Pseudorandom number generation by p-adic ergodic transformations: an addendum

TL;DR

This paper explores multivariate pseudorandom number generators based on p-adic ergodic transformations, extending univariate results to higher dimensions and analyzing their internal state sequences and output properties.

Contribution

It extends univariate p-adic ergodic generator results to multivariate cases, providing a framework for counter-dependent pseudorandom number generation.

Findings

Multivariate ergodic mappings can generate pseudorandom sequences with desirable properties.

The recurrence law defines internal states with modular arithmetic over 2^n.

Results from univariate cases are successfully extended to multivariate scenarios.

Abstract

The paper study counter-dependent pseudorandom number generators based on $m$-variate ($m>1$) ergodic mappings of the space of 2-adic integers $\Z_2$. The sequence of internal states of these generators is defined by the recurrence law $\mathbf x_{i+1}= H^B_i(\mathbf x_i)\bmod{2^n}$, whereas their output sequence is %while its output sequence is of the $\mathbf z_{i}=F^B_i(\mathbf x_i)\mod 2^n$; here $\mathbf x_j, \mathbf z_j$ are $m$-dimensional vectors over $\Z_2$. It is shown how the results obtained for a univariate case could be extended to a multivariate case.