stage-4.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cipher Challenge\n",
    "From [Simon Singh's The Code Book](https://simonsingh.net/cryptography/cipher-challenge/the-ciphertexts/)\n",
    "## Stage 4\n",
    "Vigenere Cipher"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "cipher_text = \"\"\"    K Q O W E F V J P U J U U N U K G L M E K J I\n",
    "\n",
    "    N M W U X F Q M K J B G W R L F N F G H U D W\n",
    "\n",
    "    U U M B S V L P S N C M U E K Q C T E S W R E\n",
    "\n",
    "    E K O Y S S I W C T U A X Y O T A P X P L W P\n",
    "\n",
    "    N T C G O J B G F Q H T D W X I Z A Y G F F N\n",
    "\n",
    "    S X C S E Y N C T S S P N T U J N Y T G G W Z\n",
    "\n",
    "    G R W U U N E J U U Q E A P Y M E K Q H U I D\n",
    "\n",
    "    U X F P G U Y T S M T F F S H N U O C Z G M R\n",
    "\n",
    "    U W E Y T R G K M E E D C T V R E C F B D J Q\n",
    "\n",
    "    C U S W V B P N L G O Y L S K M T E F V J J T\n",
    "\n",
    "    W W M F M W P N M E M T M H R S P X F S S K F\n",
    "\n",
    "    F S T N U O C Z G M D O E O Y E E K C P J R G\n",
    "\n",
    "    P M U R S K H F R S E I U E V G O Y C W X I Z\n",
    "\n",
    "    A Y G O S A A N Y D O E O Y J L W U N H A M E\n",
    "\n",
    "    B F E L X Y V L W N O J N S I O F R W U C C E\n",
    "\n",
    "    S W K V I D G M U C G O C R U W G N M A A F F\n",
    "\n",
    "    V N S I U D E K Q H C E U C P F C M P V S U D\n",
    "\n",
    "    G A V E M N Y M A M V L F M A O Y F N T Q C U\n",
    "\n",
    "    A F V F J N X K L N E I W C W O D C C U L W R\n",
    "\n",
    "    I F T W G M U S W O V M A T N Y B U H T C O C\n",
    "\n",
    "    W F Y T N M G Y T Q M K B B N L G F B T W O J\n",
    "\n",
    "    F T W G N T E J K N E E D C L D H W T V B U V\n",
    "\n",
    "    G F B I J G Y Y I D G M V R D G M P L S W G J\n",
    "\n",
    "    L A G O E E K J O F E K N Y N O L R I V R W V\n",
    "\n",
    "    U H E I W U U R W G M U T J C D B N K G M B I\n",
    "\n",
    "    D G M E E Y G U O T D G G Q E U J Y O T V G G\n",
    "\n",
    "    B R U J Y S\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's remove all the spaces and line breaks that appeared when copying and pasting from the web page."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "cipher_text = \"\".join(cipher_text.split())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'KQOWEFVJPUJUUNUKGLMEKJINMWUXFQMKJBGWRLFNFGHUDWUUMBSVLPSNCMUEKQCTESWREEKOYSSIWCTUAXYOTAPXPLWPNTCGOJBGFQHTDWXIZAYGFFNSXCSEYNCTSSPNTUJNYTGGWZGRWUUNEJUUQEAPYMEKQHUIDUXFPGUYTSMTFFSHNUOCZGMRUWEYTRGKMEEDCTVRECFBDJQCUSWVBPNLGOYLSKMTEFVJJTWWMFMWPNMEMTMHRSPXFSSKFFSTNUOCZGMDOEOYEEKCPJRGPMURSKHFRSEIUEVGOYCWXIZAYGOSAANYDOEOYJLWUNHAMEBFELXYVLWNOJNSIOFRWUCCESWKVIDGMUCGOCRUWGNMAAFFVNSIUDEKQHCEUCPFCMPVSUDGAVEMNYMAMVLFMAOYFNTQCUAFVFJNXKLNEIWCWODCCULWRIFTWGMUSWOVMATNYBUHTCOCWFYTNMGYTQMKBBNLGFBTWOJFTWGNTEJKNEEDCLDHWTVBUVGFBIJGYYIDGMVRDGMPLSWGJLAGOEEKJOFEKNYNOLRIVRWVUHEIWUURWGMUTJCDBNKGMBIDGMEEYGUOTDGGQEUJYOTVGGBRUJYS'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cipher_text"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Strategy\n",
    "To break the Vignere cipher, we need to find sequences of more than 4 letters that are repeated. Then we measure how many characters there are between the repetitions, so we can compute the length of the key. Then we can extract all the monoalphabetic ciphers, and work on each one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finding the length of the key\n",
    "### Figuring out repeated sequences\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "604\n"
     ]
    }
   ],
   "source": [
    "sequence_length = 10\n",
    "total_length = len(cipher_text)\n",
    "print(total_length)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KQOWEFVJPU\n"
     ]
    }
   ],
   "source": [
    "word1 = cipher_text[:sequence_length]\n",
    "print(word1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_length(sequence_length, cipher_text=cipher_text):\n",
    "    \"\"\"Check repetition of sequences of a given length in the cipher text\"\"\"\n",
    "    repeated = []\n",
    "    for i in range(1, total_length - 2 * sequence_length):\n",
    "        seq_to_test = cipher_text[i:i+sequence_length]\n",
    "        if (cipher_text.count(seq_to_test) > 1) & (seq_to_test not in repeated):\n",
