# Lecture: Collision Algorithms and the Discrete Log Problem

### Background Material

- See Lecture on primitive element theorem.

### Reading

- Sections 2.7 and 4.4 of the text.

### Topics

- Birthday Paradox.
- Discrete Log Problem.
- Shanks Babystep-Giantstep Algorithm.
- Collision Theorem.
- Collision Algorithm for Discrete Log.

### Lecture Slides and Worksheet

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

### Practice Assignment

- Review the maple worksheet that illustrates the birthday paradox.
- 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.
- Solve discrete log problem using Shanks algorithm and the randomized collision algorithm.

Created: April 25, 2012 by jjohnson AT cs DOT drexel DOT edu