Theorem to Generate Independently and Uniformly Distributed Chaotic Key Stream via Topologically Conjugated Maps of Tent Map

Zheng Guang Xu,Li Tian,Qing Tian

doi:10.1155/2012/619257

Abstract

This paper proposes a theorem to generate chaotic key stream from topologically conjugated maps of Tent Map. In this theorem, the condition for topological conjugation between Tent Map and a class of chaotic maps is first determined. Then, the chaotic attractor of the maps is divided into unequal subintervals, the chaotic orbit is sampled once in time iteration, and, finally, the independently and uniformly distributed phase key stream is obtained. The theoretical and numerical analyses show that the chaotic key stream generated by the proposed theorem successfully is independent and uniform, has a certain complex degree close to the maximum approximate entropy for 2n phase key stream, and satisfies the randomness requirement defined in NIST SP800-22. This theorem can be used in fields such as cryptography and numerical simulation.

Highlights

This paper proposes a theorem to generate chaotic key stream from topologically conjugated maps of Tent Map
Random number generation is very important in cryptography, especially in key construction
PRNGs are generally faster than TRNGs, and, PRNGs are preferable in applications requiring a large number of random numbers

Summary

Introduction

Random number generation is very important in cryptography, especially in key construction. The statistical property—independently and identically distributed IID —of chaotic key stream plays an important role in avoiding cipher-text attacking. Some studies focus on experiments that determine the selection of a suitable Tent Map parameter for different applications where the statistical independence is of interest. Complying with the fair coin tossing model in , the threshold is given according to the Tent Map parameter to obtain a statistically independent key stream. The research for generating IID key stream by topological conjugation has been limited to Logistic Map. in our study, we determine a more general condition, under which a class of chaotic systems can produce the IID key stream. The proof in 14 can be considered as the example for the theorem proposed in this paper

Theorem for Generation of IID Key Streams

Result

Results

Conclusion