Math 626 -- Schedule


I will try to keep to this schedule but will update it as needed.
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
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. .