Instructor: Poorvi Vora, poorvi@gwu.edu, 706 Philips Hall. Office Hours: Mondays: 11-noon and 1-3 pm;

TA: Prof. Mohammed Obiedat

Text: Douglas Stinson, "Cryptography: Theory and Practice", Third Edition, 2005.

Course Content: Classical ciphers and cryptanalysis, Shannon's perfect secrecy, Feistel ciphers and DES, SPN's and AES, linear and differential cryptanalysis, public-key crypto (RSA, Discrete Log), secure hash.

Prerequisites: Discrete Mathematics, some complexity theory

Grading: HWs (40%), Weekly Quizzes (35%), a final exam (25%).
Late HWs are allowed till the HW solution is made available, 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.

284 and 162 will be graded separately. If you are an undergrad, please consult your adviser before choosing to take 284; graduate credit for 284 is not automatic for undergrads, but all those enrolled in 284 will be graded together.

Course Outline

Planned Schedule

12 January 2008, Lecture 1: Classical Ciphers and their cryptanalysis. Slides errors fixed on 13 Jan. All of chapter 1 from the text except sections 1.1.5, 1.1.7, 1.2.3, 1.2.4, 1.2.5 and theorems in section 1.1.3. We will not be covering Hill Ciphers (sections 1.1.5 and 1.2.4) or cryptanalysis of the Vigenere Cipher (section 1.2.3) in this course, but we will cover stream ciphers and their cryptanalysis (sections 1.1.7 and 1.2.5) and the theorems from section 1.1.3 in later lectures. HW1 assigned: Due on 30 January, note date change Further Reading (not necessary, and you do not need any of the proofs) Modular Arithmetic Class Notes, CSCI 124 Groups Class Notes, CS 124 (the theorem in this will be covered next class)

19 January 2008, Holiday: Martin Luther King Jr. Day

26 January 2008, Lecture 2: GCD and basic Euclidean Algorithm. Notes: GCD Basic Euclidean Algorithm Euclidean Algorithm for Inverse Slides Theorem 1.1 from section 1.1.3 with a proof not in the book. Section 5.2.1 (pages 163-164). HW2 assigned: Due February 9 Quiz 1 GCD Practice Problems Modular Inverse Practice Problems

2 February 2008, Lecture 3: Block Ciphers: Substitution-Permutation Networks, Feistel Ciphers, AES, DES. Slides 3.1. 3.2, 3.5-3.7 from text, section 2 from Heys' report. Quiz 2 References H. M. Heys, Section 2, "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 AES Standard Animation of AES Encryption

9 February 2008, Lecture 4: Probability Theory Slides modified February 23, 2009 Section 2.2 from text HW3 assigned: Due February 27 Sample Input File, SPN; Sample Output File, SPN; Sample Input File, Feistel; Sample Output File, Feistel Quiz 3

16 February 2008, Holiday: Presidents' Day

23 February 2008, Lecture 5: Shannon Secrecy. Slides Sections 2.1-2.3, 2.7 from text. Quiz 4 References Claude E. Shannon, "Communication Theory of Secrecy Systems", Bell System Technical Journal, vol.28-4, page 656--715, 1949.

2 March 2008, Lecture 6: Stream Ciphers. Entropy. Slides: Stream Ciphers, Entropy Section 1.1.7, 2.4 (no Huffman encodings) from text. HW4 assigned: Due March 13 Quiz 5 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 March 2008, Lecture 7: Cryptanalysis. Slides Section 3.3, 3.4 from text. HW5 assigned: Due April 6 Only for CS 284; extra credit for CS 162 Quiz 6 References H. M. Heys, Section 2, "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.)

16 March 2008,Spring Break Practice Problems: 1.11, 3.1-3.4, 3.7

23 March 2008 Lecture 8: Efficient Exponentiation, RSA Slides: Efficient Exponentiation, RSA Sections 5.1 and 5.3 from text. See also Fast Exponentiation notes and practice examples. Quiz 7

30 March 2008 Class cancelled.

6 April 2008, Lecture 9: Number theory: Lagrange theorem on group order, CRT, RSA Correctness Proof. Sections 5.2.2 and 5.2.3 (only Thm. 5.4) from text Quiz 8

13 April 2008, Lecture 10: El Gamal Cryptosystem Quiz 9 Slides HW6 assigned: Due April 29

20 April 2008, Lecture 11: Elliptic Curves Certicom Tutorial Do one of the following by May 11, 2009: Final Exam (Theory Option); Final Exam (Implementation Option) Quiz 10

27 April 2008, Lecture 12: Secure Hash. Complete El Gamal slide set Quiz 11

29 April 2008, Wednesday, Lecture 13: Use of crytpo primitives in protocols such as digital cash and voting Quiz 12