{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6saJj6PoXkOf"
      },
      "source": [
        "# Cryptography"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Aue46UK2YMW6"
      },
      "source": [
        "**Why cryptography?**\n",
        "- Cryptographic analysis provides distinct advantages over some more en vogue comp neuro methods, like deep learning\n",
        "  - It sits at a crucial point between supervised and unsupervised learning: you don't need training labels, but you also pull on pre-existing knowledge about the structure of information in the world\n",
        "- Cryptographic analysis centers on using the underlying non-uniform distribution of data in the world to decode information\n",
        "  - This is something humans naturally do to learn -- e.g. children use morpheme co-ocurance-rates to learn language\n",
        "  - On a similar note, human adults are able to remember larger numbers of social relationships when they exhibit properties that make them representable in a lower number of bits \n",
        "\n",
        "**What will we cover in this notebook?**\n",
        "- A hands-on example of using cryptographic analysis to break a substitution cipher in English"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Run the cell below to download data and prepare our environment!"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 86
        },
        "id": "dinSRX3QXKn-",
        "outputId": "bf98b7a0-059b-46c1-f0c4-3eba91941619"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "[nltk_data] Downloading package words to /Users/f004p57/nltk_data...\n",
            "[nltk_data]   Package words is already up-to-date!\n",
            "[nltk_data] Downloading package gutenberg to\n",
            "[nltk_data]     /Users/f004p57/nltk_data...\n",
            "[nltk_data]   Package gutenberg is already up-to-date!\n"
          ]
        }
      ],
      "source": [
        "#file imports\n",
        "import nltk\n",
        "from nltk.corpus import words as wordlist\n",
        "import re\n",
        "import pandas\n",
        "from collections import Counter\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import random\n",
        "import os\n",
        "from IPython.display import HTML, display\n",
        "import string\n",
        "\n",
        "#set random seed and download corpora\n",
        "os.environ['PYTHONHASHSEED'] = '0'\n",
        "nltk.download('words')\n",
        "nltk.download('gutenberg')\n",
        "\n",
        "#make sure the display fits the width of the page\n",
        "def set_css():\n",
        "  display(HTML('''\n",
        "  <style>\n",
        "    pre {\n",
        "        white-space: pre-wrap;\n",
        "    }\n",
        "  </style>\n",
        "  '''))\n",
        "get_ipython().events.register('pre_run_cell', set_css)\n",
        "\n",
        "def get_letter_distribution(text, plot=False, title='', zipfian=False):\n",
        "  text = re.sub(r'[^a-z]', '', text.lower())\n",
        "  letter_counts = Counter(sorted(text))\n",
        "  if plot:\n",
        "    if zipfian:\n",
        "      letters, vals = zip(*letter_counts.most_common())\n",
        "      letters = np.array(letters)\n",
        "      vals = np.array(vals).astype('float64')\n",
        "      vals /= sum(vals)\n",
        "      plt.bar(letters, vals)\n",
        "    else:\n",
        "      plt.bar(letter_counts.keys(), np.array(list(letter_counts.values()))/len(text))\n",
        "    plt.ylim([0,0.2])\n",
        "    plt.xlabel('letter')\n",
        "    plt.ylabel('percentage of all letters')\n",
        "    plt.title(title)\n",
        "    plt.show()\n",
        "  return letter_counts\n",
        "\n",
        "alphabet = list(string.ascii_lowercase)\n",
        "random.shuffle(alphabet)\n",
        "cipher = dict(zip(sorted(alphabet), alphabet))\n",
        "for letter in alphabet:\n",
        "  cipher[letter.upper()] = cipher[letter].upper()\n",
        "\n",
        "original_quote = nltk.corpus.gutenberg.raw(nltk.corpus.gutenberg.fileids()[1])\n",
        "encrypted_quote = ''\n",
        "for letter in original_quote:\n",
        "  if letter in cipher.keys():\n",
        "    encrypted_quote+=(cipher[letter])\n",
        "  else:\n",
        "    encrypted_quote+=(letter)\n",
        "\n",
        "def decrypt(encrypted_quote, reverse_cipher):\n",
        "  unencrypted_quote = ''\n",
        "  for letter in encrypted_quote:\n",
        "    if letter in reverse_cipher.keys():\n",
        "      unencrypted_quote+=(reverse_cipher[letter])\n",
        "    else:\n",
        "      unencrypted_quote+=(letter)\n",
        "  return unencrypted_quote\n",
        "\n",
        "def fix_single_letter_words(encrypted_quote, reverse_cipher):\n",
        "  single_letter_words = []\n",
        "  for word in re.sub(r'[^a-zA-Z ]', '', encrypted_quote.lower()).split():\n",
        "    if len(word) == 1:\n",
        "      single_letter_words.append(word)\n",
        "  (first, count1), (second, count2) = Counter(single_letter_words).most_common()[0:2]  \n",
        "  if reverse_cipher[first] != 'a':\n",
        "    for letter in reverse_cipher.keys():\n",
        "      if reverse_cipher[letter] == 'a':\n",
        "        reverse_cipher[letter] = reverse_cipher[first]\n",
        "      if reverse_cipher[letter] == 'A':\n",
