Collatz-Weyl Generators: High Quality and High Throughput Parameterized Pseudorandom Number Generators

TL;DR

The paper presents Collatz-Weyl Generators, a new family of pseudorandom number generators based on generalized Collatz mappings, demonstrating high quality, efficiency, and potential cryptographic applications.

Contribution

Introduction of a novel PRNG family based on Collatz and Weyl sequences with strong statistical properties and practical implementation advantages.

Findings

Pass stringent randomness tests

Enable high throughput and low latency

Support multiple independent streams

Abstract

We introduce the Collatz-Weyl Generators, a family of uniform pseudorandom number generators (PRNGs) which are based on generalized Collatz mappings, derived from the Collatz conjecture and Weyl sequences. The high-quality statistical properties of our generators is demonstrated by the fact that they pass stringent randomness tests used by the research and standardization community. The proposed Collatz-Weyl Generators have a number of important properties, including solid mathematical foundations, enablement of high throughput and low latency implementation, small code and/or ASIC size, enablement of producing multiple independent streams and potential of support of cryptographic applications.