Lecture: Collision Algorithms and the Discrete Log Problem

Background Material

Reading

Topics

  1. Birthday Paradox.
  2. Discrete Log Problem.
  3. Shanks Babystep-Giantstep Algorithm.
  4. Collision Theorem.
  5. Collision Algorithm for Discrete Log.

Lecture Slides and Worksheet

  1. (Collision.ppt, Collision.pdf).
  2. birthday.mw - maple worksheet illustrating birthday paradox.

Practice Assignment

  1. Review the maple worksheet that illustrates the birthday paradox.
  2. Compute the probability given by the collision theorem for different values of m=n and N. How good is the approximation. Compute the probability for m=n = c*sqrt(N) for different values of the constant c.
  3. Solve discrete log problem using Shanks algorithm and the randomized collision algorithm.
Created: April 25, 2012 by jjohnson AT cs DOT drexel DOT edu