        "        reverse_cipher[letter] = reverse_cipher[first].upper()\n",
        "    reverse_cipher[first] = 'a'\n",
        "    reverse_cipher[first.upper()] = 'A'\n",
        "  if reverse_cipher[second] != 'i':\n",
        "    for letter in reverse_cipher.keys():\n",
        "      if reverse_cipher[letter] == 'i':\n",
        "        reverse_cipher[letter] = reverse_cipher[second]\n",
        "      if reverse_cipher[letter] == 'I':\n",
        "        reverse_cipher[letter] = reverse_cipher[second].upper()\n",
        "    reverse_cipher[second] = 'i'\n",
        "    reverse_cipher[second.upper()] = 'I'\n",
        "  return reverse_cipher\n",
        "\n",
        "english = set(wordlist.words())\n",
        "def get_percent_real(recovered):\n",
        "  english = set(wordlist.words())\n",
        "  reals = [word in english for word in re.sub(r'[^a-zA-Z ]', '', recovered.lower()).split()]\n",
        "  percent_real = sum(reals)/len(reals)\n",
        "  return percent_real\n",
        "\n",
        "import copy\n",
        "def swap_keys(reverse_cipher, L1, L2): \n",
        "  updated = copy.deepcopy(reverse_cipher)\n",
        "  L1V, L2V = reverse_cipher[L1], reverse_cipher[L2]\n",
        "  updated[L1], updated[L2] = L2V, L1V\n",
        "  updated[L1.upper()], updated[L2.upper()] = L2V.upper(), L1V.upper()\n",
        "  return updated\n",
        "\n",
        "def swap_keys_inplace(reverse_cipher, L1, L2): \n",
        "  L1V, L2V = reverse_cipher[L1], reverse_cipher[L2]\n",
        "  reverse_cipher[L1], reverse_cipher[L2] = L2V, L1V\n",
        "  reverse_cipher[L1.upper()], reverse_cipher[L2.upper()] = L2V.upper(), L1V.upper()\n",
        "\n",
        "\n",
        "def improve_deciphering(second_pass, reverse_cipher, percent_real_before):\n",
        "  english = set(wordlist.words())\n",
        "  c = get_letter_distribution(second_pass)\n",
        "  dists = np.ones((26,26))\n",
        "  for i in range(26):\n",
        "    for j in range(i+1,26):\n",
        "      dists[i,j] = abs(c[alphabet[i]] - c[alphabet[j]])/sum(c.values())\n",
        "  percent_real = percent_real_before\n",
        "  indeces = np.argsort(dists.flatten())\n",
        "  while percent_real < 0.81:\n",
        "    for idx in indeces:\n",
        "      i,j=np.unravel_index(idx, (26,26))\n",
        "      L1, L2 = alphabet[i], alphabet[j]\n",
        "      updated = swap_keys(reverse_cipher, L1, L2)\n",
        "      unencrypted_quote = ''\n",
        "      for letter in encrypted_quote:\n",
        "        if letter in updated.keys():\n",
        "          unencrypted_quote+=(updated[letter])\n",
        "        else:\n",
        "          unencrypted_quote+=(letter)\n",
        "      reals = [word in english for word in re.sub(r'[^a-zA-Z ]', '', unencrypted_quote.lower()).split()]\n",
        "      percent_real = sum(reals)/len(reals)\n",
        "      print(percent_real)\n",
        "      if percent_real > percent_real_before+(0.82-percent_real_before)/4:\n",
        "        print(percent_real, '\\t', L1, '\\t',L2,'\\n\\n')\n",
        "        print(re.sub(r'[^a-zA-Z ]', '', unencrypted_quote.lower())[35:776])\n",
        "        swap_keys_inplace(reverse_cipher, L1, L2)\n",
        "        percent_real_before = percent_real\n",
        "        break\n",
        "    return reverse_cipher"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZXKEjXeO0Sgg"
      },
      "source": [
        "Let's use some cryptanalysis to solve a letter subtitution cipher. The text below is a passage from a classic novel in which each letter has been replaced with another letter from the English alphabet, with unique pairings. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 329
        },
        "id": "Ta1c1ZqS1qn2",
        "outputId": "3d60dcc9-772a-4fec-c5b5-1d55c361f4a0"
      },
      "outputs": [
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              "  "
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              "<IPython.core.display.HTML object>"
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          "text": [
            "Skxdbjf 1\n",
            "\n",
            "\n",
            "Rcf Yxabjf Jaacpb, pq Tjaangsk Kxaa, cg Rpijfrjbrkcfj, yxr x ixg ykp,\n",
            "qpf kcr pyg xihrjijgb, gjzjf bppt hd xgn oppt ohb bkj Oxfpgjbxmj;\n",
            "bkjfj kj qphge psshdxbcpg qpf xg ceaj kphf, xge spgrpaxbcpg cg x\n",
            "ecrbfjrrje pgj; bkjfj kcr qxshabcjr yjfj fphrje cgbp xeicfxbcpg xge\n",
            "fjrdjsb, on spgbjidaxbcgm bkj acicbje fjigxgb pq bkj jxfacjrb dxbjgbr;\n",
            "bkjfj xgn hgyjaspij rjgrxbcpgr, xfcrcgm qfpi epijrbcs xqqxcfr\n",
            "skxgmje gxbhfxaan cgbp dcbn xge spgbjidb xr kj bhfgje pzjf\n",
            "bkj xaiprb jgeajrr sfjxbcpgr pq bkj axrb sjgbhfn; xge bkjfj,\n",
            "cq jzjfn pbkjf ajxq yjfj dpyjfajrr, kj sphae fjxe kcr pyg kcrbpfn\n",
            "ycbk xg cgbjfjrb ykcsk gjzjf qxcaje.  Bkcr yxr bkj dxmj xb ykcsk\n",
            "bkj qxzphfcbj zpahij xayxnr pdjgje:\n",
            "\n",
            "           \"JAACPB PQ TJAANGSK KXAA.\n",
            "\n",
            "\"\n"
          ]
        }
      ],
      "source": [
        "print(encrypted_quote[35:776])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a_CL2tY92Q6e"
      },
