Prerequisites:
Linear Algebra (Math 250) and one of Math 300, 356, or 477, or
permission of department.
Part of the course will cover the needed background material on
number theory (see below).
Date  Topic  Supplementary Material 
January 22  Section 1.1: Substitution ciphers and letter frequency  Recap (pdf or Mathematica file) 
January 25  Section 1.3: Caesar cipher and modular arithmetic  
January 29 and February 1  Vigenere Cipher (Pegden's notes, p.1436), Digraphs  Recap (pdf or Mathematica file) 
February 5  Trigraphs and the Kasiski attack on Vigenere  Recap (pdf or Mathematica file) 
February 8  Section 4.2: Index of coincidence and the Friedman attack  Recap (pdf or Mathematica file) 
February 12  Section 1.2: Modular arithmetic, GCDs  
February 15  Sections 1.3, 1.4: Fast exponentiation, finite fields  
February 19  Section 1.5: Powers in finite fields  
February 22 and 26  Sections 2.12.3: The DiffieHellman key exchange, Discrete Logarithms  
March 1  First Midterm 

March 5 and 8  Section 2.52.7: Deterministic collision attacks on discrete logarithms, birthday paradox.  
March 12  Sections 2.82.9: Chinese Remainder Theorem, PohligHellman attack for composite group orders  Recap (pdf or Mathematica file) 
March 15  Section 3.4: Making industrial strength primes  
Spring Break  
March 26  Section 3.4: MillerRabin primality test  Recap (pdf or Mathematica file) 
March 29 and April 2  Sections 3.13.2: The RSA algorithm  
April 5 and 9  Section 3.5: Pollard's factoring algorithms (supplementary handout)  Recap (pdf or Mathematica file) 
April 12  Section 3.67: Random Squares factorization (relations step)  
April 16  Second Midterm  
April 19  Section 3.67: Random Squares factorization (matrix step)  
April 23 and 26  Section 3.8: Index calculus attack on Discrete Logarithms  
April 30 and May 3  Section 4.44.5: Pollard rho for discrete logarithms  Recap (pdf) 
Assignment 1 (due Feb. 15)  1.10, 1.13, 1.19, 1.20, 1.22, 1.25, 1.26, 1.28 
Assignment 2 (due Feb. 22)  1.30, 1.32(ad only), 1.34, 2.3, 2.4, 2.5, 2.6 
Assignment 3 (due March 1)  2.16, 2.17, also solve "6^{x}=n (mod 229)" for n=166,167, and 168. 
Assignment 4 (due March 8)  2.18, 2.21, 2.28a). 
Assignment 5 (due March 15)  3.13a, 3.13b, 3.14a, 3.14b, 3.14c, 3.16a, 3.20 
Assignment 6 (due March 29)  3.1abc, 3.6, 3.7, 3.8, 3.9 
Assignment 7 (due April 5)  3.21ab, 3.22acde, 3.23, 3.25 
Assignment 8 (due April 12)  3.26, 3.28, 3.29 
Assignment 9 (due April 19)  3.35  and also do part d for the following examples, replacing the "19": 119, 1119, 11119 