    "            repeated.append(seq_to_test)\n",
    "    return repeated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "repetition = {}\n",
    "for seq_len in range(10, 3, -1):\n",
    "    repetition[seq_len] = check_length(seq_len)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{10: [],\n",
       " 9: [],\n",
       " 8: [],\n",
       " 7: ['WXIZAYG', 'NUOCZGM'],\n",
       " 6: ['WXIZAY', 'XIZAYG', 'NUOCZG', 'UOCZGM'],\n",
       " 5: ['WXIZA', 'XIZAY', 'IZAYG', 'NUOCZ', 'UOCZG', 'OCZGM', 'DOEOY'],\n",
       " 4: ['EFVJ',\n",
       "  'WXIZ',\n",
       "  'XIZA',\n",
       "  'IZAY',\n",
       "  'ZAYG',\n",
       "  'EKQH',\n",
       "  'NUOC',\n",
       "  'UOCZ',\n",
       "  'OCZG',\n",
       "  'CZGM',\n",
       "  'EEDC',\n",
       "  'DOEO',\n",
       "  'OEOY',\n",
       "  'IDGM',\n",
       "  'FTWG',\n",
       "  'WGMU']}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "repetition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We notice that some shorter words are subparts of longer words, we should remove them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_words = [word for list_of_words in repetition.values() for word in list_of_words]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "sub_words = [word for word1 in all_words for word in all_words if word in word1 and word != word1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "unique_words = set(all_words) - set(sub_words)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'EEDC', 'EFVJ', 'WXIZAYG', 'FTWG', 'IDGM', 'DOEOY', 'WGMU', 'NUOCZGM', 'EKQH'}\n"
     ]
    }
   ],
   "source": [
    "print(unique_words)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have the minimal list of repeated words, we have to find the distance between the repetition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import re"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "indices = [[m.start() for m in re.finditer(word, cipher_text)]for word in unique_words]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[193, 493],\n",
       " [4, 224],\n",
       " [105, 295],\n",
       " [438, 483],\n",
       " [349, 514, 574],\n",
       " [263, 308],\n",
       " [440, 560],\n",
       " [176, 256],\n",
       " [154, 374]]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "differences = []\n",
    "for line in indices:\n",
    "    iter_line = iter(line)\n",
    "    start = next(iter_line)\n",
    "    for i in iter_line:\n",
    "        differences.append(i - start)\n",
    "        start = i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[300, 220, 190, 45, 165, 60, 45, 120, 80, 220]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "differences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import gcd\n",
    "from functools import reduce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reduce(gcd, differences)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So there we have it, the length of the Vignere key is 5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 monoaplhabetic ciphers\n",
    "We the have 5 monoalphabetic encrypted texts that we need to decipher. The ciphers are caesar shift ciphers, so we can reuse the code from the stage 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "ciphers = [cipher_text[i::5] for i in range(5)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['KFJKKWMWFWSNKSKIAAWGFWYSYSJGWJAKDGMHZWGDEJWLSFWWMSSTZEKGSSVWYAEWMLWSWSDGWASKUMDMMATFXIDWWWTHWMMLWWJDWVJDDSAKKLWIWJKDYDUVU',\n",
       " 'QVUGJUKRGUVCQWOWXPPOQXGXNPNWUUPQUUTNGEKCCQVGKVWPTPKNGOCPKEGXGNOUEXNIUWGOGFIQCPGNVOQVKWCRGONTFGKGOGKCTGGGGWGJNRVWGCGGGGJGJ',\n",
       " 'OJULIXJLHULMCRYCYXNJHIFCCNYZUUYHXYFUMYMTFCBOMJMNMXFUMYPMHIOIOYYNBYOOCKMCNFUHPVAYLYCFLCCIMVYCYYBFJNNLVFYMMGOOYIUUMDMMUGYGY',\n",
       " 'WPNMNFBFUMPUTESTOPTBTZFSTTTGNQMUFTFORTEVBUPYTJFMHFFODEJUFUYZSDJHFVJFCVURMVDCFSVMFFUJNWUFUMBOTTBBFTEDBBYVPJEFNVHUUBBEOQOBS',\n",
       " 'EUUEMQGNDBSEEESUTLCGDANESUGREEEIPSSCURERDSNLETMERSSCOERRRECAAOLAELNREICUANEECUEAMNANEOLTSAUCNQNTTEEHUIIRLLEEORERTNIETETR']"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ciphers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def shift_text(text, n):\n",
    "    \"\"\"Shift the text by n letters\"\"\"\n",
    "    letters = \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\"\n",
    "    deciphered_text = \"\"\n",
    "    for letter in text:\n",