      "source": [
        "If we wanted to decrypt this, we could try a few approaches. We could brute force it, trying every single possible combination of unique letter replacement pairs. This comes out to $26! = 4.03e^{26}$ potential combinations, which would take a prohibitively long time to run.\n",
        "<br><br>\n",
        "A more fruitful aproach might be to use the underlying statistics of the English language to help us seed this process with educated guesses. Let's take a look at how often particular letters show up in English text (as approximated by a collection of classic novels from Project Gutenberg). "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 851
        },
        "id": "BVbthXmHutQJ",
        "outputId": "9d8570fe-be96-43e6-a816-55128bd08088"
      },
      "outputs": [
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8z5KeAbYBXsTMzPpUvSOOtnfY91Agf1J9MbBf2U4k7Us2GfGxXPH3JJ0B3AJMioiVnbSbCEwE2GGHHcq+rJmZdaHeBMCLezOQzkjaFrgUOD4iOo5KTgeeJksmU4FvAFNq20bE1LSflpaWLo+czMysnEKX43bTEmD73PawVFaIpCHA9cC3IuLejvKIeCoyK4FfkA2JmZlZL6kycUwHRkoaIWlDYDzQWqRhqn8tcEntSfB0FIIkAUcBc3o0ajMzq6uyxBERq4CTgGlk8z6uioi5kqZIOhJA0ihJi4FxwHmS5qbmnyabnT6hk8tuL5c0G5gNbA2cWdV7MDOzt6vyqioi4gbghpqyM3LPp5MNYdW2uwy4rIs+D270umZmVp0qr6oyM7N1UFNfVWVmZs2n3lDV76g/VHVkJRGZmVlTqzdU9e+9FoWZma01Gt0B0MzMbA0NFzmUNBL4PrAbMKijPCJ2qjAuMzNrUkXmcfwC+BmwCvgYcAldXCprZmbrviKJY3BE3AIoIp6IiMnA31QblpmZNasidwBcKWk94FFJJ5GtN7VJtWGZmVmzKnLEcQqwEXAysA/wWeD4KoMyM7PmVeQOgNPT0+XA56sNx8zMml2Vq+Oamdk6yInDzMxK6TJxSDo7/Tuu98IxM7NmV++I45PpZkmn91YwZmbW/OqdHP898AKwiaSXAJEteiggImJIL8RnZmZNpssjjog4LSI2B66PiCERsWn+316M0czMmkiRy3HHSHo3MCoV3RcRS6sNy8zMmlXDq6rSyfH7ye4L/mngfklji3QuabSk+ZLaJU3qZP9BkmZKWlXbp6TjJT2aHsfnyveRNDv1+aN0HsbMzHpJkSVHvg2MiohnACRtA9wMXF2vkaQBwLnAYcBiYLqk1oiYl6v2JDABOLWm7ZbAd4EWsvMqM1LbF8gWXPwicB/Z/cxHAzcWeB9mZtYDiszjWK8jaSTPFWy3L9AeEQsi4nXgCmBMvkJELIyIh4DVNW0/DvwhIp5PyeIPwGhJ2wJDIuLeiAiylXqPKhCLmZn1kCJHHL+XNA34Vdo+muwv/UaGAoty24uB/QrG1VnboemxuJPyt5E0EZgIsMMOOxR8WTMza6TIyfHTJP0dcEAqmhoR11Yb1jsXEVOBqQAtLS1d3jvdzMzKKXLEQUT8BvhNyb6XANvntoelsqJtP1rT9o+pfFg3+zQzsx5Q5VpV04GRkkZI2hAYD7QWbDsNOFzSFpK2AA4HpkXEU8BLkvZPV1MdB1xXRfBmZta5yhJHRKwCTiJLAg8DV0XEXElTJB0JIGmUpMVkl/qeJ2luavs88G9kyWc6MCWVAZwI/BfQDjyGr6gyM+tVhYaqJA0GdoiI+WU6j4gbqDmRHhFn5J5PZ82hp3y9C4ELOylvA/YoE4eZmfWcIhMAPwXMIlu7Ckl7Syo65GRmZuuYIkNVk8nmZLwIEBGzgBEVxmRmZk2sSOJ4IyKW1ZT58lYzs36qyDmOuZI+AwyQNBI4GfhTtWGZmVmzKnLE8VVgd2Al2ezxl4CvVRmUmZk1ryIzx1cA30oPMzPr5xomDkm/4+3nNJYBbcB5EfFaFYGZmQ2fdH2hegvP+puKI7G8IkNVC4DlwPnp8RLwMvDetG1mZv1IkZPjH46IUbnt30maHhGjOmZ6m5lZ/1HkiGMTSW+tS56eb5I2X68kKjMza1pFjjj+GbhL0mOAyCb/nShpY+DiKoMzs7fzuL/1tSJXVd2Q5m/smorm506I/2dlkZmZWVMqtMghMBJ4HzAI2EsSEXFJdWGZmVmzKnI57nfJbqq0G9lKt58A7iK737eZmfUzRU6OjwUOAZ6OiM8DewGbVRqVmZk1rSKJ49WIWA2skjQEeIY1bwlrZmb9SJFzHG2SNieb7DeDbDLgPZVGZWZmTavIVVUnpqc/l/R7YEhEPFRtWGZm1qyK3AHwlo7nEbEwIh7KlzVoO1rSfEntkiZ1sn+gpCvT/vskDU/lx0qalXuslrR32vfH1GfHvncVfbNmZvbOdXnEIWkQsBGwtaQtyCb/AQwBhjbqWNIA4FzgMGAxMF1Sa0TMy1U7AXghInaRNB44Gzg6Ii4HLk/97An8Nt15sMOx6d7jZmbWy+oNVX2J7L4b25Gd2+hIHC8BPynQ975Ae0QsAJB0BTAGyCeOMWS3pgW4GviJJEVEfjXeY4ArCryemZn1gi6HqiLihxExAjg1InaKiBHpsVdEFEkcQ4FFue3FvP1I5a06EbGKbLn2rWrqHE12A6m8X6Rhqu9IEp2QNFFSm6S2pUuXFgjXzMyKKHJy/MeSPgwMz9fvjZnjkvYDVkTEnFzxsRGxRNKmwDXA5+hkMmJETAWmArS0tPge6WZmPaTIzPFLgZ2BWcCbqThoPHN8CWvO9xiWyjqrs1jS+mQTC5/L7R9PzdFGRCxJ/74s6ZdkQ2KVJbEiC8p5MTkz60+KzONoAXarOe9QxHRgpKQRZAliPPCZmjqtwPFk80LGArd2vI6k9YBPAwd2VE7JZfOIeFbSBsARwM0l4zIzs3egSOKYA7wHeKpMxxGxStJJwDRgAHBhRMyVNAVoi4hW4ALgUkntwPNkyaXDQcCijpPryUBgWkoaA8iShu9CaGbWi4okjq2BeZLuB1Z2FEbEkY0aRsQNZAsj5svOyD1/DRjXRds/AvvXlL0C7FMgZjMzq0iRxDG56iDMzGztUeSqqtsl7QiMjIibJW1ENkxkZmb9UJElR75INjnvvFQ0FPhtlUGZmVnzKjJU9RWyS17vA4iIR70+lHWHL202WzcUuR/Hyoh4vWMjXRLrCXVmZv1UkSOO2yV9Exgs6TDgROB31YZl/V2RoxPwEYpZXyhyxDEJWArMJlv48Abg21UGZWZmzavIEcdgssl758Nby6UPBlZUGZiZmTWnIonjFuBQslvGQpY0bgI+XFVQZv2Jh+VsbVMkcQyKiI6kQUQsT3M5zMxKcZJcNxQ5x/GKpA92bEjaB3i1upDMzKyZFTniOAX4taQ/k90F8D1kN1cyM7N+qG7iSCfCDwR2Bd6XiudHxBtVB2ZmawdP7Ox/6g5VRcSbwDER8UZEzEkPJw0zs36syFDV3ZJ+AlwJvNJRGBEzK4vKzMyaVpHEsXf6d0quLICDez4cMzNrdkWWVf9YbwRiZmZrhyLLqr9b0gWSbkzbu0k6ofrQzMysGRWZx3ER2X3Dt0vbjwBfK9K5pNGS5ktqlzSpk/0DJV2Z9t8naXgqHy7pVUmz0uPnuTb7SJqd2vxIkorEYmZmPaNI4tg6Iq4CVgNExCrgzUaN0qW85wKfAHYDjpG0W021E4AXImIX4AfA2bl9j0XE3unx5Vz5z4AvAiPTY3SB92BmZj2k6MzxrUj34JC0P7CsQLt9gfaIWJDu53EFMKamzhjg4vT8auCQekcQkrYFhkTEvRERwCXAUQViMTOzHlIkcXwdaAV2lnQ32S/rrxZoNxRYlNtenMo6rZOOZJYBW6V9IyQ9IOl2SQfm6i9u0CcAkiZKapPUtnTp0gLhmplZEUWuqpop6a/JZo6L3pk5/hSwQ0Q8l9bG+q2k3ct0EBFTgakALS0tvmOhmVkPaZg4JA0iu+vfAWTDVXdK+nlEvNag6RJg+9z2sFTWWZ3F6Za0mwHPpWGolQARMUPSY8B7U/1hDfo0M7MKFRmqugTYHfgx8JP0/NIC7aYDIyWNkLQhMJ5syCuvFTg+PR8L3BoRIWmbdHIdSTuRnQRfEBFPAS9J2j+dCzkOuK5ALGZm1kOKzBzfIyLyV0PdJmleo0YRsUrSSWSX8g4gu4vgXElTgLaIaAUuAC6V1A48T5ZcAA4Cpkh6g+xqri9HxPNp34lklwgPBm5MDzMz6yVFEsdMSftHxL0AkvYD2op0HhE3kN2jPF92Ru75a8C4TtpdA1zTRZ9twB5FXt/MzHpekcSxD/AnSU+m7R2A+ZJmAxERf1VZdGZNwkuHm/2fIonDE+zMzOwtRS7HfaI3AjEzs7VDkauqzMzM3uLEYWZmpThxmJlZKU4cZmZWihOHmZmVUuRyXGsSReYSgOcTWP/l+Ta9w0ccZmZWihOHmZmV4sRhZmalOHGYmVkpThxmZlaKr6oyq4Cv7rF1mY84zMysFCcOMzMrxYnDzMxKqTRxSBotab6kdkmTOtk/UNKVaf99koan8sMkzZA0O/17cK7NH1Ofs9LjXVW+BzMzW1NlJ8clDQDOBQ4DFgPTJbVGxLxctROAFyJiF0njgbOBo4FngU9FxJ8l7QFMA4bm2h2b7j1uZma9rMojjn2B9ohYEBGvA1cAY2rqjAEuTs+vBg6RpIh4ICL+nMrnAoMlDawwVjMzK6jKxDEUWJTbXsyaRw1r1ImIVcAyYKuaOn8PzIyIlbmyX6Rhqu9IUs+GbWZm9TT1yXFJu5MNX30pV3xsROwJHJgen+ui7URJbZLali5dWn2wZmb9RJUTAJcA2+e2h6WyzuoslrQ+sBnwHICkYcC1wHER8VhHg4hYkv59WdIvyYbELql98