Affine ciphers

From: Neil Smith Date: Fri, 11 Jul 2014 18:12:45 +0000 (+0100) Subject: Pulled slides over from the presentation-slides branch X-Git-Url: https://git.njae.me.uk/?p=cipher-training.git;a=commitdiff_plain;h=2a4a18664ec83c035f787bbf09e85d7cc1d7fe78 Pulled slides over from the presentation-slides branch --- diff --git a/slides/affine-break.html b/slides/affine-break.html index 58b27f6..ddd8170 100644 --- a/slides/affine-break.html +++ b/slides/affine-break.html @@ -1,7 +1,7 @@ - Affine ciphers + Breaking affine ciphers + + + + + + + + + + diff --git a/slides/pocket-enigma-break.html b/slides/pocket-enigma-break.html new file mode 100644 index 0000000..2592042 --- /dev/null +++ b/slides/pocket-enigma-break.html @@ -0,0 +1,112 @@ + + + + Breaking the pocket enigma + + + + +

+
+# Breaking the Pocket Enigma
+
+![centre-aligned Pocket Engima](pocket-enigma-small.jpg)
+
+Using cribs
+
+---
+
+# Breaking the Pocket Enigma
+
+A _crib_ is a piece of plaintext we believe to be in the enciphered message.
+
+This is the way Enigma messages were broken in WWII.
+
+There are many keys, and doing the naÃ¯ve Bayes analysis was too expensive.
+
+The possible keys were filtered by finding the ones that could have produced the crib. These filtered keys could then be checked manually.
+
+At Bletchley Park, the filtering was done by the Bombes.
+
+---
+
+# Breaking by cribs
+
+```
+Given a message, a wheel spec, a crib, and the location of that crib:
+    Go through each key in turn
+    If the plaintext matches the crib:
+        Add it to the list of possible keys
+Return the possible keys
+```
+
+## Example
+```python
+pocket_enigma_break_by_crib('kzpjlzmoga', 1, 'l', 3)
+['a', 'j', 'n']
+```
+
+Using wheel 1, the `j` (`ciphertext[3]`) could become `l`  if the wheel starts the message on a, j, or n.
+
+

+ + + + + + + diff --git a/slides/pocket-enigma-encipher.html b/slides/pocket-enigma-encipher.html new file mode 100644 index 0000000..b569911 --- /dev/null +++ b/slides/pocket-enigma-encipher.html @@ -0,0 +1,277 @@ + + + + Pocket enigma + + + + +

+
+# Pocket Enigma
+
+![centre-aligned Pocket Engima](pocket-enigma-small.jpg)
+
+Stateful cipher
+
+---
+
+# Pocket Enigma
+
+Emulates the Enigma machine from WWII
+
+Mechanical cipher machine
+
+* Substitution cipher
+* Substitution changes with every letter
+
+Ciphering method: advance the wheel, then follow the lines to encipher the letter
+
+## Stateful enciphering
+
+The cipher depends on the position of the wheel
+
+We need to encapsulate that state
+
+Objects have state
+
+---
+
+# The PocketEnigma object
+
+What do we want it to do?
+
+What data should the object hold?
+
+---
+
+# The PocketEnigma object
+
+What do we want it to do?
+
+* Initialise with the appropriate wheel (and possible starting position)
+* Spin the wheel to a given position
+* Advance the wheel one position
+* Look up a letter given the wheel position
+* Encipher a letter (advance the wheel then look up the letter)
+* Encipher a message (optionally give the key)
+* Make aliases for deciphering (same as enciphering)
+
+
+* Accept user-defined wheels
+    * ...and validate them
+
+What data should it hold?
+
+* A description of the wheel being used
+* The current position of the wheel
+
+---
+
+# Data structures
+
+What's a convenient representation of the wheel
+
+1. for the object to use internally
+2. for a person to use to describe the wheel
+
+They may not be the same, and we'll have to translate between them
+
+---
+
+# Data structures
+
+### Internal use: list of transpositions. 
+
+```python
+[2, 3, 0, 1, 22, 8, 15, 12, 5, ...
+```
+
+so position 0 ('a') swaps with position 2 ('c'), position 3 ('d') swaps with position 1 ('b'), and so on.
+
+* This will be a nightmare to enter correctly
+
+### Exernal use: list of pairs
+
+```python
+[('a', 'c'), ('b', 'd'), ...]
+```
+
+Easier to enter
+
+* Need to validate the human-entered list, to check it's valid
+
+---
+
+# Validating the wheel description
+
+What tests?
+
+---
+
+# Validating the wheel specification
+
+What tests?
+
+* 13 elements...
+* ...each a pair...
+* ...and 26 letters mentioned overall
+
+Raise exceptions if the specification is invalid
+
+---
+
+# Making the PocketEnigma class
+
+```python
+class PocketEnigma(object):
+    def __init__(self, wheel=1, position='a'):
+        self.wheel1 = [('a', 'z'), ('b', 'e'), ('c', 'x'), ('d', 'k'), 
+            ('f', 'h'), ('g', 'j'), ('i', 'm'), ('l', 'r'), ('n', 'o'), 
+            ('p', 'v'), ('q', 't'), ('s', 'u'), ('w', 'y')]
+        self.wheel2 = [('a', 'c'), ('b', 'd'), ('e', 'w'), ('f', 'i'), 
+            ('g', 'p'), ('h', 'm'), ('j', 'k'), ('l', 'n'), ('o', 'q'), 
+            ('r', 'z'), ('s', 'u'), ('t', 'v'), ('x', 'y')]
+        # Rest of initialisation code here
+
+    def make_wheel_map(self, wheel_spec):
+        ...
+        self.wheel_map = ...
+        ...
+
+    def validate_wheel_spec(self, wheel_spec):
+        if len(wheel_spec) != 13:
+            raise ValueError("Wheel specification has {} pairs, requires 13".
+                format(len(wheel_spec)))
+        ...
+```
+
+---
+
+# A note on testing
+
+Testing's easier if everything returns a meaningful value
+
+Saves having to look up different values after performing each operation
+
+`__init__` can't return a value (restriction of Python)
+
+```python
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod(extraglobs={'pe': PocketEnigma(1, 'a')})
+```
+
+`pe` is now available in all tests.
+
+---
+
+# Looking up the enciphered version of a letter
+
+*Not* advancing the wheel before
+
+Keep `self.position` to record where the wheel is
+
+* `__init__` can be passed a letter, but internally it's a number
+
+But the wheel map only works if the wheel arrow is pointing at 'a'
+
+Idea: 
+
+1. Rotate the source letter back `position` spaces
+2. Do the lookup
+3. Rotate the destination letter forward `position` spaces
+
+(all mod 26)
+
+i.e. source â subtract position â lookup destination â add position
+
+---
+
+# Advance the wheel
+
+Trivial...
+
+# Encipher a letter
+
+Advance the wheel, then look up the letter
+
+---
+
+# Encipher a message
+
+```python
+ciphertext = ''
+for letter in plaintext:
+    ciphertext += encipher_letter(letter)
+return ciphertext
+```
+
+Have to be explicit as the order of the operations is important
+
+* Something like `map` might choose an order different from strict left-to-right
+
+## Test it against the physical object
+
+