    "        if letter not in letters:\n",
    "            # spaces, punctuation\n",
    "            new_letter = letter\n",
    "        else:\n",
    "            indice = letters.index(letter)\n",
    "            new_ind = (indice + n) % 26\n",
    "            new_letter = letters[new_ind]\n",
    "        deciphered_text += new_letter\n",
    "    return deciphered_text"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let also reuse the frequency analysis from stage 1, that did not work well, but could prove more useful here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import altair as alt\n",
    "import pandas as pd\n",
    "from collections import Counter\n",
    "from io import StringIO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_freq_df(text, name=\"freq\"):\n",
    "    \"\"\"Returns a dataframe with relative frequency of letters in the text\"\"\"\n",
    "    # Compute freqs from text\n",
    "    cipher_freq = sorted(Counter(text).items())\n",
    "    \n",
    "    # Get a dataframe with the whole alphabet\n",
    "    all_letters = pd.DataFrame({'letter': list(\"ABCDEFGHIJKLMNOPQRSTUVWXYZ\")})\n",
    "    freqs = pd.DataFrame.from_records(cipher_freq, columns=[\"letter\", name])\n",
    "    complete_freqs = all_letters.merge(freqs, how='left').fillna(0)\n",
    "    \n",
    "    # Normalize the frequencies\n",
    "    complete_freqs[name] = complete_freqs[name] / complete_freqs[name].sum()\n",
    "    return complete_freqs.set_index(\"letter\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>freq_0</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>letter</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>0.057851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>0.082645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>0.024793</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          freq_0\n",
       "letter          \n",
       "A       0.057851\n",
       "B       0.000000\n",
       "C       0.000000\n",
       "D       0.082645\n",
       "E       0.024793"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "create_freq_df(ciphers[0], \"freq_0\").head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "english_freq = pd.read_fwf(StringIO(\"\"\"LET COUNT\n",
    "E   445.2\n",
    "T   330.5\n",
    "A   286.5\n",
    "O   272.3\n",
    "I   269.7\n",
    "N   257.8\n",
    "S   232.1\n",
    "R   223.8\n",
    "H   180.1\n",
    "L   145.0\n",
    "D   136.0\n",
    "C   119.2\n",
    "U   97.3\n",
    "M   89.5\n",
    "F   85.6\n",
    "P   76.1\n",
    "G   66.6\n",
    "W   59.7\n",
    "Y   59.3\n",
    "B   52.9\n",
    "V   37.5\n",
    "K   19.3\n",
    "X   8.4\n",
    "J   5.7\n",
    "Q   4.3\n",
    "Z   3.2\"\"\"), names=[\"letter\", \"eng_freq\"], header=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "english_freq = english_freq.sort_values(\"letter\").set_index(\"letter\")\n",
    "english_freq[\"eng_freq\"] = english_freq.eng_freq / english_freq.eng_freq.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>eng_freq</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>letter</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>0.080396</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.014845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>0.033449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>0.038164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>0.124930</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        eng_freq\n",
       "letter          \n",
       "A       0.080396\n",
       "B       0.014845\n",
       "C       0.033449\n",
       "D       0.038164\n",
       "E       0.124930"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "english_freq.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_freqs = pd.concat((*map(create_freq_df, \n",
    "                            ciphers, \n",
    "                            [\"freq_0\", \"freq_1\", \"freq_2\", \"freq_3\", \"freq_4\"]), \n",
    "                       english_freq), \n",
    "                      axis=1)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_freqs = all_freqs.stack().reset_index().rename(columns={\"level_1\":\"text\", 0:\"freq\"})"
   ]
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  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>letter</th>\n",
       "      <th>text</th>\n",
