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.
PublicKey ciphers:
RivestShamirAdleman (RSA), DiffieHellman. Public Key Protocols.
Number Theory: Congruences. Finite fields.
Finding large primes, pseudoprimes and primality testing.
Week  Lecture dates  Sections  topics 

1  1/22, 1/25  1.11.4, 7.4, 7.7  Caesar, Affine and Substitution Ciphers, Integers mod 26 
2  1/29, 2/1  2.22.4, 3.1, 5.2  Probability& Birthday Attacks, Hash Functions, Sunday Funnies, Frequency Attacks 
3  2/5, 2/8  3.23.5  Anagrams, Transposition Ciphers, Permutations 
4  2/12, 2/15  4.14.3  Vigenère Cipher/Kasiski Attack 
5  2/19, 2/22  4.44.5, 7.8  Expected Values/Friedman Attack on Vigenère 
6  2/26, 2/29  6.16.3, 8.18.2 
Hill Cipher/Affine Hill/Attacks on Hill Cipher Linear Algebra mod n, Shannon's Criteria 
7  3/4, 3/7  7.3, 7.5, 19.4, 26.15 Handout on F_{16} 
Finite fields F_{q}, Affine ciphers over F_{q},
Multiplicative inverses, ByteSub, MIMEencoding 
8  3/11, 3/14  6.12, handouts on AES  DES (now deprecated), AES and MixColumns, Review 

3/18, 3/21  R&R  SPRING BREAK 
9a  3/25 (Tues)  ch. 18, 26  Midterm Exam 
9b  3/28 (Fri)  11.2, 11.56  Prime Number Theorem, Euler's logarithmic integral Li(x) 
10  4/1, 4/4  7.8, 12.1, 12.5, 20.45  Primitive roots, Discrete logs; Fast Exponentiation 
11  4/8, 4/11  10.110.4, 13.613.7  Public Key Ciphers (RSA, DiffeHellman, El Gamal) 
12  4/15, 4/18  13.15, 15.15, 22.5  Square root attacks, Legendre symbols 
13  4/22, 4/25  24, 27.12  Factoring attacks and discrete logarithms 
14  4/29, 5/2  28.13  Discrete Log ciphers, Elliptic Curves, review. Term Paper Due Friday 5/2 
15  5/14 (Wed)  Cumulative  Final Exam in ARC 207 (47 PM) 
The Rijndael field F_{256} is defined as F_{2}[x]/(P), P=x^{8}+x^{4}+x^{3}+x+1. Elements of this field are represented by a pair of haxadecimal digits. For example, the unit 1 is (01) and (53) is short for x^{6}+x^{4}+x+1. Note that (53)*(CA)=1 in this field.
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Last Updated: February 29, 2008