| Day | Topics | Preparation |
|---|---|---|
| Tues. 1/21 | Introduction and history of cryptography | . |
| Thurs. 1/23 | The Enigma cipher and the Polish attack. | . |
| Tues. 1/28 | The British attack on Enigma. Affine ciphers and attacks |
Koblitz III.1,2 |
| Thurs. 1/30 | Affine matrix systems and the chosen plaintext attack. | Koblitz III.2 Koblitz, I.2,3. |
| Tues. 2/4 | Public key crypto, RSA. | Koblitz I.3, IV.2 |
| Thurs. 2/6 | Attacks on RSA. | Koblitz IV.2 |
| Tues. 2/11 | Class canceled I will lecture at UCSD http://cmrr.ucsd.edu | . |
| Thurs. 2/13 | Practical aspects of RSA, digital signatures. Hash functions. |
Koblitz IV.2 |
| Tues. 2/18 | The multiplicative structure of Z/n.
A probabilistic factorization algorithm. |
Koblitz II.1 (exercise 2) Koblitz V.1 |
| Thurs. 2/20 | Pseudoprimes, polynomial time primality tests.
The Miller-Rabin primality test. Computational complexity and big O |
Koblitz V.1,3 Koblitz I.1,2,3 |
| Tues. 2/25 | Time estimates for algorithms
Time estimates for RSA Factoring, Fermat's method and generalizations |
Koblitz I.1,2,3, Bit-ops page in reader Koblitz V.3 |
| Thurs. 2/27 | Factor base algorithms | Koblitz V.3 |
| Tues. 3/4 | Finite fields, | Koblitz II.1, IV.3. My notes. |
| Thurs. 3/6 | Primitive elements, discrete log
Discrete log cryptosystems |
Koblitz IV.3 |
| Tues. 3/11 | Computing discrete logs:
The Silver-Pohlig-Hellman algorithm. |
Koblitz IV.3 |
| Thurs. 3/13 | The index calculus for computing discrete logs. The ElGamal Signature scheme |
Koblitz IV.3 An example |
| Tues. 3/18 | Knapsack cryptosystems | Koblitz IV.4 |
| Thurs. 3/20 | Mor on the knapsack. Turing machines |
Koblitz IV.4 |
| Tues. 3/25 | P and NP, some NP-complete problems | Berlekamp et al, in reader |
| Thurs. 3/27 | Codes and McEliece and Neiderreiter cryptosystems | Li et al in reader |
| Tues. 4/8 | Attacks on the McEliece cryptosystem | Li and Van Tilburg articles |
| Tues. 4/10 | The attack on the Knapsack cryptosystems | Odlyzko and Lenstra artricles |
| Tues. 4/15 | Bezout's theorem as an introduction
to algebraic geometry |
. |
| Thurs. 4/17 | Elliptic curves | Koblitz VI.1 |
| Tues. 4/22 | Group law on elliptic curves | Koblitz VI.1 |
| Thurs. 4/24 | Elliptic curve cryptosystems | Koblitz VI.2 |
| Tues. 4/29 | The Data Encryption Standard | Stinson chapter |
| Thurs. 5/1 | The Rijndael block cipher:
The new Advanced Encryption Standard |
Daemon, Rijmen |
| Tues. 5/6 | Class canceled. | . |
| Thurs. 5/8 | Presentations of projects. | . |