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.14-36), 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 2.1-2.3: The Diffie-Hellman key exchange, Discrete Logarithms | |
March 1 | First Midterm |
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March 5 and 8 | Section 2.5-2.7: Deterministic collision attacks on discrete logarithms, birthday paradox. | |
March 12 | Sections 2.8-2.9: Chinese Remainder Theorem, Pohlig-Hellman 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: Miller-Rabin primality test | Recap (pdf or Mathematica file) |
March 29 and April 2 | Sections 3.1-3.2: The RSA algorithm | |
April 5 and 9 | Section 3.5: Pollard's factoring algorithms (supplementary handout) | Recap (pdf or Mathematica file) |
April 12 | Section 3.6-7: Random Squares factorization (relations step) | |
April 16 | Second Midterm | |
April 19 | Section 3.6-7: Random Squares factorization (matrix step) | |
April 23 and 26 | Section 3.8: Index calculus attack on Discrete Logarithms | |
April 30 and May 3 | Section 4.4-4.5: 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(a-d only), 1.34, 2.3, 2.4, 2.5, 2.6 |
Assignment 3 (due March 1) | 2.16, 2.17, also solve "6x=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 |