YiYCkwFaGlpiR56T2bWj1U5sXNtum1ClUcc04GRkkZI2hAYD7TW1GkFjk/PxwK3RkRI2hy4HpgUEXd3VJa0vqSt0/MNgCOAORW+BzMzq1FZ4kjnLE4iuyLqYeCqiJgraYqkI1O1C4CtJLUDXwc6Ltk9CdgFOKPmstuBwDRJDwGzyI5Yzq/qPZiZ2dtVulZVRNwA3FBTdkbu+WvAuE7anQmc2UW3+/RkjGZmVo4XObS3eGE+MyvCiaOP+Ze1ma1tnDis25z0zPqnpp7HYWZmzceJw8zMSvFQldk6zkOK1tN8xGFmZqX4iKOH+a87M1vX+YjDzMxKceIwM7NSnDjMzKwUn+Owfsnnosy6z0ccZmZWihOHmZmV4sRhZmalOHGYmVkpThxmZlaKr6oys37LV9d1j484zMyslEoTh6TRkuZLapc0qZP9AyVdmfbfJ2l4bt/pqXy+pI8X7dPMzKpV2VCVpAHAucBhwGJguqTWiJiXq3YC8EJE7CJpPHA2cLSk3YDxwO7AdsDNkt6b2jTq08zeAQ/fWCNVnuPYF2iPiAUAkq4AxgD5X/JjgMnp+dXATyQplV8RESuBxyW1p/4o0KeZWZ8rkoCh+0m4LxO8IqKajqWxwOiI+Ie0/Tlgv4g4KVdnTqqzOG0/BuxHlkzujYjLUvkFwI2pWd0+c31PBCamzfcB83vw7W0NPFtR/Sr7brb6zRRL1fWbKZaq6zdTLGXrN1MsvVG/kR0jYpvawnX2qqqImApMraJvSW0R0VJF/Sr7brb6zRRL1fWbKZaq6zdTLGXrN1MsvVG/u6o8Ob4E2D63PSyVdVpH0vrAZsBzddoW6dPMzCpUZeKYDoyUNELShmQnu1tr6rQCx6fnY4FbIxs7awXGp6uuRgAjgfsL9mlmZhWqbKgqIlZJOgmYBgwALoyIuZKmAG0R0QpcAFyaTn4/T5YISPWuIjvpvQr4SkS8CdBZn1W9hzrKDoGVqV9l381Wv5liqbp+M8VSdf1miqVs/WaKpTfqd0tlJ8fNzGzd5JnjZmZWihOHmZmV4sRREUnD0zyV3nityZJOraDfkyU9LOnyHu63W5+NpD9VUb878UhaXqa+vXOSNpd0Yl/HYU4cVt+JwGERcWxfBwIQER+usr71LGV68nfM5mTfSetjThwlSPqtpBmS5qaZ6Y2sL+ny9Ff71ZI2atD/cZIekvSgpEsb1P2WpEck3UU2M75R7J+VdL+kWZLOS2uJ1av/c2An4EZJ/1Sg/++kxSfvkvSrAkdAAySdnz7LmyQNLvAapf7K785RgaSdJD0gaVTZtjX9DJf0P5IuSv9Pl0s6VNLdkh6VtG+ddg8X/WwkfV3SnPT4WsGYynwn3/qeFfl/Ta8xX9IlwBzWnHdVW3djSden7/scSUfX6xs4C9g5fYfPKRDHnNz2qZIm16l/lqSv5La7PIqXdJqkk9PzH0i6NT0/uLOjc0mj0s/1oPSe50rao04sU/L/l5K+J+mUBu/3y+lzmSXpcUm31av/jkWEHwUfwJbp38FkPxRb1ak7HAjgI2n7QuDUOvV3Bx4Bts6/Vhd19wFmAxsBQ4D2Bn2/H/gdsEHa/ilwXIH3u7Ajngb1RgGzgEHAprCWHMwAAAWySURBVMCjDeIZTnaZ9d5p+yrgswVeZ3nJ/69C9VM8c8gS8APAXu+079x73JPsD7QZ6TvQsRbbb9/pZ5P7HmwMbALMBT7Qg9/JUt+z3GusBvYv8Bn+PXB+bnuzIv9PZf5Pc9unApPr1P8AcHtuex6wfRd19wd+nZ7fSTbHbAPgu8CXumhzJvDvZIu0nl4g9pnp+XrAY9T5XVPTdoMU06eK1O/uw0cc5Zws6UHgXrK/pEY2qL8oIu5Ozy8DDqhT92CyL+OzABHxfJ26BwLXRsSKiHiJxpMgDyH7JTBd0qy0vVODNmV8BLguIl6LiJfJklQjj0fErPR8BtkPS1/aBrgOODYiHuyhPh+PiNkRsZrsl/otkf10z6b++y362RxA9j14JSKWA78h+27UU+Y7WfZ71uGJiLi3QL3ZwGGSzpZ0YEQsK9h/j4uIB4B3SdpO0l5kq3Yv6qL6DGAfSUOAlcA9QAvZ53VnF22mkK3q3QL8/waxLASek/QB4HDggYh4ruBb+SHZROoiP4Pdts6uVdXTJH0UOBT4UESskPRHsr+w66mdJNNXk2YEXBwRp/fR63dmZe75m2RHcX1pGfAk2S/SnlptOf8eV+e2V1P/Z6/Kz6Y3vpOvFAok4hFJHwQ+CZwp6ZaImNJDMaxizaH4Rj+rAL8mW8HiPcCVXVWKiDckPQ5MAP4EPAR8DNgFeLiLZluRHRVukGJp9Bn9V+r/PWRHhg1JmgDsCLxt0dee5iOO4jYj+ytkhaRdyQ5XG9lB0ofS888Ad9WpeyswTtJWAJK2rFP3DuAoSYMlbQp8qkEctwBjJb2ro29JOxaIv6i7gU+lMdxNgCN6sO/e8jrwt8Bxkj7T18EUdCfZ92AjSRuTxd/VX7wdynwny37PSpG0HbAislWwzwE+2KDJy2RDoUX8hewIYitJAyn2nbySbPWKsWRJpJ47yYa/7kjPv0x2ZNBVIj4P+A5wOdl9hxq5FhhNNgw8rVFlSfukeD6bjnAr5SOO4n4PfFnSw2RLtBc5FJ8PfEXShWR/xf6sq4qRLbPyPeB2SW+SjbVP6KLuTElXAg8Cz5Ct4dWliJgn6dvATcqucnkD+ArwRIH30FBETJfUSvaX11/IhiD6bNghp9Rf0xHxiqQjgD9IWh7ZsjhNK30PLiIbYwf4rzTkUk+Z72Sp71k37AmcI2k12XfyH+tVjojn0sUFc4AbI+K0OnXfULa80f1kC6H+T6Ng0s/gpsCSiHiqQfU7gW8B96TvzWt0kbQlHQe8ERG/VHZRyp8kHRwRt9aJ5fV0gvvFSMstNXASsCVwmyTIlnX6hwLtusVLjliPkLRJRCxPV+ncAUyMiJl9GM9WZCcYe/LIaq2m7NbM/x0RXV7R06D9ZLKLAv69B8OyTqQ/8GYC4yLi0b6Op5aHqqynTE0n3mcC1/Rx0tiO7ISlf8HZWkfZrbPbyS6maLqkAT7iMDOzknzEYWZmpThxmJlZKU4cZmZWihOHWQ9Sg/WxVLPCa1pTaW2ZN2IGOHGY9bbaFV6Hk03EK0yS519Zn3LiMKtIWkV1eloZ9V9Tce0Kr2cBB6btf5I0QNI5uXZfSn19VNKdaaJlTy2JYtYt/svFrAKSDidbBHNfsrXCWiUdBEwC9oiIvVO9j5KtOHtE2p4ILIuIUWmpjLsl3ZS6/WBq+3jvvhuzNTlxmFXj8PToWAJkE7JE8mSBdn8laWza3iy1ex2430nDmoETh1k1BHw/Is5bozBb9qNRu69GxBoL26Ujk0KrzppVzec4zKoxDfhCWi0YSUPT6sS1K7zWbk8D/lHSBqnde9PKt2ZNw0ccZhWIiJskvR+4J61WupxsyevH8iu8At8E3kw3CLuI7EY8w4GZyhouBY7qg7dg1iWvVWVmZqV4qMrMzEpx4jAzs1KcOMzMrBQnDjMzK8WJw8zMSnHiMDOzUpw4zMyslP8FmN7ui83q4XIAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "for fileid in nltk.corpus.gutenberg.fileids()[-3:]:\n",
        "  words = re.sub(r'[^a-z]', '', nltk.corpus.gutenberg.raw(fileid).lower())\n",
        "  get_letter_distribution(words, plot=True, title=fileid)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kXcnEeaj0UyB"
      },
      "source": [
        "From the above distributions, you can see that some letters are used consistently more frequently than others across these texts. Let's take a look at the distribution defined be the average of all of these texts:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "id": "YO6n9vk_0Wwk",
        "outputId": "10d1e8ad-4050-4007-ab6d-2d36f031a961"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "  <style>\n",
              "    pre {\n",
              "        white-space: pre-wrap;\n",
              "    }\n",
              "  </style>\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "text/html": [
              "\n",
              "  <style>\n",
              "    pre {\n",
              "        white-space: pre-wrap;\n",
              "    }\n",
              "  </style>\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "words = ''\n",
        "for fileid in nltk.corpus.gutenberg.fileids():\n",
        "  words += re.sub(r'[^a-z]', '', nltk.corpus.gutenberg.raw(fileid).lower())\n",
        "get_letter_distribution(words, plot=True, title='Averaged Distribution');\n",
        "get_letter_distribution(words, plot=True, title='Averaged Distribution; Re-Ordered', zipfian=True);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rfY5CytS1EQU"
      },
      "source": [
        "With this knowledge about expected patterns of letter occurances, let's see how they compare to the statistics of our encrypted text."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "id": "c7Mqrp-46HCV",
