Cryptography

1
Cryptography

• What? When? How?
• Don Walker
• St Aidans College

2
Aims

• To give a brief introduction to coding.
• To give a brief history of the topic, explaining
  its importance.
• To go through some examples of different types of
  codes.

3
Some Terminology

• Cryptography - "cryptography is about
  communication in the presence of adversaries.
• Key - Information that defines how we encrypt or
  decrypt a cipher.
• Code - Substitution of whole phrases or words.
• Cipher - Substitution of letters.
• Plaintext - The message before it gets encrypted.
• Ciphertext - The encrypted message.

4
Simple Examples

• Codeword - The substitution of a phrase in
  exchange for a word.
• e.g. Apples Attack at dawn
• Cipher - The substitution of one letter for
  another
• e.g. Attack at dawn becomes
• Zggzxp zg wzdm
• using

5
Quick History

• Approx 405BC Greek servants wrote messages on
  their belts so that when wrapped around a staff
  they would spell out a message.
• Also used by the Greeks was the grid on the left,
  where A11, B12. This was used to send
  messages, for example maths would be
• 32 11 44 23 43
• This system was still used in the First World
  War.

6
Quick History

• Julius Caesar invented the Caesar shift to send
  messages to his armies.
• In the 16th Century Mary Queen of Scots sent
  coded messages to her supporters in a plot to
  murder the Queen. These were decrypted by Sir
  Francis Walsingham and led to Mary being executed
  for treason.
• Viginere cipher invented in 16th Century.

7
Quick History

• Morse code was invented in 1838 by Samuel Morse.
  It converts our alphabet into a series of dots
  and dashes. Was used in both World Wars to
  communicate important orders.

8
Quick History

• Enigma is probably the most famous code.
• First developed in 1918 by Arthur Scherbus though
  was continually updated.
• Works on a rotor system where the substitution is
  continually changing.
• Enigma code was broken at Bletchley Park.
• Enigmaco.de is a website which has a virtual
  enigma machine where you can encode your own
  messages.

9
Quick History

• Asymmetric key algorithms invented in the early
  1970s by GCHQ though not published to 1997.
• 1976 asymmetric-key cryptosystem is published,
  first published practical method for sharing a
  public key without needing a prior secret.
• RSA developed in 1977 by Rivest, Shamir and
  Adleman.

10
Caesar Shift

• Named after Julius Caesar.
• Simplest kind of cipher.
• Uses simple substitution by moving the whole
  alphabet along so that each letter corresponds to
  another.

11
Caesar Shift

• Algebraically we can show the encryption and
  decryption of the Caesar shift as being
• Ci (Pi n) mod26
• Pi (Ci - n) mod26
• Where Pi is the letter of the plaintext, Ci is
  the letter of the ciphertext and n is the shift
  used.

12
Frequency analysis

• Frequency analysis is used to break substitution
  ciphers by observing how often each letter
  appears.
• In any piece of writing you would expect some
  letters to appear more often than others.
• As you can see the letter E is the most used
  while Z is one of the least used letters.

13
Frequency Analysis

• It is also possible to prevent frequency analysis
  by simply avoiding the use of certain letters.
• What follows is an excerpt from A Void by
  Georges Perec, which was translated into English
  by Gilbert Adair. Notice that the letter e is
  not used once, and while some words seem a little
  strange it is still readable.

14
The Void

• Noon rings out. A wasp, making an ominous sound,
  a sound akin to a klaxon or a tocsin, flits
  about. Augustus, who has had a bad night, sits up
  blinking and purblind. Oh what was that word (is
  his thought) that ran through my brain all night,
  that idiotic word that, hard as I'd try to pun it
  down, was always just an inch or two out of my
  grasp - fowl or foul or Vow or Voyal? - a word
  which, by association, brought into play an
  incongruous mass and magma of nouns, idioms,
  slogans and sayings, a confusing, amorphous
  outpouring which I sought in vain to control or
  turn off but which wound around my mind a
  whirlwind of a cord, a whiplash of a cord, a cord
  that would split again and again, would knit
  again and again, of words without communication
  or any possibility of combination, words without
  pronunciation, signification or transcription but
  out of which, notwithstanding, was brought forth
  a flux, a continuous, compact and lucid flow an
  intuition, a vacillating frisson of illumination
  as if caught in a flash of lightning or in a mist
  abruptly rising to unshroud an obvious sign - but
  a sign, alas, that would last an instant only to
  vanish for good.

15
Viginere Cipher

• First proposed by Blaise de Viginere from the
  French court in the 16th Century.
• This is an example of a polyalphabetic
  substitution cipher i.e. more than one cipher is
  used, so instead of there being a one to one
  relationship between letters and their
  substitutes there is a one to many relationship.
• Is a combination of 26 Caesar shifts used so as
  to eliminate the use of frequency analysis.
• A variation of the Viginere cipher was used in
  Germany called the Gronsfeld cipher, where
  instead of using a keyword a key number is used,
  therefore this is actually a weaker version of
  the Viginere cipher as there can only be 10
  shifts as opposed to 26 in the Viginere cipher.

16
Viginere Tableau
17
Viginere Cipher

• First take a key word (e.g Teaching)
• Layout your keyword and plaintext as follows
• Then use the Vignere tableau to create the
  ciphertext by choosing the letter at which the
  letters from the keyword and plaintext intersect.

18
Viginere Tableau
19
Viginere Cipher

• So reading off the table we get
• This is a lot more secure than a simple
  substitution cipher as it is immune to frequency
  analysis.
• Our ciphertext includes 2 Xs both replacing
  different letters.

20
Viginere Cipher

• We can also illustrate what is happening
  algebraically by setting
• Ci ith letter of ciphertext,
• Ki ith letter of keyword,
• Pi ith letter of plaintext.
• So written algebraically we have
• Ci (Pi Ki) mod26
• Pi (Ci - Ki) mod26

21
Viginere Cipher

• However this can still be broken by a brute force
  attack where every possible keyword is tried.
• Also the key word needs to only be known by the
  sender and the recipient or anyone can decode the
  message.
• It is this problem with transmitting keys that
  has led to the development of public key
  encryption.

22
Questions?