Instructor: Poorvi Vora

Text: Douglas Stinson, "Cryptography: Theory and Practice", Second Edition, 2002. Errata

Course Content: Classical ciphers and cryptanalysis, Shannon's perfect secrecy, Feistel ciphers and AES, public-key crypto (RSA, Discrete Log), one-way functions and hashes, digital signatures. Time permitting, we will cover some or all of: secret sharing, zero-knowledge, pseudo-random number generators. The required mathematics: introductory number theory, probability theory, will be taught in class, as will some introductory complexity theory: big-Oh notation, P, NP.

Grading: HWs, assigned most weeks, and a final class project chosen from here. While it is possible to do a project outside of this list, such projects must be approved by the instructor by the date noted below. The HWs will be about 50% theory and 50% implementation. Late HWs are allowed, but will be multiplied by a factor of (1.0 - n*0.1) where n is the number of days the submission is delayed. So, for example, if you submit your HW two days late, your grade on that HW will be multiplied by 0.8. HW solutions will be put up after every student registered has submitted a HW, or after 10 days, whichever is earlier. No final or mid-term.

Note change in project presentation dates

Planned Schedule

12 January 2004, Lecture 1: Shift Ciphers; Affine Ciphers; Number Theory: gcd, invertible elements in Z_m. Classical Ciphers I Classical Ciphers II HW 1. due 11 February 2004.

19 January 2004, Holiday: Martin Luther King, Jr., Birthday.

26 January 2004, Class cancelled: weather.

2 February 2004, Lecture 2: Substitution, Permutation, Vigenere, Hill and Stream Ciphers Classical Ciphers II Classical Ciphers III References Coppersmith, Krawczyk, Mansour, "The Shrinking Generator", Crypto '93, LNCS 773, pages 22-39. Springer-Verlag, 1994. Beth and Piper, "The stop-and-go-generator" in Advances in Cryptology: Proceedings of Eurocrypt 84, Lecture Notes in Computer Science, Berlin: SpringerVerlag 1985, vol. 209, pp. 88-92.

9 February 2004, Lecture 3: Number theory: Euler Phi Function. Elementary Probability Theory. Project exception requests due. Shannon Secrecy HW 2 due 25 February 2004.

16 February 2004, Holiday: Presidents' Day

23 February 2004, Lecture 4: One-time pad, Shannon: Perfect Secrecy. Examples: secret sharing. Shannon Secrecy References Claude E. Shannon, "Communication Theory of Secrecy Systems", Bell System Technical Journal, vol.28-4, page 656--715, 1949. Lidong Zhou's notes on secret sharing

1 March 2004, Lecture 5: Shannon secrecy: some proofs. Product Cryptosystems. Shannon Secrecy HW3 due 10 March 2004.

8 March 2004, Lecture 6: Substitution-Permutation, Linear Cryptanalysis, DES Project proposals due. Block Ciphers: SPNs and Cryptanalysis Block Ciphers: DES and AES HW4 due 24 March 2004. References H. M. Heys, "A Tutorial on Linear and Differential Cryptanalysis", Technical Report CORR 2001-17, Centre for Applied Cryptographic Research, Department of Combinatorics and Optimization, University of Waterloo, Mar. 2001. (Also appears in Cryptologia, vol. XXVI, no. 3, pp. 189-221, 2002.) DES Standard

15 March 2004, No Class: DIMACS Privacy Workshop, Spring Break.

22 March 2004, Lecture 7: Differential Cryptanalysis. AES. Number Theory: Euler phi function; Euclid's algorithms for gcd and inverses in Z_m; Chinese Remainder Theorem. Block Ciphers: SPNs and Cryptanalysis Block Ciphers: DES and AES Classical Ciphers II HW5 due 31 March 2004. References H. M. Heys, "A Tutorial on Linear and Differential Cryptanalysis", Technical Report CORR 2001-17, Centre for Applied Cryptographic Research, Department of Combinatorics and Optimization, University of Waterloo, Mar. 2001. (Also appears in Cryptologia, vol. XXVI, no. 3, pp. 189-221, 2002.) AES Standard Extended Euclidean Algorithm (Richard Koch, Univ. of Oregon) The Euclidean Algorithm - Some History (Chris Christensen, Northern Kentucky University)

29 March 2004, Lecture 8: Computational Complexity. Security of Hash functions: Pre-images, Collision. SHA-1. One Way Functions HW6 due 7 April 2004.

5 April 2004, Lecture 9: RSA, Implementation: fast powers mod n. Number theory: Langrange theorem on group order, proof of RSA. RSA HW7 due 14 April 2004.

12 April 2004, Lecture 10: Factoring: Pollard p-1; El Gamal; Discrete Log: Shanks', Pollard-Rho; Diffie-Hellman Key Exchange RSA Discrete Log

19 April 2004, Lecture 11: Digital Signatures, Steganography, Voting Digital Signatures Steganography Voting

26 April 2004, Lecture 12: Project Presentations Schedule

28 April 2004, Wednesday, Lecture 13: Project Presentations Schedule

Make-up day: 29 April 2004, Thursday, Lecture 14: Project Presentations Schedule