+ + + + + + + diff --git a/slides/pocket-enigma-small.jpg b/slides/pocket-enigma-small.jpg new file mode 100644 index 0000000..5f30f4f Binary files /dev/null and b/slides/pocket-enigma-small.jpg differ diff --git a/slides/pocket-enigma.jpg b/slides/pocket-enigma.jpg new file mode 100644 index 0000000..e49e47f Binary files /dev/null and b/slides/pocket-enigma.jpg differ diff --git a/slides/transposition-break.html b/slides/transposition-break.html new file mode 100644 index 0000000..9077c12 --- /dev/null +++ b/slides/transposition-break.html @@ -0,0 +1,157 @@ + + + + Breaking transposition ciphers + + + + +

+
+# Breaking transposition ciphers
+
+    attack the fort at dawn
+
+    a t t a c
+    k t h e f
+    o r t a t
+    d a w n
+
+    akod ttra aean cft
+
+Generally quite familiar...
+
+## Try all the keys, pick the one that looks most like Englilsh
+
+---
+
+# ...Pick one that looks most like English
+
+But the naÃ¯ve Bayes score will always be the same!
+
+* Same letters, just a different order.
+
+Score by probability of substrings of letters
+
+* Bigrams, trigrams, _n_-grams
+
+---
+
+# Finding _n_-grams
+
+Given `count_2l.txt` and `count_3l.txt`, counts of bigrams and trigrams in English
+
+# Write a function that returns all the _n_-grams for a text, given _n_
+    * Assume the text is already sanitised
+
+# Build `P2l`, `P3l` (after `Pl`), `Pbigrams`, `Ptrigrams` (after `Pletters`)
+
+---
+
+# Breaking scytale
+
+What are the possible keys? 
+
+---
+
+# Try all the keys...
+
+*All* the keys?
+
+What's the transposition of 'cat'?
+
+* 'bat'?
+* 'car'?
+* 'wry'?
+* 'babe'?
+* 'powwow'?
+
+---
+
+# Equivalence classes and canonical forms
+
+Lots of words yield the same transposition
+
+* They're all in the same equivalence class
+* Only need to test one from the class
+
+General idea: if there are different ways to represent something, pick one to make comparisons easier
+
+* Canonical form, canonical representation
+
+---
+
+# Finding the transpositions to try
+
+```
+For each word:
+    if it's a new transposition:
+        add it to the list
+```
+
+What data structure to use to store the transpositions?
+
+
+

+ + + + + + + + diff --git a/slides/transposition-encipher.html b/slides/transposition-encipher.html index 0c09a4b..af03f75 100644 --- a/slides/transposition-encipher.html +++ b/slides/transposition-encipher.html @@ -1,7 +1,7 @@ - Keyword ciphers + Transposition ciphers