| Number |
Due |
Problems |
| Tuesday, 1/19 | Read sections 1.1-1.3 |
| Thursday, 1/21 | Read sections 1.4 |
| 1 | Tuesday, 1/26 | Problems 1.4, 1.6, 1.9, 1.10a, 1.11c, 1.14, 1.17, 1.18 |
| Thursday, 1/28 | Read sections 1.5, 2.1-2.3; skim 1.6 |
| 2 | Tuesday, 2/2 | Problems 1.30 (calculating values of ordp), 1.33 ("Let p be a prime and let q be a prime that divides p-1..."), 1.34ab ("Recall that g is called a primitive root modulo p if the powers of g..."), 1.38 (compute the value for primes between 3 and 20 and make a conjecture), 2.4 ("Compute the following discrete logarithms") |
| Tuesday, 2/2 | Read 2.4, 2.7, 2.8 |
| Thursday, 2/4 |
Read 2.9, 3.1
| 3 | Tuesday, 2/9 | Problems 2.6 ("Alice and Bob agree..."), 2.9 ("Suppose that Eve is able to solve the Diffie-Hellman"), 2.11 (The group S3), 2.18 (simultaneous systems of congruences), 2.24 ("This exercise investigates the square root of a modulo powers of p") |
| Tuesday, 2/9 | Read 3.2, 3.3 |
| Thursday, 2/11 | Read 3.4, 3.5 |
| 4 | Tuesday, 2/16 | Problems 3.1 ("Solve the following congruences"), 3.4 (Euler's phi function and the proof of Euler's formula), 3.5, 3.7, 3.9
|
| 5 | Tuesday, 2/23 | Problems 3.8 (Bob chooses too small a modulus), 3.14ab (showing that 561 and others are Carmichael numbers), 3.15 (use the Miller-Rabin test), 3.22 (use Pollar's p-1 method)
|
| Tuesday, 2/23 | Read 4.1, 4.2, 4.3 |
| 6 | Tuesday, 3/1 | Problems 4.1 (Samantha uses the RSA scheme with p=541), 4.3 (forge Samantha's signature), 4.5 (Elgamal with p=6961). Choose a paper topic and identify two sources you would like to use to base your paper on. |
| 7 | Tuesday, 3/15 | Problems 5.20a-c (use the definition of probability to prove basic facts), 5.21 (probabilities from coin tossing), 5.25 (coins from urns), 5.37 (top eight cards from a deck turned over), start reading sources and write a list of topics you expect to cover |
| 8 | Tuesday, 3/22 | Problems 5.40 (use Pollard's method from table), 5.55 (use induction to prove Jensen's inequality), 5.56 (entropies of two random variables) |
| Tuesday, 3/29 | Detailed outline of paper |
| 9 | Tuesday, 4/5 | Problems 6.1 (compute sums of points on an elliptic curve), 6.5 (list points on elliptic curves), 6.6a (addition table for an elliptic curve), 6.8 (solve a discrete logarithm problem in an elliptic curve over a finite field) |
| Tuesday, 4/12 | First draft of paper |