        "outputId": "2e96736b-155f-4ec0-938a-81e905f3cec1"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "  <style>\n",
              "    pre {\n",
              "        white-space: pre-wrap;\n",
              "    }\n",
              "  </style>\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "text/html": [
              "\n",
              "  <style>\n",
              "    pre {\n",
              "        white-space: pre-wrap;\n",
              "    }\n",
              "  </style>\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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ibv53NvBH4F3AfGAjSV0Br1KdZma2/Mp0Vd0tabykYyT9c9ejRLmJwNB8FdSawEhgfJMyAEh6k6S18vNNgfcBMyIiSN1kXVdgHQdcW6ZOMzNrjTKBY23SL/39gIPz46BmhfI4xGhgAvBX4Io8RjJW0iEAkoZJ6gQOB86RND0XfzswSdK9pEBxZkTMyPu+BHxB0izSmMd55Q7VzMxaQelH/Kqto6MjJk2atKKbYWa2UpE0OSI6GtPLzBzfQdJNkqbl7X+S9JU6GmlmZu2vTFfVuaTLcV8FyPMuRtbZKDMza19lAse6EXFXQ9qibnOamdkqr0zgeFLSdkAA5DWl5tXaKjMza1u9TgDMPk2aSLejpLnAg6TlR8zMrB8qEzgiIvaXtB6wWkQ8J2mbuhtmZmbtqUxX1VUAEfFCRDyX067sJb+Zma3CejzjkLQjafn0DRtmig8kTQo0M7N+qLeuqreRZohvRJot3uU54FN1NsrMzNpXj4EjIq4FrpW0d0T8qbhP0vtqb5mZmbWlMmMc3+sm7QetboiZma0cehvjeA/wXmAzSV8o7BpIuTsAmpnZKqi3MY41gfVzng0K6c/yxrLmZmbWz/Q2xnELcIukCyPiYUnrRsSLfdg2MzNrQ2XGOLaQNAP4G4Ckd0r6Ub3NMjOzdlV2cPxDpJs5ERH3AnvX2SgzM2tfZQIHETGnIWlxDW0xM7OVQJm1quZIei8QktYAPku6FWy/MGTMb5rmeejMj/ZBS8zM2kOZM44TSSvkDgLmArvm7aYkDZc0U9IsSWO62b+3pCmSFuXl2rvSd5V0u6Tpku6TdGRh34WSHpR0T37sWqYtZmbWGk3POCLiSZZhGXVJA4CzgQOATmCipPERMaOQ7RHgeOCUhuIvAsdGxP2StgAmS5oQEU/n/V+MCC+0aGa2AvQ2AfAH5Js3dSciTm5S9+7ArIiYneu7DDgUeD1wRMRDed9rDXX/vfD8UUmPA5sBT2NmZitUb2cck5az7kFAcVC9E9ijaiWSdidNRnygkPwNSacBNwFjImJhN+VGAaMABg8eXPVlzcysB71NALyoLxvSHUmbA5cAx0VE11nJqcBjpGAyDvgSMLaxbESMy/vp6Ojo8czJzMyqKXU57jKaC2xV2N4yp5UiaSDwG+DLEXFHV3pEzItkIXABqUvMzMz6SJ2BYyIwVNI2ktYERgLjyxTM+a8GLm4cBM9nIUgScBgwraWtNjOzXtUWOCJiETAamECa93FFREyXNFbSIQCShknqBA4HzpE0PRc/gjQ7/fhuLru9VNJUYCqwKXBGXcdgZmZLq/OqKiLieuD6hrTTCs8nkrqwGsv9DPhZD3Xu1+x1zcysPnVeVWVmZqugtr6qyszM2k9vXVXX0XtX1SG1tMjMzNpab11V3+mzVpiZ2Uqj2R0AzczMltB0kUNJQ4FvAjsBa3elR8S2NbbLzMzaVJl5HBcAPwYWAfsCF9PDpbJmZrbqKxM41omImwBFxMMRcTrgOxeZmfVTZe4AuFDSasD9kkaT1ptav95mmZlZuypzxvFZYF3gZGA34GjguDobZWZm7avMHQAn5qfPA/9Sb3PMzKzd1bk6rpmZrYIcOMzMrJIeA4eks/K/h/ddc8zMrN31dsbxkXyzpFP7qjFmZtb+ehsc/y3wFLC+pGcBkRY9FBARMbAP2mdmZm2mxzOOiPhiRGwE/CYiBkbEBsV/+7CNZmbWRspcjnuopLcAw3LSnRHxRL3NMjOzdtX0qqo8OH4X6b7gRwB3SRpRpnJJwyXNlDRL0phu9u8taYqkRY11SjpO0v35cVwhfTdJU3Od38/jMGZm1kfKLDnyFWBYRDwOIGkz4PfAlb0VkjQAOBs4AOgEJkoaHxEzCtkeAY4HTmkouzHwNaCDNK4yOZd9irTg4qeAO0n3Mx8O3FDiOMzMrAXKzONYrStoZPNLltsdmBURsyPiFeAy4NBihoh4KCLuA15rKPsh4HcRsSAHi98BwyVtDgyMiDsiIkgr9R5Woi1mZtYiZc44fitpAvCLvH0k6Zd+M4OAOYXtTmCPku3qruyg/OjsJn0pkkYBowAGDx5c8mXNzKyZMoPjX5T0z8D7c9K4iLi63mYtv4gYB4wD6Ojo6PHe6WZmVk2ZMw4i4lfAryrWPRfYqrC9ZU4rW3afhrJ/zOlbLmOdZmbWAnWuVTURGCppG0lrAiOB8SXLTgAOlPQmSW8CDgQmRMQ84FlJe+arqY4Frq2j8WZm1r3aAkdELAJGk4LAX4ErImK6pLGSDgGQNExSJ+lS33MkTc9lFwD/RQo+E4GxOQ3gJOCnwCzgAXxFlZlZnyrVVSVpHWBwRMysUnlEXE/DQHpEnFZ4PpElu56K+c4Hzu8mfRKwS5V2mJlZ65SZAHgwcA9p7Sok7SqpbJeTmZmtYsp0VZ1OmpPxNEBE3ANsU2ObzMysjZUJHK9GxDMNab681cysnyozxjFd0ieAAZKGAicDf6m3WWZm1q7KnHF8BtgZWEiaPf4s8Lk6G2VmZu2rzMzxF4Ev54eZmfVzTQOHpOtYekzjGWAScE5EvFxHw8zMrD2VGeOYDWzGkoscPgfsAJwLHFNP01ZOQ8b8pmmeh878aB+0xMysHmUCx3sjYlhh+zpJEyNiWNdMbzMz6z/KDI6vL+n1dcnz8/Xz5iu1tMrMzNpWmTOO/wD+LOkBQKTJfydJWg+4qM7GmZlZ+ylzVdX1ef7GjjlpZmFA/Hu1tczMzNpSqUUOgaHA24C1gXdKIiIurq9ZZmbWrspcjvs10k2VdiKtdPth4M+k+32bmVk/U2ZwfATwQeCxiPgX4J3AhrW2yszM2laZrqqXIuI1SYskDQQeZ8lbwtpy8LwPM1vZlAkckyRtRJrsNxl4Hri91laZmVnbKnNV1Un56U8k/RYYGBH31dssMzNrV2XuAHhT1/OIeCgi7iumNSk7XNJMSbMkjelm/1qSLs/775Q0JKcfJemewuM1SbvmfX/MdXbte3PZgzUzs+XX4xmHpLWBdYFNJb2JNPkPYCAwqFnFkgYAZwMHAJ3AREnjI2JGIdsJwFMRsb2kkcBZwJERcSlwaa7nHcA1+c6DXY7K9x43M7M+1ltX1b+R7ruxBWlsoytwPAv8sETduwOzImI2gKTLgEOBYuA4lHRrWoArgR9KUkQUV+P9OHBZidczM7M+0GPgiIj/Bf5X0mci4gfLUPcgYE5huxPYo6c8EbFI0jPAJsCThTxHkgJM0QWSFgNXAWc0BBoAJI0CRgEMHjy4cfdKqcwVWOCrsMysXmUGx38g6b3AkGL+vpg5LmkP4MWImFZIPioi5kragBQ4jqGbyYgRMQ4YB9DR0eF7pJuZtUiZmeOXANsB9wCLc3LQfOb4XJac77FlTusuT6ek1UkTC+cX9o/kjfuApBeOmJv/fU7Sz0ldYp7F3g2foZhZHcrM4+gAduquO6iJicBQSduQAsRI4BMNecYDx5HmhYwAbu56HUmrAUcAe3VlzsFlo4h4UtIawEHA7yu2y8zMlkOZwDENeCswr0rFecxiNDABGACcHxHTJY0FJkXEeOA84BJJs4AFpODSZW9gTtfgerYWMCEHjQGkoHFulXaZmdnyKRM4NgVmSLoLWNiVGBGHNCsYEdeTFkYspp1WeP4ycHgPZf8I7NmQ9gKwW4k2m5lZTcoEjtPrboSZma08ylxVdYukrYGhEfF7SeuSuonMzKwfKrPkyKdIk/POyUmDgGvqbJSZmbWvMl1VnyZd8nonQETc7/WhVk1e4t3MyihzI6eFEfFK10a+JNYT6szM+qkygeMWSf8JrCPpAOCXwHX1NsvMzNpVma6qMaRVbKeSFj68HvhpnY2ylYO7tsz6pzKBYx3S5L1z4fXl0tcBXqyzYWZm1p7KBI6bgP1Jt4yFFDRuBN5bV6Ns1eQzFLNVQ5kxjrUjoitokJ+vW1+TzMysnZUJHC9IenfXhqTdgJfqa5KZmbWzMl1VnwV+KelR0l0A30q6uZKZmfVDvQaOPBC+F7Aj8LacPDMiXq27Yda/+V4iZu2r166qiFgMfDwiXo2IafnhoGFm1o+V6aq6TdIPgcuBF7oSI2JKba0yM7O2VSZw7Jr/HVtIC2C/1jfHzMzaXZll1ffti4aYmdnKocyy6m+RdJ6kG/L2TpJOqL9pZmbWjsrM47iQdN/wLfL234HPlalc0nBJMyXNkjSmm/1rSbo8779T0pCcPkTSS5LuyY+fFMrsJmlqLvN9SSrTFjMza40ygWPTiLgCeA0gIhYBi5sVypfyng18GNgJ+LiknRqynQA8FRHbA98FzirseyAids2PEwvpPwY+BQzNj+EljsHMzFqk7MzxTcj34JC0J/BMiXK7A7MiYna+n8dlwKENeQ4FLsrPrwQ+2NsZhKTNgYERcUdEBHAxcFiJtpiZWYuUCRxfAMYD20m6jfRl/ZkS5QYBcwrbnTmt2zz5TOYZYJO8bxtJd0u6RdJehfydTeoEQNIoSZMkTXriiSdKNNfMzMooc1XVFEkfIM0cF30zc3weMDgi5ue1sa6RtHOVCiJiHDAOoKOjw3csNDNrkaaBQ9LawEnA+0ndVbdK+klEvNyk6Fxgq8L2ljmtuzyd+Za0GwLzczfUQoCImCzpAWCHnH/LJnWamVmNynRVXQzsDPwA+GF+fkmJchOBoZK2kbQmMJLU5VU0HjguPx8B3BwRIWmzPLiOpG1Jg+CzI2Ie8KykPfNYyLHAtSXaYmZmLVJm5vguEVG8GuoPkmY0KxQRiySNJl3KO4B0F8HpksYCkyJiPHAecImkWcACUnAB2BsYK+lV0tVcJ0bEgrzvJNIlwusAN+SHmZn1kTKBY4qkPSPiDgBJewCTylQeEdeT7lFeTDut8Pxl4PBuyl0FXNVDnZOAXcq8vpmZtV6ZwLEb8BdJj+TtwcBMSVOBiIh/qq11ZmbWdsoEDk+wMzOz15W5HPfhvmiImZmtHMqccZi1Pd8x0KzvOHBYv1Qm0DjImHWvzDwOMzOz1zlwmJlZJQ4cZmZWiQOHmZlV4sBhZmaVOHCYmVklDhxmZlaJA4eZmVXiwGFmZpU4cJiZWSUOHGZmVokDh5mZVeLAYWZmldQaOCQNlzRT0ixJY7rZv5aky/P+OyUNyekHSJosaWr+d79CmT/mOu/JjzfXeQxmZrak2pZVlzQAOBs4AOgEJkoaHxEzCtlOAJ6KiO0ljQTOAo4EngQOjohHJe0CTAAGFcodle89btYnvAy72RvqvB/H7sCsiJgNIOky4FCgGDgOBU7Pz68EfihJEXF3Ic90YB1Ja0XEwhrba9YyDjS2Kquzq2oQMKew3cmSZw1L5ImIRcAzwCYNeT4GTGkIGhfkbqqvSlJrm21mZr1p6zsAStqZ1H11YCH5qIiYK2kD4CrgGODibsqOAkYBDB48uA9aa7ZsfNtbW9nUGTjmAlsVtrfMad3l6ZS0OrAhMB9A0pbA1cCxEfFAV4GImJv/fU7Sz0ldYksFjogYB4wD6OjoiBYdk9kK50BjK1qdXVUTgaGStpG0JjASGN+QZzxwXH4+Arg5IkLSRsBvgDERcVtXZkmrS9o0P18DOAiYVuMxmJlZg9rOOCJikaTRpCuiBgDnR8R0SWOBSRExHjgPuETSLGABKbgAjAa2B06TdFpOOxB4AZiQg8YA4PfAuXUdg9mqwAP11mq1jnFExPXA9Q1ppxWevwwc3k25M4Azeqh2t1a20cyW5EBjzbT14LiZtT8Hmv7HS46YmVklDhxmZlaJA4eZmVXiMQ4z6zOeg7JqcOAws7blQNOe3FVlZmaVOHCYmVklDhxmZlaJA4eZmVXiwXEzW2V4Fnvf8BmHmZlV4sBhZmaVOHCYmVklDhxmZlaJB8fNrN/yYPqy8RmHmZlV4sBhZmaVOHCYmVkltQYOScMlzZQ0S9KYbvavJenyvP9OSUMK+07N6TMlfahsnWZmVq/aBsclDQDOBg4AOoGJksZHxIxCthOApyJie0kjgbOAIyXtBIwEdga2AH4vaYdcplmdZma1qDKYviovCV/nVVW7A7MiYjaApMuAQ4Hil/yhwOn5+ZXADyUpp18WEQuBByXNyvVRok4zs5VO1UCzIq8IU0TUU7E0AhgeEZ/M28cAe0TE6EgVF/gAAAh+SURBVEKeaTlPZ95+ANiDFEzuiIif5fTzgBtysV7rLNQ9ChiVN98GzGzh4W0KPFlT/jrrbrf87dSWuvO3U1vqzt9Obamav53a0hf5m9k6IjZrTFxl53FExDhgXB11S5oUER115K+z7nbL305tqTt/O7Wl7vzt1Jaq+dupLX2Rf1nVOTg+F9iqsL1lTus2j6TVgQ2B+b2ULVOnmZnVqM7AMREYKmkbSWuSBrvHN+QZDxyXn48Abo7UdzYeGJmvutoGGArcVbJOMzOrUW1dVRGxSNJoYAIwADg/IqZLGgtMiojxwHnAJXnwewEpEJDzXUEa9F4EfDoiFgN0V2ddx9CLql1gVfLXWXe75W+nttSdv53aUnf+dmpL1fzt1Ja+yL9MahscNzOzVZNnjpuZWSUOHGZmVokDxzKQ9JcSeYbkeSr9Ql8cr6STJf1V0qV1vk6TNizTcZb5zPRnkk6XdMoKbsNGkk5akW0okvT8im5DTxw4lkFEvHdFt2FVoqTMZ/Ek4ICIOKruNrWaPzMrhY1InzFrwoFjGVT4JbC6pEvzr+QrJa3bS53DJN0naW1J60maLmmXXvIPkfS3CvV/NS8O+WdJv2j2607Ssbk990q6pNzhvl52W0l3SxrWpP0zJV0MTGPJ+Tnd5f8JsC1wg6TPN8l7jaTJ+T0c1VvenP9oSXdJukfSOXmdtd4MkHRurv9GSeuUeI1Sn5n8f/+b/L5Pk3RkL3nHSvpcYfsbkj7bpP4vS/p7mc9B/j/6a7NjLXwWL8x1Xyppf0m3Sbpf0u491P96W0irO/RK0hfyezKteNy95D8x/5/eI+lBSX9oUuRMYLuc/9u91PtFSSfn59+VdHN+vl93Z8OSzpT06cJ2S8+uGs+CJZ0i6fRW1d+tiPCj4gN4vkSeIUAA78vb5wOnNClzBvAd0kKOp7aqfmAYcA+wNrABcH9vbSEtLvl3YNO8vXHJ451G+gK4G3hnifyvAXtWeN8f6mpTk3wb53/XyW3apJe8bweuA9bI2z8Cjm3S7kXArnn7CuDoVnxmcr6PAecWtjds0pYp+flqwANNjnU3YCqwLjAQmNXkc1DqWAv53pHbMTl/HrvWnbumBW3pyr8esD4wHXhXyfd0DeBW4OAyn+ES9e0J/DI/v5U0x2wN4GvAv3WT/13ALYXtGcBWLfzMLNFu4BTg9DJll/XhM456zYmI2/LznwHvb5J/LGnl3w7gWy2s/33AtRHxckQ8R/qi7M1+pD+MJwEiYkGJtgBsBlwLHBUR95bI/3BE3FGy7ipOlnQvcAfpTGZoL3k/SPpSmijpnry9bZP6H4yIe/LzyaQ/3FaZChwg6SxJe0XEMz1ljIiHgPmS3gUcCNwdEfN7qXsv4OqIeDEinqXc5Nmyx/pgREyNiNdIX+o3RfoWm9pDmapteX/O/0JEPA/8KtdRxv+SJhc3+9yXNRnYTdJAYCFwO+lvdi9SIFlCRNwNvFnSFpLeSVoRfE6L2rJCrLJrVbWJxkkyzSbNbEL6NbUG6ezghRbXX7dngEdIf+RlVixudnyVSdoH2B94T0S8KOmPpPeyxyLARRFxaoWXWVh4vph0ZtMSEfF3Se8GPgKcIemmiBjbS5GfAscDbyX9ym+1ssdazPdaYfs1VuD3jKTjga2BpRZCXVYR8aqkB0nv+1+A+4B9ge2Bv/ZQ7Jek1THeClzeqrZki1hy2KG3z3tL+IyjXoMlvSc//wTw5yb5zwG+ClxKujdJq+q/DTg4j5+sDxzUpN6bgcMlbQIgaeMSbQF4Bfg/wLGSPlGyTKttSPpF96KkHUndCr25CRgh6c2QjlXS1nU3sieStgBejLQy9LeBdzcpcjUwnNQdOaFJ3j8Bh0laR9IGwMHL297lULUtt+b860paj/Q5W+rXfZGk3UjdNkfnM6FmniN15ZZxa677T/n5iaQzvp5+vF1OWhljBCmItNI/SGc0m0hai+Z/38vNZxzLpuwv+5nApyWdT/oF/uOeMko6Fng1In6eB2f/Imm/iLh5eeuPiImSxpN+Gf2D1H3QWxfIdEnfAG6RtJg0ZnF8L+0oln1B0kHA7yQ9H2lpmb70W+BESX8lvT+9doVFxAxJXwFuVLqy61Xg08DDtbe0e+8Avi3ptdyWf+8tc0S8kgd9n468LE8veadIuhy4F3ictPbbClG1LTn/haTxBICf5i6g3owGNgb+IAnSUkef7OU15ucB/WnADRHxxV7qvhX4MnB7/sy/TC+BLP9NbQDMjYh5TdpdST4DGkt6b+YCf2tl/d3xkiMV5V/hUyJihf0qze0YAvw6Inq88qoh//oR8bzSlVd/AkZFxJQam2h9IAe7KcDhEXF/xbKnkwZgv1NH22zV5a6qCnI3wu2kK59WNuPy4O8U4CoHjZWf0i2WZ5EGoisFDbPl4TMOMzOrxGccZmZWiQOHmZlV4sBhZmaVOHCYtVCzNanUsAJrXmdoRc15MVsmDhxmfatxBdYhpMmbpUny/CtboRw4zGqSV1GdqLTK8NdzcuMKrGcCe+Xtz0saIOnbhXL/luvaR9KteSJnmeVczGrjXy5mNZB0IGlxxd1J62GNl7Q3MAbYJSJ2zfn2Ia0Ke1DeHgU8ExHD8vIRt0m6MVf77lz2wb49GrMlOXCY1ePA/OhaFmN9UiB5pES5f5I0Im9vmMu9AtzloGHtwIHDrB4CvhkR5yyRmJaKaVbuMxGxxIKF+cyk5asJmy0Lj3GY1WMC8K95NWIkDcor8DauwNq4PQH4d0lr5HI75NVgzdqGzzjMahARN0p6O3B7Xpn1edLy3g8UV2AF/hNYnG88dSHppkNDgClKBZ8ADlsBh2DWI69VZWZmlbiryszMKnHgMDOzShw4zMysEgcOMzOrxIHDzMwqceAwM7NKHDjMzKyS/w9DSDv2bSS+RAAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "get_letter_distribution(encrypted_quote, plot=True, title='Encrypted Distribution');\n",
        "get_letter_distribution(encrypted_quote, plot=True, title='Encrypted Distribution; Re-Ordered', zipfian=True);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i6j1ATgyLvaX"
      },
      "source": [
        "As the above distribution shows us, even though each individual letter in the encrypted text no longer has the same occurance probability as it does in typical English text, the general shape of the re-ordered distribution is still the same. We can use this to build a first-pass remapping to attempt deciphering the encrypted text, substituting each encrypted letter with the English letter closest in usage frequency.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 17
        },
        "id": "7MG6KBzi7hit",
        "outputId": "e34e2765-1a1f-4514-9145-0b190de67534"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "  <style>\n",
