Improving the statistical properties of number sequences produced by pseudorandom generators derived from the Rényi chaotic map

A new method to improve the statistical properties of number sequences generated by maximum-period nonlinear congruential generators derived from the Renyi chaotic map is proposed. The characteristic feature of the method is the simultaneous usage of numbers generated by the Renyi map implemented in a finite-state machine, and symbols generated by the same map. The period of sequences generated can be significantly longer than the period of sequences produced by previously defined generators using the same map. It is shown that output sequences obtained with the proposed method can pass all, or almost all, statistical tests from the standard NIST 800-22 statistical test suite for many integer or non-integer values of the parameter.