Problems in bold are proofs or arguments. Read 2.9, 3.1
Number Due Problems
Tuesday, 1/19Read sections 1.1-1.3
Thursday, 1/21Read sections 1.4
1Tuesday, 1/26Problems 1.4, 1.6, 1.9, 1.10a, 1.11c, 1.14, 1.17, 1.18
Thursday, 1/28Read sections 1.5, 2.1-2.3; skim 1.6
2Tuesday, 2/2Problems 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, 2/2Read 2.4, 2.7, 2.8
Thursday, 2/4
3Tuesday, 2/9Problems 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, 2/9Read 3.2, 3.3
Thursday, 2/11Read 3.4, 3.5
4Tuesday, 2/16Problems 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
5Tuesday, 2/23Problems 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, 2/23Read 4.1, 4.2, 4.3
6Tuesday, 3/1Problems 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.
7Tuesday, 3/15Problems 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
8Tuesday, 3/22Problems 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, 3/29Detailed outline of paper
9Tuesday, 4/5Problems 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, 4/12First draft of paper