The Mathematics of Public-Key Cryptography, Lecture 11

October 17, 2000

Summary of material covered in lecture 11

• detailed description of an algorithm to invert the trapdoor permutation f, given an algorithm for the plaintext distinguishability problem, in the random oracle model
  • specification of the "random" function G
  • analysis of success probability
• introduction to the discrete logarithm problem
  • the discrete log problem in a general group
  • overview of groups commonly used as settings for the DLP, and the most efficient known algorithms to solve them
  • solving the DLP in (Z_n,+) using the extended Euclidean algorithm