Fast and robust PRNGs based on jumps in N-cubes for simulation, but not exclusively for that

Abstract

Pseudo-Random Number Generators (PRNG) are omnipresent in computer science: they are embedded in all approaches of numerical simulation (for exhaustiveness), optimization (to discover new solutions), testing (to detect bugs) cryptography (to generate keys), and deep learning (for initialization, to allow generalizations).. .. PRNGs can be basically divided in two main categories: fast ones, robust ones. The former have often statistical biases such as not being uniformly distributed in all dimensions, having a too short period of time,.. .. In the latter case, statistical quality is present but the generators are not fast. This is typically what is encountered when running a cryptographically secure PRNG. In this paper, we propose alternative architectures, based on jumps in N-cubes, that provide fast and robust PRNGs for efficient simulations, but not exclusively for that.