Improving the Statistical Qualities of Pseudo Random Number Generators

Abstract

Pseudo random and true random sequence generators are important components in many scientific and technical fields, playing a fundamental role in the application of the Monte Carlo methods and stochastic simulation. Unfortunately, the quality of the sequences produced by these generators are not always ideal in terms of randomness for many applications. We present a new nonlinear filter design that improves the output sequences of common pseudo random generators in terms of statistical randomness. Taking inspiration from techniques employed in symmetric ciphers, it is based on four seed-dependent substitution boxes, an evolving internal state register, and the combination of different types of operations with the aim of diffusing nonrandom patterns in the input sequence. For statistical analysis we employ a custom initial battery of tests and well-regarded comprehensive packages such as TestU01 and PractRand. Analysis results show that our proposal achieves excellent randomness characteristics and can even transform nonrandom sources (such as a simple counter generator) into perfectly usable pseudo random sequences. Furthermore, performance is excellent while storage consumption is moderate, enabling its implementation in embedded or low power computational platforms.