Math 139 Fall 2007: Explorations in Cryptology

Daily Schedule

# Date Topics Handouts Reading Homework
1 F 9/7 Introduction - Singh Ch 1, Barr p. 1-4 -
2 M 9/10 Shift ciphers, arithmetic mod 26 Letters <-> numbers This is in Barr 2.1 HW 1: Barr p. 66: 1 (due 9/12)
3 W 9/12 Modular arithmetic: addition (table), subtraction, multiplication (table), inverses, decoding shift ciphers Letter frequencies, bar graph In Barr 2.1 -
4 F 9/14 Number line, smallest remainder (find using long division or a calculator), find multiplicative inverses (look in multiplication table) Mystery cipher #1 (due 10am F 9/21) In Barr 2.1 HW 2: Barr p. 80: 1 (due 9/17)
5 M 9/17 Multiplicative ciphers ("decimation" ciphers) - Barr 2.2 HW 3: Barr p. 66: 4, 6; p. 80: 2, 3 (due 9/19)
6 W 9/19 Affine ciphers - Barr 2.2 -
7 F 9/21 Transposition ciphers - Barr 2.4 HW 4: p. 80: 4, 5, 7. p. 105: 1, 2, 5 (due 9/26)
8 M 9/24 Substitution ciphers. This is the most well known cipher system, but it's not really mathematical, so we won't spend much time on it. "ETNAN ..." and "YIFQF..." Barr 2.3 HW 5: Please finish "ETNAN..." (due 9/28). Do some work on "YIFQF..."; it's not necessary to finish it. (due 10/1)
9 W 9/26 Vigenere ciphers: encipher, decipher Vigenere square; "AWY..." (Vigenere CT with three letter keyword) Barr 2.5, Singh p. 48-51, 67-78 -
10 Fri 9/28 Vigenere cipher: cyptanalysis: find keyword given its length second mystery cipher Barr p. 111-115 HW 6: p. 118: 1a, 2a, 3a, 6 (don't forget to explain your answer for this problem). Due 10/3
11 M 10/1 Vigenere cipher: cryptanalysis: find the length of the keyword using the Kasiski test "JSQIJ..." Barr: p. 139-140; Singh p. 69-72, 78 HW 7: p. 141: 8 (due 10/5)
12 W 10/3 Permutations and combinations - Barr 2.6 -
13 F 10/5 Probability - Barr 2.6. Additional reading: Barr p. 5-17, Singh ch. 2 HW 8: p. 130: 1ab, 2ab, 3, 4, 5a, 6a (due 10/12)
14 W 10/10 Friedman's index of coincidence - Barr 2.7 -
15 F 10/12 Quiz 1 (on shift ciphers; like the homework p. 66, including #11) - - HW 9: p. 141: 1ab, 2, 3 (it's better to do this one with someone else, though both of you should hand it in), 4 (due 10/17)
16 M 10/15 Vigenere autokey cipher - Kahn p. 147; Wikipedia "autokey cipher" -
- - Playfair cipher (Note that there are different ways of doing it (cf. eg Barr and Singh) - Barr p. 16; Singh p. 372; Kahn p. 198-202 -
17 W 10/17 Binary arithmetic - Barr 3.1 (p. 178-179) -
18 F 10/19 Quiz 2 (on affine ciphers; like the homework p. 80) - - -
- - Binary arithmetic (addition mod 2); binary Vigenere, LFSR ASCII table (better: see Wikipedia entry for "ASCII") Barr section 3.4, Singh p. 245-247 -
19 Mon 10/22 Counting in binary; Introduction to LFSR - Barr 3.4 -
20 Weds 10/24 Quiz 3 (on transposition and Vigenere ciphers) - - -
- - LFSR (con't): Vigenere using ASCII; maximal length key - full ASCII table HW 10: p. 185 (binary): 1ab, 4, 5. p. 36 (Playfair): 16, 17. p. 219 (LFSR): 1, 2, 3ab. (due 10/30)
21 Fri 10/26 LFSR (con't) - - -
- - Alberti cipher disk - Barr p. 7-9; Kahn p. 125-130 HW 11: p. 34: 7, 8 (due 10/31)