              "    pre {\n",
              "        white-space: pre-wrap;\n",
              "    }\n",
              "  </style>\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "text/html": [
              "\n",
              "  <style>\n",
              "    pre {\n",
              "        white-space: pre-wrap;\n",
              "    }\n",
              "  </style>\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "quote_dist = list(map(lambda x: x[0], Counter(re.sub(r'[^a-z]', '', encrypted_quote.lower())).most_common()))\n",
        "english_dist = list(map(lambda x: x[0], Counter(re.sub(r'[^a-z]', '', words.lower())).most_common()))\n",
        "reverse_cipher = dict(zip(quote_dist, english_dist))\n",
        "for letter in alphabet:\n",
        "  reverse_cipher[letter.upper()] = reverse_cipher[letter].upper()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 329
        },
        "id": "kso6pkEXZeuE",
        "outputId": "1ad4fc0d-8661-49fa-a657-a86a6a954228"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "  <style>\n",
              "    pre {\n",
              "        white-space: pre-wrap;\n",
              "    }\n",
              "  </style>\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "text/html": [
              "\n",
              "  <style>\n",
              "    pre {\n",
              "        white-space: pre-wrap;\n",
              "    }\n",
              "  </style>\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Fiabter 1\n",
            "\n",
            "\n",
            "Snr Wadter Eddnot, oc Keddyhfi Iadd, nh Somersetsinre, was a mah wio,\n",
            "cor ins owh amusemeht, hever took ub ahy pook put tie Parohetage;\n",
            "tiere ie couhl offubatnoh cor ah nlde iour, ahl fohsodatnoh nh a\n",
            "lnstressel ohe; tiere ins cafudtnes were rousel nhto almnratnoh ahl\n",
            "resbeft, py fohtembdatnhg tie dnmntel remhaht oc tie eardnest batehts;\n",
            "tiere ahy uhwedfome sehsatnohs, arnsnhg crom lomestnf accanrs\n",
            "fiahgel haturaddy nhto bnty ahl fohtembt as ie turhel over\n",
            "tie admost ehldess freatnohs oc tie dast fehtury; ahl tiere,\n",
            "nc every otier deac were bowerdess, ie foudl real ins owh instory\n",
            "wnti ah nhterest winfi hever candel.  Tins was tie bage at winfi\n",
            "tie cavournte vodume adways obehel:\n",
            "\n",
            "           \"EDDNOT OC KEDDYHFI IADD.\n",
            "\n",
            "\"\n"
          ]
        }
      ],
      "source": [
        "first_pass = decrypt(encrypted_quote, reverse_cipher)\n",
        "print(first_pass[35:776])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DqPKao5xaJnj"
      },
      "source": [
        "While our first pass definitely gets us closer to the original text, it's not quite good enough (unless you, like yours truly, happen to be both a Jane Austen fan and one accustomed to reading through heavy mispellings). \n",
        "<br><br>\n",
        "At this point, we'll want to use some basic facts about English to help us out. For example, we want to make sure that any single-letter words are either assigned to A or I. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 329
        },
        "id": "laJUmPcSPL5f",
        "outputId": "982727da-ecb0-45ab-bed7-745fef887157"
      },
      "outputs": [
        {
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              "  <style>\n",
              "    pre {\n",
              "        white-space: pre-wrap;\n",
              "    }\n",
              "  </style>\n",
              "  "
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              "<IPython.core.display.HTML object>"
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          "text": [
            "Fnabter 1\n",
            "\n",
            "\n",
            "Sir Wadter Eddiot, oc Keddyhfn Nadd, ih Somersetsnire, was a mah wno,\n",
            "cor nis owh amusemeht, hever took ub ahy pook put tne Parohetage;\n",
            "tnere ne couhl offubatioh cor ah ilde nour, ahl fohsodatioh ih a\n",
            "listressel ohe; tnere nis cafudties were rousel ihto almiratioh ahl\n",
            "resbeft, py fohtembdatihg tne dimitel remhaht oc tne eardiest batehts;\n",
            "tnere ahy uhwedfome sehsatiohs, arisihg crom lomestif accairs\n",
            "fnahgel haturaddy ihto bity ahl fohtembt as ne turhel over\n",
            "tne admost ehldess freatiohs oc tne dast fehtury; ahl tnere,\n",
            "ic every otner deac were bowerdess, ne foudl real nis owh nistory\n",
            "witn ah ihterest wnifn hever caidel.  Tnis was tne bage at wnifn\n",
            "tne cavourite vodume adways obehel:\n",
            "\n",
            "           \"EDDIOT OC KEDDYHFN NADD.\n",
            "\n",
            "\"\n"
          ]
        }
      ],
      "source": [
        "reverse_cipher = fix_single_letter_words(encrypted_quote, reverse_cipher)\n",
        "second_pass = decrypt(encrypted_quote, reverse_cipher)\n",
        "print(second_pass[35:776])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MC6_2FSeb8W5"
      },
      "source": [
        "Intuitively, this text feels closer to English text than the previous two. But at this point, we might decide that we want a better metric to determine closeness to the original text than our gut feeling of what looks better.\n",
