# | WEEK OF | ~ | SECTIONS | TOPICS |
~ | Sep 8 | ~ | 2.1 | An overview of the course. Divisibility. |
1 | Sep 12-16 | ~ | 2.1-2.2 | Divisibility. Primes. |
2 | Sep 19-23 | ~ | 2.3-2.4 | Unique factorization. Elementary factoring methods. |
3 | Sep 26-30 | ~ | 2.5-2.6 | GCD and LCM. Linear Diophantine equations. |
4 | Oct 3-7 | ~ | 3.1-3.3 | Congruences. Inverses mod p. Chinese remainder theorem. |
5 | Oct 10-14 | ~ | 4.1-4.4 | Fermat's theorem. Euler's Phi function. Euler's theorem. Lagrange's theorem. |
6 | Oct 17-21 | midterm 1; assg. 1 due | 5.1 | Classical cryptosystems. |
7 | Oct 24-28 | ~ | 5.2-5.3 | Public-Key cryptography. The RSA scheme. |
8 | Oct 31-Nov 4 | ~ | 6.1, 6.3-6.4 | Pseudoprimes and Carmichel numbers. Pollard's p-1 and rho factorization methods. |
9 | Nov 7-11 | ~ | 7.1-7.4 | Order. Discrete logarithm. Lucas-Lehmer test. |
10 | Nov 14-18 | midterm 2 | 8.1, 10.1 | ElGamal cryptosystem. Identification schemes. |
11 | Nov 21-25 | assg. 2 due | 8.2, 9.1 | Signature schemes. Quadratic residues. |
12 | Nov 28-Dec 2 | ~ | 17.1-17.3 or 12.2 | Quadratic reciprocity law or quadratic sieve. Review. |