       "      <th>freq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>A</td>\n",
       "      <td>freq_0</td>\n",
       "      <td>0.057851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A</td>\n",
       "      <td>freq_1</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A</td>\n",
       "      <td>freq_2</td>\n",
       "      <td>0.008264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>A</td>\n",
       "      <td>freq_3</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>A</td>\n",
       "      <td>freq_4</td>\n",
       "      <td>0.066667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  letter    text      freq\n",
       "0      A  freq_0  0.057851\n",
       "1      A  freq_1  0.000000\n",
       "2      A  freq_2  0.008264\n",
       "3      A  freq_3  0.000000\n",
       "4      A  freq_4  0.066667"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
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   "source": [
    "all_freqs.head()"
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  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
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",
      "text/plain": [
       "<VegaLite 2 object>\n",
       "\n",
       "If you see this message, it means the renderer has not been properly enabled\n",
       "for the frontend that you are using. For more information, see\n",
       "https://altair-viz.github.io/user_guide/troubleshooting.html\n"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alt.Chart(all_freqs).mark_bar().encode(\n",
    "    x=alt.X(\"letter:O\", axis=alt.Axis(labelAngle=0)),\n",
    "    y=alt.Y(\"freq:Q\", axis=alt.Axis(title=None)),\n",
    "    row=alt.Row(\"text:N\", header=alt.Header(title=None)),\n",
    "    tooltip=\"letter:O\"\n",
    ").properties(\n",
    "    height=80,\n",
    "    width=500\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the patterns, it seems like the first text is shifted with the letter **\"S\"** corresponding to **\"A\"**. We can see that by the 2 spikes separated by 3 lower values, and some other moderately high values a bit later.\n",
    "Following the same approach, I find the letters __C, U, B and A__ , which gives **SCUBA** for the key.\n",
    "\n",
    "## Deciphering the whole text\n",
    "\n",
    "Now, we can decipher the message given the key."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import zip_longest, chain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vignere(text, key):\n",
    "    key_length = len(key)\n",
    "    # Split the text\n",
    "    ciphers = [text[i::key_length] for i in range(key_length)]\n",
    "\n",
    "    # Get the numerical values of the keys\n",
    "    # The -1 is because we want to go back to the english letter from the key\n",
    "    key_values = [\"ABCDEFGHIJKLMNOPQRSTUVWXYZ\".index(letter)*(-1) for letter in key]\n",
    "    \n",
    "    # Apply the shift for each text\n",
    "    deciphered = map(shift_text, ciphers, key_values)\n",
    "\n",
    "    # Zip to reconstruct the text in the correct order\n",
    "    deciphered = zip_longest(*deciphered, fillvalue=\"\")\n",
    "\n",
    "    # Flatten the iterable and return a string\n",
    "    return \"\".join(chain.from_iterable(deciphered))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'SOUVENTPOURSAMUSERLESHOMMESDEQUIPAGEPRENNENTDESALBATROSVASTESOISEAUXDESMERSQUISUIVENTINDOLENTSCOMPAGNONSDEVOYAGELENAVIREGLISSANTSURLESGOUFFRESAMERSAPEINELESONTILSDEPOSESSURLESPLANCHESQUECESROISDELAZURMALADROITSETHONTEUXLAISSENTPITEUSEMENTLEURSGRANDESAILESBLANCHESCOMMEDESAVIRONSTRAINERACOTEDEUXCEVOYAGEURAILECOMMEILESTGAUCHEETVEULELUINAGUERESIBEAUQUILESTCOMIQUEETLAIDLUNAGACESONBECAVECUNBRULEGUEULELAUTREMIMEENBOITANTLINFIRMEQUIVOLAITLEPOETEESTSEMBLABLEAUPRINCEDESNUEESQUIHANTELATEMPETEETSERITDELARCHERBAUDELAIREEXILESURLESOLAUMILIEUDESHUEESLEMOTPOURETAGEQUATREESTTRAJANSESAILESDEGEANTLEMPECHENTDEMARCHER'"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vignere(cipher_text, \"SCUBA\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Victory! The text is in french, we were lucky that the letter distribution is roughly the same as english.\n",
    "\n",
    "The text is [L'Albatros](https://fr.wikipedia.org/wiki/L%27Albatros_(po%C3%A8me)) a poem by Charles Baudelaire."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
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