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.
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) |
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Last Updated: April 23, 2006