Math 139 Fall 2009: Explorations in cryptology

Syllabus

Note: The page numbers given below are the basic references; for more look in the index of the book concerned.

Basic topics

These topics will be covered in the order given.

Topic Date References - - - -
- - Barr Singh Pincock Kahn Other
Caesar cipher, shift ciphers 100 BC 2.1, also p. 5 p. 10 p. 12 p. 84 -
Multiplicative ciphers - Sec 2.2 - - - -
Substitution ciphers - Sec 2.3 p. 20 p. 37 - -
[Keyword] Transposition ciphers - 2.4 - - - -
Vigenere cipher: encrypt, decrypt 1586 Sec. 2.5 p. 48 p. 48 p. 145 -
Vigenere cipher: Find keyword given its length - p. 111-115 - - - -
Vigenere cipher: Find length of keyword using Kasiski test - p. 139 69-72, 78 - - -
Permutations and combinations - 2.6 - - - -
Probability - 2.6 - - - -
Friedman's index of coincidence - 2.7 - - - -
The Enigma WW II - Ch. 4, 5 Ch. 4 - -
Public key ciphers: introduction - p. 26 Ch. 6 Ch. 5 p. 982 -
Knapsack ciphers 1976 4.2 - - - -
RSA 1978 4.4 p. 272f. p. 129-140 - -
Diffie-Hellman key exchange 1976 4.3 p. 260-267 - - -
Digital signatures - 4.6 - - - -
Hash functions - 3.6 - - - -
Data encryption standard (DES) 1970's 5.1 - p. 141 - -
Advanced encryption standard: Rijndael 2001 p. 30 - - - (demonstration)
PGP - 5.2 Ch. 7 p. 144 - -

Miscellaneous topics

These smaller topics will be covered at various times.

Topic Date References - - - -
- - Barr Singh Pincock Kahn Other
Atbash c. 500 BC p. 3 - - - -
Polybius 100 AD p. 5 - p. 15 p. 83 -
Nomenclators c. 1400 p. 6 p. 31 p. 27 p. 107 -
Alberti's cipher disk 1466 p. 7 p. 45 p. 41 p. 126 -
Porta 1563 p. 10 - - p. 137 -
Playfair cipher 1854 p. 16 p. 372 p. 78 p. 197 Novel Have his carcase by Dorothy Sayers
ADFGVX WW I p. 21 p. 374 p. 94 pp. 339-350 -
M209B WW II - - - p. 459-432 demonstration
One-time pads 1920's - p. 120 p. 122 p. 403 -
Passwords, bank cards, https, etc. - - - - - -
Stenography - p. 12, 49 p. 5 p. 14 many references--makes interesting reading! -

Topics covered, time permitting

Topic Date References - - - -
- - Barr Singh Pincock Kahn Other
Affine ciphers - Sec 2.2 - - - -
Feedback shift registers - 3.4 - - - -
Quantum cryptography - p. 31 Ch. 8 Ch. 6 - -
Privacy issues - Sec. 5.4 - - - -