22 Mon 10/29 Introduction to the Enigma You can find an Enigma simulator here. Click on the link on the left side of the page. It needs to be downloaded. Singh Ch. 3; the mechanism is described p. 127-142. Barr p. 23-25 -
23 Weds 10/31 The Enigma (con't): parts (rotors, rings, reflector, plugboard), setup Page from a German codebook - -
24 Fri 11/2 Test 1. Information, practice problems - - -
25 Mon 11/5 The Enigma (con't): number of possible settings; use of the machine (doubled message indicators; cracking the Enigma (Polish effort, Bletchley Park - Singh Ch. 4 -
26 Weds 11/7 Introduction to public key ciphers (discrete log, RSA, knapsack). - Barr p. 26-28 -
- - Knapsack ciphers - Barr 4.2 HW 12: p. 272: 1abc, 2, 3 (due 11/12)
27 Fri 11/9 Knapsack ciphers: theory - - -
28 Mon 11/12 Knapsack ciphers: demonstration The knapsack cipher - HW13: p. 272: 4 (here 91^(-1) mod 8017 is 881), 5 (here 5^(-1) mod 1009 is 202), 7, 9 (here 6^(-1) mod 4091 is 682) (due 11/16)
29 Weds 11/14 Prime numbers: properties Copy of table of primes in Barr p. 370 (use for problems 2 and 4) Barr 4.1 HW 14: Barr p. 260 (4.1): 1,2,4,5,6ab (due 11/19)
30 Fri 11/16 Introduction to the RSA cipher - Barr 4.4 -
- - - Reading: A cryptologist in Iraq Singh Ch 5, 6. -
31 Mon 11/19 Polybius checkerboard - Barr p. 5; Kahn p. 83 -
- - ADFGVX cipher - Barr p. 21; Singh p. 374; Kahn p. 339-350 HW 15: Barr p. 36: 20, 21 (due 11/28)
- - Test1A (optional, but must be taken by 11/28.) Anyone can take this test. It is 50 minutes and closed book; download it when you're ready to take it. You may use a calculator. - -
- - - - - Mystery cipher 3: Cryptograms in foreign languages. Use Letter frequencies in foreign languages. (due 11/28)
32 Mon 11/26 The discrete logarithm problem - Barr p. 297-299 -
- - The key exchange problem; padlocked box - Singh p. 256-260 -
33 Wed 11/28 Diffie-Hellman key exchange - Barr p. 299-301; Singh p. 260-267 -
- - Digital signatures using RSA - Barr 4.6 p. 307; Schneier p. 473 -
- - Test II (take home, due 12/10) Test II: Answers - -
34 Fri 11/30 digital signatures (con't); hashing - Barr 3.6 -
35 Mon 12/3 hashing (con't) - - HW 16 (due 12/10): RSA exercises and Enigma exercises
36 Weds 12/5 PGP (guest speaker Ron Peterson) - Singh Ch. 7 HW 17: Barr p. 241 (3.6): 1, 2; also key exchange, and digital signatures. (due 12/12)
37 Fri 12/7 "Spies" (video on codebreaking. It will be on reserve at the library.) - Reading: Sharing the Burden: Women in Cyrptology during WWII (find this title on the NSA page) -
38 Mon 12/10 The M209B. Guest speaker: Professor Emeritus Curtis Smith. You will get a chance to use these small WWII coding machines. You can find a simulator here. - - -
39 Weds 12/12 Final exam - - -
- - DES An online DES Barr 5.1. (Also the wikipedia entry is pretty good.) -
- - AES (Rijndael) An online Rijndael, a visualization of how it works, and an animation of this process. The wikipedia entry is pretty good. (This is so new that there's nothing in our texts.) All homework is due on Weds 12/12 at 11:59 pm.


Here are some useful websites. Use with care--their accuracy can't be guaranteed.