Pseudo-random numbers

Goal:

To generate chance, computers use pseudo-random numbers. These are numbers that are supposed to be close to a statistically perfect hazard, as one would for instance obtain by successively throwing a fair coin. Because they are usually created by an algorithm, pseudo-random numbers cannot be considered completely random. This is why different methods have been developed over the years to test the quality and properties of a pseudo-random number generator, which play a central role in many applications, including simulations (Monte Carlo method), electronic games (initialization), and cryptography. The aim of this project is to test the good randomness of two families of pseudo-random numbers. The first family will be classical, and generated by a linear congruence. The second family to be tested will be that invented in 2006 by Alain Schumacher (under patent), who will act as an external expert.

Supervisors: Laurent Loosveldt, Ivan Nourdin, Gabor Wiese

External expert: Alain Schumacher

Difficulty level: Advanced

Bibliography: Upon request

FSTM -- University of Luxembourg