The Mathematics of Public-Key Cryptography, Lecture 7

October 3, 2000

Summary of material covered in lecture 7

• random squares algorithm for factoring: see "Notes" on the course home page
  • choosing integers close to sqrt(kn) to increase the likelihood of factoring over the factor base
  • including -1 in the factor base
  • probability that a random integer factors over the factor base
  • choosing the optimal size for the factor base
  • heuristic analysis of complexity of algorithm
• equivalence of factoring n and computing phi(n) whne n is the product of two primes