Math 139 (Explorations in Cryptology)

Spring 2004

Syllabus

The following is tentative, since there is probably more material than we can cover in a semester. The topics may be covered in a slightly different order or omitted. Additional references will be added. Also more 200-level topics will be added.


x
Topic References Notes 200-level
Introduction - - -
Shift ciphers [B] 2.1, also p. 5 [B] 2.1, also p. 5 Also modular arithmetic -
Affine ciphers [B] 2.2 - Hill cipher (1929) [B] 2.9
Substitution ciphers [B] 2.3 ["Adventure of the dancing men"] -
Transposition ciphers [B] 2.4 - -
Nomenclators (c. 1400) [B] p. 6 - -
Stenography [B] p. 12, 49 - -
Vigenere cipher (1523-1596), a polyalphabetic cipher [B] 2.5; [K] p. 145-9 Kasisinski test; Friedman Index of coincidence (including probablilty [B] 2.6) -
Other polyalphabetic ciphers: Polybius (205-123 BC) [B] p. 5, 94; Alberti cipher disk (1404-72) [B] p. 7; Jefferson cipher wheel; Plairfair [B] p. 16; ADFGVX (WW I)[B] p. 21, [K] p. 339f. - [Dorothy Sayers "Have his carcase"] -
Block ciphers: Porta (1535-1615) [B] p. 10 - -
One-time pad (1917--) [B] p. 20 - Information capacity (Shannon 1949) [B] p. 25
The Enigma (WW II) - - -
M-209-B (WW II) - - -
Women in WW II - - -
Error correcting codes - - -
Public key ciphers: Knapsack (1970's) [B] 4.2 - -
RSA [B] 4.4 Also [B] 4.1, 4.3 -
Key agreement [B] 4.5 - -
Digital signatures [B] 4.6 - -
Data encryption standard (DES) (1970's) [B] 5.1 - -
PGP [b} 5.2 - -
Bank cards, passwords, https, etc. - - -
Feedback shift registers [B] p. 212 - -
Advanced encryption standard (AES) [B] p. 30 - -
Rijndael (2001) - - Mathematics of Rijndael
Quantum cryptography - - -
Privacy issues [B] 5.4 - -


References