiles, + expressed as dictionaries. + Assumes every key in frequencies1 is also in frequencies2 + + >>> harmonic_mean({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) + 1.0 + >>> harmonic_mean({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) + 1.0 + >>> harmonic_mean({'a':2, 'b':2, 'c':2}, {'a':1, 'b':5, 'c':1}) # doctest: +ELLIPSIS + 1.285714285... + >>> harmonic_mean(normalise({'a':2, 'b':2, 'c':2}), \ + normalise({'a':1, 'b':5, 'c':1})) # doctest: +ELLIPSIS + 0.228571428571... + >>> harmonic_mean(normalise({'a':2, 'b':2, 'c':2}), \ + normalise({'a':1, 'b':1, 'c':1})) # doctest: +ELLIPSIS + 0 + >>> harmonic_mean(normalise({'a':2, 'b':2, 'c':2}), \ + normalise({'a':1, 'b':1, 'c':0})) # doctest: +ELLIPSIS + 0.2 + """ + total = 0 + for k in frequencies1: + if abs(frequencies1[k] - frequencies2[k]) == 0: + return 0 + total += 1 / abs(frequencies1[k] - frequencies2[k]) + return len(frequencies1) / total + + +def cosine_distance(frequencies1, frequencies2): + """Finds the distances between two frequency profiles, expressed as dictionaries. + Assumes every key in frequencies1 is also in frequencies2 + + >>> cosine_distance({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS + 1.0000000000... + >>> cosine_distance({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS + 1.0000000000... + >>> cosine_distance({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS + 0.5773502691... + >>> cosine_distance({'a':0, 'b':1}, {'a':1, 'b':1}) # doctest: +ELLIPSIS + 0.7071067811... + """ + numerator = 0 + length1 = 0 + length2 = 0 + for k in frequencies1: + numerator += frequencies1[k] * frequencies2[k] + length1 += frequencies1[k]**2 + for k in frequencies2.keys(): + length2 += frequencies2[k] + return numerator / (length1 ** 0.5 * length2 ** 0.5) + + + +if __name__ == "__main__": + import doctest + doctest.testmod() diff --git a/segment.py b/segment.py new file mode 100644 index 0000000..ba3ddd7 --- /dev/null +++ b/segment.py @@ -0,0 +1,19 @@ +import language_models +import sys +from functools import lru_cache +sys.setrecursionlimit(1000000) + +@lru_cache() +def segment(text): + """Return