A Class of Maximum-Period Nonlinear Congruential Generators Derived From the Rényi Chaotic Map

Author

Addabbo, T. ; Alioto, M. ; Fort, A. ; Pasini, A. ; Rocchi, S. ; Vignoli, V.

Author_Institution

Dept. of Inf. Eng., Siena Univ.

Volume

54

Issue

4

fYear

2007

fDate

4/1/2007 12:00:00 AM

Firstpage

816

Lastpage

828

Abstract

In this paper, a family of nonlinear congruential generators (NLCGs) based on the digitized Reacutenyi map is considered for the definition of hardware-efficient pseudorandom number generators (PRNGs), and a theoretical framework for their study is presented. The authors investigate how the nonlinear structure of these systems eliminates some of the statistical regularities spoiling the randomness of sequences generated with linear techniques. In detail, in this paper, a necessary condition that the considered NLCGs must satisfy to have maximum period length is given, and a list of such maximum period PRNGs for period lengths up to 2³¹-1 is provided. Referring to the NIST800-22 statistical test suite, two PRNG examples are presented and compared to well-known PRNGs based on linear recurrencies requiring a similar amount of resources for their implementation

Keywords

chaos generators; logic design; random number generation; random sequences; NIST800-22 statistical test; Renyi chaotic map; digital circuits; nonlinear congruential generators; nonlinear systems; pseudorandom number generators; Chaos; Circuit simulation; Circuit testing; Cryptography; Digital circuits; Logic; Nonlinear systems; Random number generation; Stochastic systems; System testing; Digital circuits; nonlinear systems; random number generators (RNGs); sequences;

fLanguage

English

Journal_Title

Circuits and Systems I: Regular Papers, IEEE Transactions on

Publisher

ieee

ISSN

1549-8328

Type

jour

DOI

10.1109/TCSI.2007.890622

Filename

4155019