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Conventional crypto. Diffusion and confusion How Mary Queen of Scots lost her head Various hand operable ciphers Various Enigmas. Confusion and diffusion. Confusion Replacing one element by another of the same size, seemingly randomly chosen

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Conventional crypto

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Conventional crypto l.jpg

Conventional crypto

Diffusion and confusion

How Mary Queen of Scots lost her head

Various hand operable ciphers

Various Enigmas

Conventional crypto - Noack


Confusion and diffusion l.jpg

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 don’t expand the text rely on confusion and diffusion

    • Concealment ciphers bury the content in noise or nondata

Conventional crypto - Noack


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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

Conventional crypto - Noack


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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

Conventional crypto - Noack


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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

Conventional crypto - Noack


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Monoalphabetic cipher example

  • Note the use of the frequency table

  • A bit easier – Excel wasn’t available in those days

  • These often have nonstandard letter frequencies

  • Also they have blanks

Conventional crypto - Noack


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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

Conventional crypto - Noack


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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

Conventional crypto - Noack


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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

Conventional crypto - Noack


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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

Conventional crypto - Noack


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