Math 139 Spring 2006

Daily Schedule

# Date Topic Homework
1 M 1/30 Introduction Read Ch. 1 of Code Book
2 W 2/1 Shift ciphers: their encoding and decoding Barr p. 66 (2.1) 1 (due 2/3)
3 F 2/3 Discuss methods for cryptanalysis of shift cipher. Associate letters with numbers mod 26. Modular arithmetic (Barr 2.1: 59-63) HW 1: Barr p. 66 (2.1): 2 (due 2/6)
4 M 2/6 Modular arithmetic: addition, multiplication, inverses (Barr p. 73-76) HW 2: Barr p. 80: 1, 2 (due 2/8)
5 W 2/8 Decimation ciphers (Barr 2.2) Singh Cipher Stage 2, p. 354 (due 2/13)
6 F 2/10 Affine ciphers (2.2) -
7 M 2/13 Transposition ciphers (2.4) HW 3: p. 80: 3ab, 4ab, 5ab, 7 (due 2/15)
8 W 2/15 Substitution ciphers (2.3) HW 4: Finish "Etnan ...". Optional: Singh Stage 1 (or some of it)
- - - HW 5: p. 105 (2.4): 2, 4, 5. p. 118: 1a, 2a (due 2/20)
9 F 2/17 Vigenere cipher (2.5): encipher, decipher, cryptanalysis when keyword length is known -
10 M 2/20 - Finish handout "AWYVPQ..."
11 W 2/22 Quiz 1 (on material in 2.1) -
- - Kasiski test HW 6: p. 141: 8 (due 2/24)
12 F 2/24 [no class] -
13 M 2/27 Quiz 2 (on material through 2.2) -
14 W 3/1 - Practice problems for test (do not hand in): p. 80: 3c, 5c, 6 / p. 106: 5 / p. 118: 2b
15 F 3/3 Test I (on material through 2.5, also Singh ch. 1) -
16 M 3/6 Two methods to solve Vigenere cipher when keyword length is known (Barr p. 112f, Koblitz) -
- - Permutations (2.6) HW 7: p. 118: 6, p. 130: 1ab (due 3/8)
17 W 3/8 Combinations (2.6), Index of coincidence (2.7) HW 8 (2.6): p. 130: 2ab, 3, 4
18 F 3/10 More on index of coincidence HW 9 (2.7): p. 141: 1ab, 2, 3 (due 3/17)
- - Polybius cipher, homophonic ciphers (handout: Kahn p. 107) -
19 M 3/13 [hand back tests] -
20 W 3/15 Playfair cipher HW 10: p. 36: 16, 17 (due 4/31)
- F 3/17 [no class] -
22 M 3/27 Introduction to the Enigma (handout of pictures, code book) Read Singh p. 127-142
23 W 3/29 A detailed reference for the Enigma and a good Enigma simulator -
24 F 3/31 The Enigma: the number of possible keys Read Singh Ch 4. HW 11: see below (due 4/5)
- - Prime numbers (Barr 4.1) HW 12: p. 260: 1, 2, 4, 5, 6ab (due 4/7)
- - - HW 17: Cryptograms in foreign languages. Use Letter frequencies in foreign languages. (due 4/21)
25 M 4/3 Ingredients of the RSA cipher: primes, factoring, gcd, modular exponentiation, Fermat's little theorem (Barr p. 277) HW 13: p. 94: 7 (due 4/7)
26 W 4/5 - -
27 F 4/7 - -
28 M 4/10 Demo RSA using Maple -
- - Numbers in binary (Barr 3.1) HW 14: p. 185: 1ab, 2ab, 4 (due 4/14)
29 W 4/12 More on binary numbers -
- - Knapsack ciphers (Barr 4.2) -
30 F 4/14 - HW 15: RSA homework
- - - HW 16: Enigma message
31 M 4/17 Review for test -
- - Knapsack ciphers (con't) -
32 W 4/19 Test II (note change in date) -
33 F 4/21 The M209-B (guest speaker Prof. Curtis Smith) -
34 M 4/24 Knapsack ciphers (con't) HW 18: p. 272: 1abc, 2, 3abd, 4, 6 (due 4/28)
- - - HW 19: p. 272: 7 (due 5/1) For this exercise you will need the inverse of 91 mod 8017; this is 881.
35 W 4/26 Digital signatures (Barr 4.6), Hashing (Barr 3.6) -
36 F 4/28 [hand back tests] -
37 M 5/1 Movie "Spies" -
38 W 5/3 ADFGVX cipher (Barr p. 21, Singh p. 374) HW 20: p. 36: 20 (due 5/8)
- - Hashing (Barr 3.6) HW 22: p. 241: 1, 2 (due 5/9)
- - DES (Barr p. 323) ( An online DES) -
39 F 5/5 - HW 21: Digital signatures
- - - Reading: Sharing the Burden: Women in Cyrptology during WWII -
40 M 5/8 Cryptography in the present day: passwords, login, steganography and more Final examination


HW 11

  1. In how many ways can 3 rotors be selected from 5 and put into the machine? (This is similar to what happens in the simulator.)
  2. On 3 rotors how many possible ring settings are there? (Again look at the simulator and try changing the ring setting on a rotor.)
For both of these questions explain your answers!