a list of words that is the best segmentation of text. + """ + if not text: return [] + candidates = ([first]+segment(rest) for first,rest in splits(text)) + return max(candidates, key=language_models.Pwords) + +def splits(text, L=20): + """Return a list of all possible (first, rest) pairs, len(first)<=L. + """ + return [(text[:i+1], text[i+1:]) + for i in range(min(len(text), L))] + diff --git a/unknown-word-probability-investigation.ipynb b/unknown-word-probability-investigation.ipynb new file mode 100644 index 0000000..cba89bf --- /dev/null +++ b/unknown-word-probability-investigation.ipynb @@ -0,0 +1,179 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "from math import log10\n", + "from cipherbreak import *\n", + "from language_models import *" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "fractions = [1.0]\n", + "for wordlen in range(1, 20):\n", + " known_words = len([w for w in keywords if len(w) == wordlen])\n", + " possible_words = 26 ** wordlen\n", + " fractions += [known_words / possible_words]\n", + "fractions" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 2, + "text": [ + "[1.0,\n", + " 1.0,\n", + " 0.34615384615384615,\n", + " 0.05974055530268548,\n", + " 0.007654668954168271,\n", + " 0.0005913456488541394,\n", + " 3.6129588927177356e-05,\n", + " 1.8010883826943671e-06,\n", + " 7.107795165409739e-08,\n", + " 2.4355817367258945e-09,\n", + " 7.469162662303339e-11,\n", + " 1.979378237044537e-12,\n", + " 4.875878520286003e-14,\n", + " 1.1095648437193016e-15,\n", + " 2.199659830168053e-17,\n", + " 4.185399254019551e-19,\n", + " 6.83349209784038e-21,\n", + " 1.199477188056649e-22,\n", + " 2.0013901045062867e-24,\n", + " 1.5656245928341226e-26]" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot(fractions)\n", + "plt.ylabel(\"Probability of word\")\n", + "plt.xlabel(\"Word length\")\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot([log10(f) for f in fractions])\n", + "plt.plot([log10(f) for f in fractions], 'bo')\n", + "plt.ylabel(\"Log probability of word\")\n", + "plt.xlabel(\"Word