Designing a pseudorandom bit generator based on LFSRs and a discrete chaotic map

Abstract

A new method for the generation of pseudorandom numbers, based on two linear feedback shift registers (LFSRs) and a discrete-space chaotic map is presented. The proposed method consists of multiple stages; in stage one a pseudorandom sequence is generated. In stage two a selection of output bits is conducted in order to produce sequences with high randomness. Because many previous methods based on LFSRs and XOR operations are not able to resist chosen and known plaintext attack, stage one of the proposed method is designed to be resistant to this problem. Relations between two LFSRs and the parameters of the chaotic map are established in such a way that based on known output bits of a proposed generator it is impossible to obtain any part of the secret key without guessing the whole secret key. The randomness of generated sequences is confirmed using NIST, TestU01, and the DIEHARD test. The advantages of the proposed method are virtually unlimited key space and resistance to digital degradation.