Math 139 Fall 2007: Explorations in Cryptology

Schedule for 200-level section

# Date Topics Handouts Reading Homework
1 Th 9/20 Using Excel to do affine ciphers (handout on this) - Do Barr p. 80: 7 using the spreadsheet. Hand in with the rest of your homework
2 Th 9/27 The Hill cipher - Barr 2.9 HW A: p.171: 1ab, 2ab, 3ab, 4 (for 3ab) (due 10/4)
3 Th 10/4 [no class] - - HW B: Barr p. 173: 5, 6, 8, 9.
4 Th 10/11 Known plaintext attack on Hill cipher - Barr p. 170 Finish correcting Barr p. 179; also finish HW B.
5 Th 10/18 Polynomials with coefficients mod 2: adding, multiplying, dividing - - -
6 Th 10/25 Characteristic polynomial of a LFSR diagram. Did 3-bit LFSR with taps at positions 1, 2 and 3. - - HW C: 1. Is the characteristic polynomial of 3-bit LFSR with taps at positions 1 and 3 irreducible? Try to factor it.
- - - - - (con't) 2. Completely analyse the 3-bit LFSR with taps at positions 2 and 3: (a) Is the output sequence of maximal length? (b) Find its characteristic polynomial. (c) Is it irreducible? Try to factor it. (due 11.1)
7 Th 11/1 Introduction to Maple. To do modular arithmetic mod 5, just type "mod 5" at the end of the command Handout with this title, also exercises (don't hand in) - -
8 Th 11/8 Maple (con't): Linear algebra Handout with this title - HW D: Do the following problems in Barr using Maple: p. 80: 2, 3, 4; p. 171: 1ab, 2ab, 3ab, 4. Print this out and hand it in. You've already done these problems by hand, so check that the Maple answers agree with these. (due 11/12)
9 Th 11/15 Knapsack ciphers using Maple Handout with this title (to come) - HW E: (1) Using Maple, make your private sequence, modulus and multiplier. Print out, and also save on your webspace. (2) Make your public sequence, and send to me and I will put it on our website. (3) Send a message to someone else in the class, and also receive one. (Just one or two letters are enough.)
- - - - - Table of public knapsack sequences
10 Th 11/29 - - - -
11 Th 12/6 - - - -
- - - - - Table of public RSA keys