Math 458 SPRING 2015, List of lectures

  • On this page I will post content of all lectures. All handouts also will be posted here.
  • Monday, March 30: Simple substitution ciphers. Idea of asymmetric cryptography. Divisibility. Sections 1.1-1.2, 1.7. Reading assignment: Read Section 1.1.1.
  • Wednesday, April 1: Euclidean algorithm. Section 1.2. Please find your homework!
  • Friday, April 3: More on Euclidean algorithm. Congruences. Sections 1.2-1.3.
  • Monday, April 6: Modular arithmetic. Section 1.3.
  • Wednesday, April 8: Fast powering. Prime numbers and unique factorization. Sections 1.3-1.4.
  • Friday, April 10: Fermat little theorem. Primitive roots. Section 1.5. New homework!
  • Monday, April 13: Symmetric ciphers and public key cryptography. Sections 1.7 and 2.1. Reading assignment: Read Section 1.6.
  • Wednesday, April 15: The discrete logarithm problem and its applications. Sections 2.2-2.4.
  • Friday, April 17: How to solve DLP. Sections 2.6-2.7. New homework!
  • Monday, April 20: The Chinese Remainder Theorem. Section 2.8.
  • Wednesday, April 22: The Pohlig-Hellman algorithm. Sections 2.9. Please find solutions to theoretical problems in Homework 2.
  • Friday, April 24: MIDTERM. Here are the solutions.
  • Monday, April 27: More on Pohlig-Hellman algorithm. Roots of high degree. Sections 2.9, 3.1. New homework!
  • Wednesday, April 29: RSA cryptosystem. Section 3.2. Reading assignment: Read Section 3.3.
  • Friday, May 1: Primality testing. Section 3.4.
  • Monday, May 4: Factorization: Pollard p-1 algorithm. Section 3.5. New homework!
  • Wednesday, May 6: Towards quadratic sieve. Section 3.6.
  • Friday, May 8: Quadratic sieve. Section 3.7.
  • Monday, May 11: Discrete log again: index calculus. Section 3.8. New homework!
  • Wednesday, May 13: Quadratic residues and nonresidues. Section 3.9.
  • Friday, May 15: Goldwasser-Micali cryptosystem. Section 3.10. We will have MIDTERM next Friday. Please find here review problems.
  • Monday, May 18: Rings, fields, and polynomials. Section 2.10. New homework!
  • Wednesday, May 20: Midterm review.
  • Friday, May 22: MIDTERM. Here are the solutions.
  • Monday, May 25: Memorial Day, no classes.
  • Wednesday, May 27: Construction of finite fields. Section 2.10.
  • Friday, May 29: Elliptic curves. Section 6.1. Last homework!
  • Monday, May 25: Elliptic curves over finite fields. Section 6.2.
  • Wednesday, May 27: Cryptography with elliptic curves. Sections 6.3-6.4. Please find here review problems for the final.
  • Friday, May 29: Factorization with elliptic curves. Section 6.6. Here are the answers and solutions to review problems.
  • THE END