CS 290X Methods of Cryptography Fall 2007-08

Course Syllabus and Readings

Instructor: J. Yellin, yellin@soe.ucsc.edu

Meetings: WMF 11-1210pm, JBE 169

Office Hours: W 1045-1140am BE 173, or by appointment x9-2195

Course topics: Theory and practice of encryption and decryption. Classic ciphers. Shannon’s information theoretic approach. The DES standard. Public key algorithms - RSA. Elliptic key cryptography. Stream and block encoding. Security protocols, digital signatures. Quantum computing and cryptography.

Texts: Yellin, course notes; Barr, Invitation to Cryptology, Prentice-Hall 2002

Background reading: Levy, Crypto, Penguin, 2001; Singh, The Code Book, Anchor, 1999; Kahn, The Codebreakers, Scribner, 1996.

Required prerequisite material is taught in the following courses: Calculus (MA19), linear algebra (MA21), discrete mathematics (CE16), AMS 27.

Topic list and readings

1. Introduction: Cryptography and Information Theory.

Reading; Class Notes pp.1-10, Barr, Chapt.1.

2. Shannon Entropy, measuring information

Reading: Class Notes pp.10-25.

3. Classical ciphers: Transposition, substitution, statistics of plaintexts.

Reading: Class Notes pp.27-31, Barr, Chapt. 2.

4. Shannon’s theory of encription: entropy, unicity distance, error probabilities.

Reading: Class Notes, pp.31-40.

5. Stream and Block Encoding, S-DES, DES.

Reading: Barr, Sec.3.4-3.5, 5.1. Class notes, Sec.11.

6. Cryptographic tools: probabilistic algorithms, modular arithmetic, algorithmic number theory.

Reading: Class notes, Secs. 12-14. Barr, Sec. 4.1.

7. Public key systems: Diffie-Hellman, RSA, knapsack algorithms, discrete logs.

Reading: Barr, pp. 243-305. Class notes, secs. 15-16.

8. Elliptic Curve Cryptography

Reading: Class notes, Sec. 18.

9. Message integrity and authentication: Digital signing, hash functions.

Reading: Barr, pp. 233-42, 307-13, class notes, pp. 40-41, sec. 17.

10. Quantum computation and cryptography: qubits, measurement and authentication, quantum algorithms.

Reading: Class notes, Sec. 19-21.

Evaluation of performance: midterm(s), final examination, crypto project, class quizzes.

Last day of class: 12/1. Holidays: 11/12, 11/22-23. Final Examination: Wed 12/12, 4-7pm.