Non-Archimedean Ergodic Theory and Pseudorandom Generators

TL;DR

This paper introduces a novel approach to designing pseudorandom number generators by modeling processor instructions as continuous functions on 2-adic integers and analyzing them through non-Archimedean ergodic theory.

Contribution

It develops a new theoretical framework for constructing PRNGs using non-Archimedean ergodic theory applied to processor instruction models.

Findings

PRNGs can be modeled as dynamical systems on 2-adic integers.

The approach enables analysis of uniform distribution properties.

Provides a foundation for designing more secure and efficient PRNGs.

Abstract

The paper develops techniques in order to construct computer programs, pseudorandom number generators (PRNG), that produce uniformly distributed sequences. The paper exploits an approach that treats standard processor instructions (arithmetic and bitwise logical ones) as continuous functions on the space of 2-adic integers. Within this approach, a PRNG is considered as a dynamical system and is studied by means of the non-Archimedean ergodic theory.