Non-Archimedean Ergodic Theory and Pseudorandom Generators

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.

Submitted to The Computer Journal

References in corpus (1)

• Non-Archimedean analysis, T-functions, and cryptography

Cited by in corpus (6)

• T-functions revisited: New criteria for bijectivity/transitivity
• Ergodicity criteria for non-expanding transformations of 2-adic spheres
• The Non-Archimedean Theory of Discrete Systems
• $p$-adic dynamical systems of $(2,2)$-rational functions with unique fixed point
• Dynamical systems of the $p$-adic $(2,2)$-rational functions with two fixed points
• Linear Relation on General Ergodic T-Function