        "<br><br>\n",
        "As we go through the decrypted text (which is significantly larger than the single-paragraph sample displayed above), we can use a cannonical list of English words, then check what percentage of the words in our recovered text are true English words.  "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "93peeSaFwrOj",
        "outputId": "57dd7c76-eaf3-426c-f5a2-c380ea1ca427"
      },
      "outputs": [
        {
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              "        white-space: pre-wrap;\n",
              "    }\n",
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              "  "
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              "<IPython.core.display.HTML object>"
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          "text": [
            "0.29535548269005385 % of recovered words were valid English\n"
          ]
        }
      ],
      "source": [
        "percent_real_before = get_percent_real(second_pass)\n",
        "print(percent_real_before,'% of recovered words were valid English')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5X0JnV5QdbGY"
      },
      "source": [
        "We can definitely do better than 30% -- in fact, the original text contains 81.7% accepted English words. In order to improve our decryption, we'll try swapping out letter mappings for letters that have the most similar probabilities in English (i.e. R and S both constitute approximately 7.2% of letters used in this corpus). If the percentage of accepted English words improves by making a substitution, we keep it. Let's watch this technique at work. *N.B. This make take a few minutes; feel free to make a nice cup of tea while the next cell runs!*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "oxKSeu6d3h1k",
        "outputId": "2ad83429-c92a-4671-8fd1-aea9925a6148"
      },
      "outputs": [
        {
          "ename": "NameError",
          "evalue": "name 'get_letter_distribution' is not defined",
          "output_type": "error",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-1-682153299df3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m#@markdown Run this to improve the deciphering!  { display-mode: \"form\" }\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_letter_distribution\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msecond_pass\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mdists\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mones\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m26\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m26\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m26\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m   \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m26\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'get_letter_distribution' is not defined"
          ]
        }
      ],
      "source": [
        "c = get_letter_distribution(second_pass)\n",
        "dists = np.ones((26,26))\n",
        "for i in range(26):\n",
        "  for j in range(i+1,26):\n",
        "    dists[i,j] = abs(c[alphabet[i]] - c[alphabet[j]])/sum(c.values())\n",
        "percent_real = percent_real_before\n",
        "indeces = np.argsort(dists.flatten())\n",
        "while percent_real < 0.81:\n",
        "  for idx in indeces:\n",
        "    i,j = np.unravel_index(idx, (26,26))\n",
        "    L1, L2 = alphabet[i], alphabet[j]\n",
        "    updated = swap_keys(reverse_cipher, L1, L2)\n",
        "    unencrypted_quote = ''\n",
        "    for letter in encrypted_quote:\n",
        "      if letter in updated.keys():\n",
        "        unencrypted_quote += (updated[letter])\n",
        "      else:\n",
        "        unencrypted_quote += (letter)\n",
        "    reals = [word in english for word in re.sub(r'[^a-zA-Z ]', '', unencrypted_quote.lower()).split()]\n",
        "    percent_real = sum(reals)/len(reals)\n",
        "    if percent_real > percent_real_before+(0.82-percent_real_before)/4:\n",
        "      print('swap', L1.upper(), 'and',L2.upper(),'\\tpercent valid English words:', percent_real,'\\n\\n')\n",
        "      # print(re.sub(r'[^a-zA-Z ]', '', unencrypted_quote.lower())[35:776])\n",
        "      print(unencrypted_quote[35:776])\n",
        "      swap_keys_inplace(reverse_cipher, L1, L2)\n",
        "      percent_real_before = percent_real\n",
        "      break"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EnhDUjmsqueW"
      },
      "source": [
        "And here we find outselves with the fully recovered opening paragraph of Jane Austen's timeless classic *Persuasion*, decrypted in a computationally feasible timeframe, based solely on our pre-existing knowledge of how frequently different letters are used in the English language.\n",
        "<br><br>\n",
        "Now that you (hopefully!) have a stronger intuition for frequency-based decryption techniques, my recommended reading is [A cryptography-based approach for movement decoding](https://www.nature.com/articles/s41551-017-0169-7) from Eva Dyer and her colleagues in Konrad Kording's lab, who used this frequency-based approach to decode motor activity from macaque neural recordings. "
      ]
    }
  ],
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