Conventional crypto

1. Conventional crypto Diffusion and confusion How Mary Queen of Scots lost her head Various hand operable ciphers Various Enigmas Conventional crypto - Noack

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 don’t expand the text rely on confusion and diffusion • Concealment ciphers bury the content in noise or nondata Conventional crypto - Noack

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 Conventional crypto - Noack

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 Conventional crypto - Noack

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 Conventional crypto - Noack

6. 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

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 Conventional crypto - Noack

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 Conventional crypto - Noack

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 Conventional crypto - Noack

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 Conventional crypto - Noack