## Math 348 Cryptography (An Introduction to Cryptology)

#### Spring 2006

• Lectures: TF2 ARC 207 (Busch Campus); go to lecture table
• Classwork: Homework assignments
• Text: Making, Breaking Codes; an introduction to Cryptology
by Paul Garrett, Prentice Hall, 2001. (Here are the on-line Errata to 2nd edition and Errata to 1st edition)
• This is an upper level MATH course. It is directed at students in mathematics, electrical engineering, or computer science who have strong interest in mathematics and want to learn about the exciting applications of algebra and number theory to cryptography (encryption/decryption) and cryptanalysis (attacking encrypted messages).
Topics to be covered include:

Cryptography: Simple Ciphers and Cryptograms. Vigenere Cipher, Hill Cipher, Data Encryption Standard.
Cryptanalysis: Attacks on encrypted messages. Depth, probabilistic methods, trapdoors.
Public-Key ciphers: Rivest-Shamir-Adleman (RSA), Diffie-Hellman. Public Key Protocols.
Number Theory: Congruences. Finite fields. Finding large primes, pseudoprimes and primality testing.

#### Tentative Course Syllabus

Homework Assignments are on a separate web page.

supplement
 Week Lecture dates Sections topics 1 1/17, 1/20 1.1-1.4, 7.7 Caesar, Affine and Substitution Ciphers, Integers mod 26 2 1/24,1/37 2.2-2.4, 3.1 Probability& Birthday Attacks, Hash Functions, Sunday Funnies, Frequency Attacks 3 1/31,2/3 3.2-3.5 Anagrams, Transposition Ciphers, Permutations 4 2/7, 2/10 4.1-5 Vigenère Cipher/Kasiski Attack/Friedman Attack on Vigenère 5 2/14, 2/17 6.1-6.3, 8.2 Shannon's Criteria, DES, Introduction to Discrete Logs 6 2/21, 2/24 8.3-8.5 Diffie Hellman, El Gamal encryption methods 7 2/28, 3/3 8.1-8.2 RSA 8 3/7, 3/10 supplement, 9 Introduction to Hash Functions, Review 3/14, 3/17 R&R SPRING BREAK 9a 3/21 (T) ch. 1-8, 26 Midterm Exam 9b 3/24 (F) 18 The Prime Number Theorem 10 3/28, 3/31 16 Primality Testing 11 4/4, 4/7 8.4 More Diffie-Hellman and discrete logarithms 12 4/11, 4/14 26 Attacks on discrete logarithms 13 4/18, 4/21 27 Factoring attacks 14 4/25, 4/28 24 More factoring attacks, review. Term Paper Due Friday 4/28 15 5/4 (Thursday) Cumulative Final Exam in ARC 207 (12-3 PM)