length\")\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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lRZs2bZg2bRr33nuv3UPeTuskRKQot3eRHT8+nIiITkyZAv/8J/zrX9C6tdEp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\n7dmwYQP33nsvJpOJOnXqkJm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+ "text": [ + "" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot([log10(f) for f in fractions], 'bo')\n", + "plt.plot([i for i in range(2,20)], [-(i-2) for i in range(2,20)], 'g-')\n", + "plt.ylabel(\"Log probability of word\")\n", + "plt.xlabel(\"Word length\")\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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zmjp16mSquF6KU2CJDKPyXiXW/rKWfaIaCaP0bjJHTBJEhsX1Fo0DkwQR6aV2X+6VeStx\n7tdzXG9hZZgkiMhgausWGSUZrFtYCYN2gQ0JCQEAfPrpp/pFRUQWqXa9xflp59knqhFTOZLw9vbG\n3/72N0RHR2PLli0QBKFeMau235IYOJIgayVG/ydNsW5h+Qx6u2n79u1ITU3F0aNH0bt37wbf//HH\nH3WL0gCYJMgaKev/5OY2H4mJYWaTKIDf6xar8lbh7K9nWbewIEapSSxatAhffPGFXoEZGpMEWaOw\nsM+Rnb1YyfEFyMr6swgRqVe7v8XO8ztZt7AARtmZ7osvvkBmZiZmzZqFTz75BLt27dI5QCJSzZz6\nP2mK+1tYP7VJYs6cOUhKSkKPHj3QvXt3JCUlYe7cuaaIjahRMcf+T5pyauWEBHkCyj4qwwjPEZi+\ndzpk38qwsXAjqmuqxQ6P9KD2dpNUKkVhYSFsbZ//NVNTUwM/Pz8UFRWZJEBleLuJrJHymsQ8JCaa\nV3sPTTwTnin2t2DdwnwYZdMhiUSCqqoqtG37/H9uVVUVl+wTGYEl9H/S1It9orgvt+VSO5LYunUr\n5syZg+DgYAiCgJ9++gnLly/HmDFjTBVjAxxJEFmeG/duIOWXFPaJEpHRVlxfu3YNJ06cgEQiQZ8+\nfdCxY0edgzQEJgkiy8X1FuJhWw4ishhcb2F6TBJEZJG43sI0mCSIyKKxbmFcRkkScXFxiImJQY8e\nPfQKzpCYJIiUM+feT9p4+OQhviv6DqvyVrFuYUBGSRLr1q1DWloanjx5gujoaIwdOxaOjo56Baov\nJgmihiyl95M2WLcwLKPebiopKUFaWhq2bNmC/v37Y+LEiQgODtYpUH0xSRA1ZIm9n7TB/S30Z5Te\nTcDzVdYlJSU4f/482rdvD19fX6xatQqjR4/WKVAiMjxL7P2kDe5vIQ61SWLmzJnw9PTE3r17MX/+\nfJw8eRKfffYZdu3ahcLCQlPESEQasOTeT9p4rdVrSvtE/f3039knygjU3m7asGEDRo0ahZYtWzb4\nXlVVFVq3bm204FTh7Saihqyp95M2XuwTNb3vdEzqNYl1CyWMUpMYPHgwDh06VO9YSEgIDh48qH2E\nBsIkQaTcnj2HkZx8oE7vp1CrThAvYt3i5QyaJB4+fIgHDx4gODgYOTk5iuN37txBeHg4SkpK9ApW\nH0wSRPQylfcqsfaXtfjml2/Q17kvZgbO5HoLGDhJrFmzBomJibh27Ro6deqkOO7g4IAPP/wQ06dP\n1y9aPTBJEJEmHj55iE1nNmHN8TVcbwEj3W5KTk7GjBkz9ArM0JgkiEgb3N/iOYMmiUOHDmHw4MHY\nsWOH0iFaVFSUblEaAJMEEemqMdctDJokFi5ciISEBPzpT39SmiQ2bNigW5QGwCRBRPqqW7doLH2i\nLKbB3/bt2xEfH4+SkhKcOHEC/v7+AICysjJ0794dXl5eAICgoCCkpKQ0+HkmCSLjsZb+T5p6cX+L\nmYEzMabnGDS1ayp2aAZn0O1LV65cqfICEokEcXFx2kf4P1KpFBkZGZg0aVKD77m7u6OgoEDncxOR\n7pSttSgtnQ8AVpsomts3x8ReExHjH6PoEzX34FxM6zMNk3pPQrsW7cQOUVQqV1zfvXsX9+7dq/d1\n9+5dxZc+vLy80K1bN73OQUSGl5SUXS9BAEBp6RIkJx8QKSLTsZHYINw9HNnvZWP/u/txqeoSPJI9\nMHn3ZJTcFG/Kv9hUjiTi4+NNGMbvLl++DJlMBkdHRyxevBj9+/dX+rq68cnlcsjlctMESGTFrL3/\nk6akTlKkRqZi6eClSPklBYPSBllk3SInJ6feOjddqKxJrFixAp999pnS6a8SiQRJSUkvPXFoaCgq\nKysbHF+6dCkiIiIAAMHBwVi5cqWiJlFdXY379++jTZs2OHXqFEaOHIlz587BwcGhwfVZkyAyPGvv\nJKurunULe1t7xAXGWWTdwqA1CW9vbwBAr169lF5InQMHtB+eNmnSBE2aPF/k4u/vDzc3N1y8eFGR\nRIjIuGJjh6K0dH6D/k8zZoSLGJX4Xla3sPb1FhrPbrp9+zZsbGwa/FWvj+DgYHz11VeKRHTz5k20\nadMGtra2uHTpEgYOHIizZ882aCLIkQSR8TT2/k+assR9uY0yBfbEiROIjo7GnTt3AACtW7dGamoq\nevfurXOgGRkZiI2Nxc2bN+Ho6AiZTIZ9+/Zhx44dWLhwIezt7WFjY4NFixZh+PDhDYNmkiAiM2FJ\n+3IbJUlIpVKkpKRgwIABAIAjR45g6tSpOHPmjO6R6olJgojMzYvrLcyxT5RRkoRMJmuwbsHf3x+n\nTp3SPkIDYZIgInNlzvtyGzRJnDx5EgCwadMmPHz4EGPHjgUApKeno1mzZli9erWe4eqOSYKILIG5\n9YkyaJKQy+WKe2q1q6zrPv7xxx/1DFd3TBJEZEnMpU+UxfRu0heTBBFZIrHrFkZLErt370ZxcTEe\nPXqkOPbFF19oH6GBMEkQmbfG1iRQW8rqFqboE2XQxXS1Jk2ahIcPH+LQoUOYOHEitm/fjoCAAJ2D\nJCLr1hibBGqrtk9UuHu4Yr2FR7IHRvcYjY8DP4ZXOy+xQ1TQaApsUVERfHx8cObMGdy7dw/h4eE4\ncuSIqWJsgCMJIvPF1h66McV6C11+d6rsAlurefPmAIAWLVqgoqICdnZ2SnsyEREBbBKoK6dWTkiQ\nJ6DsozKM9BqJ6Xunw+9bP2ws3IjHTx+LFpfaJBEREYHffvsNs2fPhr+/P1xdXRXTYYmIXtS06VOl\nx5s1qzFxJJapuX1zfOD/Ac5NPYcVQ1Zgy9ktcE10xeLDi/HwyUOTx6PV7KbHjx/j0aNHcHR0NGZM\navF2E5H5UlaTcHObh8TEcNYkdFR0owhpp9OwYsgK2NmoLSWrZJTZTQ8fPkRKSgqOHDkCiUSCAQMG\nYMqUKWjWrJnOgeqLSYLIvLFJoHkySpJ455138Morr+Ddd9+FIAjYsmULbt++je3bt+sVrD6YJIiI\ntGeUJOHt7Y3i4mK1x0yJSYKISHtGmd3k7++PvLw8xfPjx48r3YiIiIisj8oKiFQqBQA8ffoUr7/+\nOjp37gyJRIIrV67A09O8N9YgIiLDUHm7qaysrP4L6zT4AwBXV1ejBvYyvN1ERKQ9o/VuKiwsRG5u\nrmJ2k6+vr85BGgKTBJH1Y/8nwzNK76bExESsW7cOUVFREAQB7777LiZOnIjY2FidAyUiehn2fzIf\nGvVuOn78OFq2bAkAuH//PgIDA1FUVGSSAJXhSILIurH/k3EYZXYTANjY2Ch9TERkDOz/ZD7U3m6a\nMGECAgICFLebvv/+e0RHR5siNiJqpNj/yXy89HbTs2fPkJeXh2bNmtVryyGTyUwZYwO83URk3dj/\nyTiMMrvJz88PhYWFegVmaEwSRNaP/Z8MzyhJ4pNPPkFgYCDefvttk2/arQqTBBGR9oySJFq1aoUH\nDx7A1tZW0flVIpHgzp07ukeqJyYJIiLtGW0xnblhkiAi0p5RFtMJgoCdO3fiyJEjsLGxQf/+/fHW\nW2/pHCQREVkOtSOJKVOmoLS0FGPHjoUgCEhPT4ebmxtSUlJMFWMDHEkQEWnPKLebvLy8UFxcrFhE\n9+zZM3h7e6OkpETnQGfPno3du3ejSZMmcHNzw4YNGxRboi5btgzr16+Hra0tkpKSMHTo0IZBM0kQ\nEWnNKCuu3d3dceXKFcXzK1euwN3dXfvo6hg6dCjOnTuH06dPo1u3bli2bBkAoLi4GOnp6SguLkZW\nVhamTp2KZ8+e6XUtIiLSndokcefOHXTv3h2DBg2CXC6Ht7c37t69i4iICERGRup00dDQUMXIJCAg\nAFevXgUAZGZmYuzYsbC3t4erqyvc3d2Rn5+v0zWIqHHbs+cwwsI+h1wej7Cwz7Fnz2GxQ7JIagvX\nixYtanCsdshiiHUT69evx9ixYwEA165dQ2BgoOJ7Li4uqKioUPpz8fHxisdyuRxyuVzvWIjIOrCL\n7HM5OTnIycnR6xxqk4Suv3xDQ0NRWVnZ4PjSpUsREREBAFiyZAmaNGmCcePGqTyPqkRUN0kQEdWV\nlJRdL0EAQGnpEiQnL2hUSeLFP6ATEhK0PofaJKGrAwcOvPT7aWlp2Lt3Lw4ePKg45uzsjPLycsXz\nq1evwtnZ2VghEpGVYhdZwxGl73dWVha+/PJLZGZmKlZxA0BkZCS2bduG6upqXL58GRcvXkTfvn3F\nCJGILBi7yBqO0UYSLzNjxgxUV1cjNDQUABAUFISUlBR4e3tj1KhR8Pb2hp2dHVJSUsymXxQRWY7Y\n2KEoLZ3foIvsjBnhIkZlmTTame7FubWOjo7o06cPPv/8c7Rt29boQb6I6ySISB12kW3IKIvpZs+e\nDTs7O4wbNw6CIGDbtm148OABXnvtNRw9ehS7du3SK2hdMEkQEWnPKElCJpOhoKBA6TGpVCrKXtdM\nEkRE2jPKiuuamhr8/PPPiuf5+fmKVdB2dqKUNIiIyETU/pZPTU3FhAkTcO/ePQCAg4MDUlNTcf/+\nfcydO9foARIRkXg03k/i9u3bAKBoxCcm3m4iItKeUW43VVVVYebMmRg8eDAGDx6MWbNmKRIGERFZ\nN7UjiaioKEilUowfPx6CIGDTpk04c+YMdu7caaoYG+BIgohMYc+ew0hKysbjx3Zo2vQpYmOHWvQ0\nWqPMbvL19cXp06fVHjMlJgkiMjZlTQLd3OYjMTHMYhOFUW43NW/eHLm5uYrnR44cQYsWLbSPjojI\ngqhuEvjyvnTWRu3spm+++Qbvv/++og7Rpk0bbNy40eiBERGJiU0Cn1ObJPz8/HDmzJl6s5vWrFkD\nX19fowdHRCQWNgl8TuMusI6OjorprytXrjRaQERE5iA2dijc3ObXO/a8SWCoSBGJg0umiYiUqC1O\nJycvqNMkMNxii9a60ngxXV2dO3eutzmQqXF2ExGR9nT53alyJNGqVSuVezk8ePBAu8iIiMgi6TSS\nEBtHEkRE2jPKOgkiImq8mCSIiEglJgkiIlKJU2CJiIzI0psEMkkQERmJsiaBpaXPF+hZSqLg7SYi\nIiOxhiaBTBJEREZiDU0CmSSIiIzEGpoEMkkQERmJNTQJ5IprIiIj2rPnMJKTD9RpEhgqWtHaKNuX\nmiMmCSIi7bEtBxERGZQoSWL27Nno3r07fH19ERUVpdj1rqysDM2bN4dMJoNMJsPUqVPFCI+IiP5H\nlNtNBw4cQEhICGxsbDBnzhwAwPLly1FWVoaIiAgUFRW99Od5u4mISHsWc7spNDQUNjbPLx0QEICr\nV6+KEQYREakhek1i/fr1GDZsmOL55cuXIZPJIJfLceTIEREjIyIio/VuCg0NRWVlZYPjS5cuRURE\nBABgyZIlaNKkCcaNGwcA6NSpE8rLy9GmTRucOnUKI0eOxLlz5+Dg4NDgPPHx8YrHcrkccrncKP8d\nRESWKicnBzk5OXqdQ7QpsGlpaVi3bh0OHjyIZs2aKX1NcHAwVq5cCX9//3rHWZMgItKexdQksrKy\n8OWXXyIzM7Negrh58yZqap4vV7906RIuXryIrl27ihEiERFBpJGEh4cHqqur8eqrrwIAgoKCkJKS\ngh07dmDhwoWwt7eHjY0NFi1ahOHDhzcMmiMJImpEDLUnBVdcExFZGWV7Uri5zUdiYpjWicJibjcR\nEZFmxN6TgkmCiMiMib0nBZMEEZEZE3tPCiYJIiIzJvaeFCxcExGZOUPtScHZTUREpBJnNxERkUEx\nSRARkUpMEkREpBKTBBERqcQkQUREKjFJEBGRSkwSRESkEpMEERGpxCRBREQqMUkQEZFKTBJERKQS\nkwQREanEJEFERCoxSRARkUpMEkREpBKTBBERqcQkQUREKjFJEBGRSkwSRESkEpMEERGpxCRBREQq\nMUkQEZFKoiSJBQsWwNfXF35+fggJCUF5ebnie8uWLYOHhwe8vLyQnZ0tRniNTk5OjtghWBW+n4bF\n91NcoiSJTz/9FKdPn0ZhYSFGjhyJhIQEAEBxcTHS09NRXFyMrKwsTJ06Fc+ePRMjxEaF/wgNi++n\nYfH9FJcoScLBwUHx+N69e2jXrh0AIDMzE2PHjoW9vT1cXV3h7u6O/Px8MUIkIiIAdmJdeP78+di0\naROaN2+CIL0NAAAIa0lEQVSuSATXrl1DYGCg4jUuLi6oqKgQK0QiokZPIgiCYIwTh4aGorKyssHx\npUuXIiIiQvF8+fLluHDhAjZs2IAZM2YgMDAQf/zjHwEAH3zwAYYNG4aoqKj6QUskxgiZiMjqafsr\n32gjiQMHDmj0unHjxmHYsGEAAGdn53pF7KtXr8LZ2bnBzxgprxER0QtEqUlcvHhR8TgzMxMymQwA\nEBkZiW3btqG6uhqXL1/GxYsX0bdvXzFCJCIiiFSTmDt3Li5cuABbW1u4ublh7dq1AABvb2+MGjUK\n3t7esLOzQ0pKCm8tERGJSbAw+/btEzw9PQV3d3dh+fLlYodj8f7whz8IUqlU8PPzE/r06SN2OBZl\nwoQJQocOHYSePXsqjt26dUsYMmSI4OHhIYSGhgq//fabiBFaFmXv58KFCwVnZ2fBz89P8PPzE/bt\n2ydihJblypUrglwuF7y9vYUePXoIiYmJgiBo/xm1qBXXNTU1mD59OrKyslBcXIytW7fi/PnzYodl\n0SQSCXJyclBQUMDpxlqaMGECsrKy6h1bvnw5QkND8c9//hMhISFYvny5SNFZHmXvp0QiQVxcHAoK\nClBQUIDw8HCRorM89vb2WL16Nc6dO4fjx4/j66+/xvnz57X+jFpUksjPz4e7uztcXV1hb2+PMWPG\nIDMzU+ywLJ7AiQA6GTBgANq0aVPv2A8//IDx48cDAMaPH4/vv/9ejNAskrL3E+DnU1evvfYa/Pz8\nAACtWrVC9+7dUVFRofVn1KKSREVFBTp37qx4znUU+pNIJBgyZAh69+6NdevWiR2Oxbtx4wacnJwA\nAE5OTrhx44bIEVm+5ORk+Pr6IiYmBlVVVWKHY5HKyspQUFCAgIAArT+jFpUkWMQ2vKNHj6KgoAD7\n9u3D119/jdzcXLFDshoSiYSfWT1NmTIFly9fRmFhITp27IhZs2aJHZLFuXfvHt5++20kJibW63YB\naPYZtagk8eI6ivLycri4uIgYkeXr2LEjAKB9+/Z46623WJfQk5OTk2IR6fXr19GhQweRI7JsHTp0\nUPwi++CDD/j51NKTJ0/w9ttv47333sPIkSMBaP8Ztagk0bt3b1y8eBFlZWWorq5Geno6IiMjxQ7L\nYj148AB3794FANy/fx/Z2dmQSqUiR2XZIiMjsXHjRgDAxo0bFf8wSTfXr19XPM7IyODnUwuCICAm\nJgbe3t74+OOPFce1/owafR6Wge3du1fo1q2b4ObmJixdulTscCzapUuXBF9fX8HX11fo0aMH308t\njRkzRujYsaNgb28vuLi4COvXrxdu3bolhISEcAqsDl58P1NTU4X33ntPkEqlgo+PjzBixAihsrJS\n7DAtRm5uriCRSARfX996U4i1/YwarXcTERFZPou63URERKbFJEFERCoxSRARkUpMEkREpBKTBFmt\nmTNnIjExUfE8LCwMEydOVDyfNWsWVq9erdO5c3Jy6m2epe64vjIzM+v1KZPL5Th58qTBr0P0IiYJ\nslr9+/fHsWPHAADPnj3DrVu3UFxcrPh+Xl4eXn/9dY3O9ezZM6PEqKmMjIx6sXMlN5kKkwRZraCg\nIOTl5QEAzp07h549e8LBwQFVVVV4/Pgxzp8/D39/fxw8eBD+/v7w8fFBTEwMqqurAQCurq6YM2cO\nevXqhe3btyMrKwvdu3dHr169kJGRofb69+/fR3R0NAICAuDv748ffvgBAJCWloaoqCi88cYb6Nat\nGz777DPFz6SmpsLT0xMBAQH48MMPMWPGDOTl5WHXrl2YPXs2/P39cenSJQDA9u3bERAQAE9PTxw5\ncsTQbx8RAJE2HSIyhU6dOsHOzg7l5eXIy8tDUFAQKioqkJeXh1deeQU+Pj6oqanBhAkTcOjQIbi7\nu2P8+PFYu3YtPvroI0gkErRr1w4nT57Eo0eP0K1bN/z4449wc3PD6NGj1f41v2TJEoSEhGD9+vWo\nqqpCQEAAhgwZAgA4ffo0CgsL0aRJE3h6eiI2NhYSiQSLFy9GQUEBWrVqhcGDB8PPzw9BQUGIjIxE\nREREvf3ea2pq8PPPP2Pfvn1ISEjQeMtgIm1wJEFWrV+/fjh27BiOHTuGoKAgBAUF4dixY4pbTRcu\nXECXLl3g7u4O4Hnr5MOHDyt+fvTo0QCAkpISdOnSBW5ubgCAd999V20L6+zsbCxfvhwymQzBwcF4\n/Pgxrly5AolEgpCQEDg4OKBp06bw9vZGWVkZ8vPzMWjQILRu3Rp2dnZ455136l3jxevVJgx/f3+U\nlZXp/V4RKcORBFm1119/HUePHkVRURGkUik6d+6Mr776Co6OjoiOjm7wekEQ6o0QWrZsqfS8mjYq\n2LlzJzw8POod+/nnn9G0aVPFc1tbWzx9+rTByOTFa7z4/dpz1P48kTFwJEFWrV+/fti9ezfatm0L\niUSCNm3aoKqqCnl5eejXrx+6deuGsrIylJaWAgA2bdqEQYMGNTiPl5cXysrKFPWArVu3qr12WFgY\nkpKSFM8LCgoAKE8wEokEffr0wU8//YSqqio8ffoUO3bsUCQGBwcH3LlzR/s3gEhPTBJk1Xr27Ilb\nt24hMDBQcczHxwetW7fGq6++imbNmmHDhg1455134OPjAzs7O0yePBlA/b/cmzVrhr/+9a8YPnw4\nevXqBScnJ6U1ibr9+RcsWIAnT57Ax8cHPXv2xMKFCxu8pq5OnTph3rx56Nu3L/r3748uXbrA0dER\nADBmzBh8+eWX6NWrlyJRvXhdImNggz8iM3L//n20bNkST58+RVRUFGJiYjBixAixw6JGjCMJIjMS\nHx8PmUwGqVSKrl27MkGQ6DiSICIilTiSICIilZgkiIhIJSYJIiJSiUmCiIhUYpIgIiKVmCSIiEil\n/w+H/CoI41pxawAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot([log10(f) for f in fractions], 'bo')\n", + "plt.plot([i for i in range(2,20)], [-(i-2) for i in range(2,20)], 'g-')\n", + "plt.plot([i for i in range(2,20)], [-(i-3)*1.5 for i in range(2,20)], 'r-')\n", + "plt.plot([i for i in range(2,20)], [-(i-2)*1.4 for i in range(2,20)], 'r^-')\n", + "plt.ylabel(\"Log probability of word\")\n", + "plt.xlabel(\"Word length\")\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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Rs2ZNM6Uv02TuJlFqxMXBzJmGFfD8/QmtXp2wCRPoHxiIdtiwf9avOHIEFi82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\nk2zZskVuykKIfJk4sS+dK7/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