ERGODIC TRANSFORMATIONS: AN ADDENDUM

Title: ERGODIC TRANSFORMATIONS: AN ADDENDUM

Research Question: How can multivariate ergodic mappings be used to improve the performance of counter-dependent pseudorandom number generators?

Methodology: The study uses m-variate (m > 1) ergodic mappings of the space of 2-adic integers Z2 to create a multivariate representation of univariate mappings. This method allows for the extension of results obtained for univariate cases to a multivariate context.

Results: The paper introduces a way to derive multivariate ergodic functions from univariate ones, which can be used to improve the periods of coordinate sequences. It also describes how to lift an arbitrary m-variate permutation with a single cycle to a permutation with a single cycle of (n + K)-bit words. This allows for the construction of multivariate output functions that can improve the performance of counter-dependent pseudorandom number generators.

Implications: The use of multivariate ergodic mappings can lead to more effective pseudorandom number generators with better performance. This can have significant implications for applications that rely on the generation of pseudorandom numbers, such as cryptography and simulation.

Link to Article: https://arxiv.org/abs/0402060v1 Authors: arXiv ID: 0402060v1