Conventional crypto

1
Conventional crypto

• Diffusion and confusion
• How Mary Queen of Scots lost her head
• Various hand operable ciphers
• Various Enigmas

2
Confusion and diffusion

• Confusion
• Replacing one element by another of the same
  size, seemingly randomly chosen
• The substitution must be one-to-one so it can be
  undone
• Diffusion
• Permuting the elements from place to place in a
  seemingly random fashion
• Permutations rather than random scrambles must be
  used so the rearrangement can be undone
• Expansion and hiding
• Ciphers that dont expand the text rely on
  confusion and diffusion
• Concealment ciphers bury the content in noise or
  nondata

3
Confusion methods

• Monoalphabetic substitution
• Trivial example Caesar cipher
• He replaced each letter of the plaintext by one
  three letters before
• Weakness is the fixed scheme once diagnosed,
  the Gauls win
• Fairly trivial example randomly chosen permuted
  alphabet
• 26! Of these alphabets exist a very large
  number
• Frequency table is used to break this one
  plaintext has nonuniform distribution of
  characters and diphthongs
• Polyalphabetic substitution
• A sequence of permutation alphabets is used
• Methods include
• Vigenere table (very simplistic)
• Code strips and such (bulky)
• Rotor machine

4
Comments on permutations

• A permutation is
• A one-to-one mapping of a set onto itself
• With the underlying operation it forms a group
  (more later)
• A permutation of a permutation is still a
  permutation
• An substitution alphabet is a permutation, but
  the resulting cipher is not a permutation
• Permutations have unique inverses
• The simple transposition ciphers are permutations

5
Diffusion methods

• Transposition ciphers
• General idea is to rearrange the characters
  without changing them to produce a
  random-appearing text.
• Example Playfair cipher named for its inventor

6
Monoalphabetic cipher example

• Note the use of the frequency table
• A bit easier Excel wasnt available in those
  days
• These often have nonstandard letter frequencies
• Also they have blanks

7
How Mary Queen of Scots lost her head
Note This is nothing but a monoalphabetic
cipher with some word substitution
From Singh, Simon, The Code Book
8
The 4-rotor Enigma, with wiringpictures from
Budiansky, Stephen, Battle of Wits

• Uses the polyalphabetic principle
• Repositioning the rotors gives a new alphabet
• The rotors are stepped at each character
• It was broken at least partly because of operator
  carelessness

9
The Bombe , used to break Enigma messages

• Comments
• This is actually a copy of the machine conceived
  by Turing
• It still used a plugboard approach rather than a
  strictly electronic stored program
• Material captured from ships and submarines was
  also used
• This was a combination of known plaintext and
  brute force cryptanalysis
• It is not a Turing machine in the computer
  science sense

picture from Budiansky, Stephen, Battle of Wits
10
The Vigenere table and an example

• Weaknesses
• Only one simple shifted translation alphabet
• Relatively short period
• Can be broken by frequency analysis of spaced
  groups
• Could be strengthened somewhat with a longer
  keyword and different alphabets