Math 626: Cryptography
Spring 2005

Instr: Mike O'Sullivan


I will try to keep to this schedule but will update it as needed.
Day Topics Preparation
Mon. 1/24 Introduction and history of cryptography. .
Wed. 1/26 Affine ciphers and attacks. Koblitz III.1,2, Reader 1
Fri. 1/28 Affine ciphers using digraphs and attacks. Koblitz III.1,2
Mon. 1/31 Affine matrix systems and the chosen plaintext attack.
Koblitz III.2
Koblitz, I.2,3.
Wed. 2/2 Ciphering machines.
The Enigma cipher and the Polish attack.
Fri. 2/4 The British attack on Enigma.
Mon. 2/7 The Data Encryption Standard Reader 2.
Wed. 2/9 The Rijndael block cipher:
The new Advanced Encryption Standard
Reader 3
Fri. 2/11 Public key cryptography. Koblitz I.3, IV.2
Mon. 2/14 Euler's theorem
Chinese Remainder Theorem.
Koblitz I.3
Wed. 2/16 The RSA cryptosystem. Koblitz IV.2
Fri. 2/18 Attacks on RSA. Koblitz IV.2
Mon. 2/21 Practical aspects of RSA, digital signatures.
Hash functions.
Koblitz IV.2
Wed. 2/23 Polynomial rings and Finite fields, Koblitz II.1, IV.3.
Fri. 2/25 Finite fields, discrete logs. Koblitz IV.3
Mon. 2/28 A probabilistic factorization algorithm.
Discrete log cryptosystems
Koblitz IV.3
Wed. 3/2 Computing discrete logs:
The Silver-Pohlig-Hellman algorithm.
Koblitz IV.3
Fri. 3/4 Some problems.
Signatures using discrete logs.
Koblitz IV.3
Mon. 3/7 The digital signature standard.
Computational complexity and big O
Koblitz I.1,2,3, Bit-ops page in reader
Wed. 3/9 Computational complexity and big O Koblitz I.1,2,3, Bit-ops page in reader
Fri. 3/11 P and NP, some NP-complete problems .
Mon. 3/14 Knapsack cryptosystems Koblitz IV.4
Wed. 3/16 Attacks on Knapsack cryptosystems Odlyzko and Lenstra articles
Fri. 3/18 Codes and McEliece and Neiderreiter cryptosystems Li et al in reader
Mon. 3/21 Codes and McEliece and Neiderreiter cryptosystems Li et al in reader
Wed. 3/23 Attacks on the McEliece cryptosystem Li and Van Tilburg articles
Fri. 3/25 Maple: Meet in the lab. .
Mon. 4/4 Pseudoprimes, polynomial time primality tests. Koblitz V.1
Wed. 4/6 The Miller-Rabin primality test. Koblitz V.1
Fri. 4/8 EXAM Affine, DSA, AES, RSA, discrete-log, knapsack cryptosystems
Mon. 4/11 Factor base algorithms Koblitz V.3
Wed. 4/13 Bezout's theorem as an introduction
to algebraic geometry
Fri. 4/15 Elliptic curves Koblitz VI.1
Mon. 4/18 Group law on elliptic curves Koblitz VI.1
Wed. 4/20 Elliptic curve cryptosystems Koblitz VI.2
Fri. 4/22 More on factor base algorithms
The index calculus for computing discrete logs.
Koblitz V.3
Koblitz IV.3
Mon. 5/2 Questions and discussion of projects. .
Wed. 5/4 Meet in the lab. 405 .
Mon. 5/9 Colleen, David. .
Wed. 5/11 . .
Mon. 5/16 Marcel. .