slides/pocket-enigma-encipher.html

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  47
  48 # Pocket Enigma
  49
  50 ![centre-aligned Pocket Engima](pocket-enigma-small.jpg)
  51
  52 Stateful cipher
  53
  54 ---
  55
  56 # Pocket Enigma
  57
  58 Emulates the Enigma machine from WWII
  59
  60 Mechanical cipher machine
  61
  62 * Substitution cipher
  63 * Substitution changes with every letter
  64
  65 Ciphering method: advance the wheel, then follow the lines to encipher the letter
  66
  67 ## Stateful enciphering
  68
  69 The cipher depends on the position of the wheel
  70
  71 We need to encapsulate that state
  72
  73 Objects have state
  74
  75 ---
  76
  77 # The PocketEnigma object
  78
  79 What do we want it to do?
  80
  81 What data should the object hold?
  82
  83 ---
  84
  85 # The PocketEnigma object
  86
  87 What do we want it to do?
  88
  89 * Initialise with the appropriate wheel (and possible starting position)
  90 * Spin the wheel to a given position
  91 * Advance the wheel one position
  92 * Look up a letter given the wheel position
  93 * Encipher a letter (advance the wheel then look up the letter)
  94 * Encipher a message (optionally give the key)
  95 * Make aliases for deciphering (same as enciphering)
  96
  97
  98 * Accept user-defined wheels
  99     * ...and validate them
 100
 101 What data should it hold?
 102
 103 * A description of the wheel being used
 104 * The current position of the wheel
 105
 106 ---
 107
 108 # Data structures
 109
 110 What's a convenient representation of the wheel
 111
 112 1. for the object to use internally
 113 2. for a person to use to describe the wheel
 114
 115 They may not be the same, and we'll have to translate between them
 116
 117 ---
 118
 119 # Data structures
 120
 121 ### Internal use: list of transpositions.
 122
 123 ```python
 124 [2, 3, 0, 1, 22, 8, 15, 12, 5, ...
 125 ```
 126
 127 so position 0 ('a') swaps with position 2 ('c'), position 3 ('d') swaps with position 1 ('b'), and so on.
 128
 129 * This will be a nightmare to enter correctly
 130
 131 ### Exernal use: list of pairs
 132
 133 ```python
 134 [('a', 'c'), ('b', 'd'), ...]
 135 ```
 136
 137 Easier to enter
 138
 139 * Need to validate the human-entered list, to check it's valid
 140
 141 ---
 142
 143 # Validating the wheel description
 144
 145 What tests?
 146
 147 ---
 148
 149 # Validating the wheel specification
 150
 151 What tests?
 152
 153 * 13 elements...
 154 * ...each a pair...
 155 * ...and 26 letters mentioned overall
 156
 157 Raise exceptions if the specification is invalid
 158
 159 ---
 160
 161 # Making the PocketEnigma class
 162
 163 ```python
 164 class PocketEnigma(object):
 165     def __init__(self, wheel=1, position='a'):
 166         self.wheel1 = [('a', 'z'), ('b', 'e'), ('c', 'x'), ('d', 'k'),
 167             ('f', 'h'), ('g', 'j'), ('i', 'm'), ('l', 'r'), ('n', 'o'),
 168             ('p', 'v'), ('q', 't'), ('s', 'u'), ('w', 'y')]
 169         self.wheel2 = [('a', 'c'), ('b', 'd'), ('e', 'w'), ('f', 'i'),
 170             ('g', 'p'), ('h', 'm'), ('j', 'k'), ('l', 'n'), ('o', 'q'),
 171             ('r', 'z'), ('s', 'u'), ('t', 'v'), ('x', 'y')]
 172         # Rest of initialisation code here
 173
 174     def make_wheel_map(self, wheel_spec):
 175         ...
 176         self.wheel_map = ...
 177         ...
 178
 179     def validate_wheel_spec(self, wheel_spec):
 180         if len(wheel_spec) != 13:
 181             raise ValueError("Wheel specification has {} pairs, requires 13".
 182                 format(len(wheel_spec)))
 183         ...
 184 ```
 185
 186 ---
 187
 188 # A note on testing
 189
 190 Testing's easier if everything returns a meaningful value
 191
 192 Saves having to look up different values after performing each operation
 193
 194 `__init__` can't return a value (restriction of Python)
 195
 196 ```python
 197 if __name__ == "__main__":
 198     import doctest
 199     doctest.testmod(extraglobs={'pe': PocketEnigma(1, 'a')})
 200 ```
 201
 202 `pe` is now available in all tests.
 203
 204 ---
 205
 206 # Looking up the enciphered version of a letter
 207
 208 *Not* advancing the wheel before
 209
 210 Keep `self.position` to record where the wheel is
 211
 212 * `__init__` can be passed a letter, but internally it's a number
 213
 214 But the wheel map only works if the wheel arrow is pointing at 'a'
 215
 216 Idea:
 217
 218 1. Rotate the source letter back `position` spaces
 219 2. Do the lookup
 220 3. Rotate the destination letter forward `position` spaces
 221
 222 (all mod 26)
 223
 224 i.e. source → subtract position → lookup destination → add position
 225
 226 ---
 227
 228 # Advance the wheel
 229
 230 Trivial...
 231
 232 # Encipher a letter
 233
 234 Advance the wheel, then look up the letter
 235
 236 ---
 237
 238 # Encipher a message
 239
 240 ```python
 241 ciphertext = ''
 242 for letter in plaintext:
 243     ciphertext += encipher_letter(letter)
 244 return ciphertext
 245 ```
 246
 247 Have to be explicit as the order of the operations is important
 248
 249 * Something like `map` might choose an order different from strict left-to-right
 250
 251 ## Test it against the physical object
 252
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