| 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 |
IV.3 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. | . |