Analysis of the Time Series Generated by a New High-Dimensional Discrete Chaotic System

Chuanfu Wang,Chunlei Fan,Kai Feng,Qun Ding,Xin Huang

doi:10.1155/2018/9818520

Abstract

The chaotic behavior of low-dimensional digital chaotic systems is seriously degraded, and the output sequence has a short period. In this study, a digital sequence generator based on a high-dimensional chaotic system is proposed to ensure performance and security. The proposed generator has low resource consumption, and the digital pseudo-random output sequence has a large period. To avoid the nonchaotic state, the multistability in the high-dimensional discrete chaotic system is analyzed. The statistical performance of the output sequence of the proposed digital high-dimensional chaotic system is evaluated, and the results demonstrate that it is a suitable candidate for a long-period pseudo-random sequence generator.

Highlights

Random sequence generators are used in several engineering applications including compressed sensing, image encryption, secure communication, spread-spectrum communication, and distance measurement [1,2,3,4,5,6,7]
Pseudo-random sequence generators are designed by using certain mathematical algorithms, such as linear feedback shift register (LFSR), nonlinear feedback shift register (NLFSR), linear congruence, nonlinear congruence, and BBS (Blum Blum Shub)
The output sequence of the digital Sawtooth chaotic map consists of integers

Summary

Introduction

Random sequence generators are used in several engineering applications including compressed sensing, image encryption, secure communication, spread-spectrum communication, and distance measurement [1,2,3,4,5,6,7]. Pseudo-random sequence generators are designed by using certain mathematical algorithms, such as linear feedback shift register (LFSR), nonlinear feedback shift register (NLFSR), linear congruence, nonlinear congruence, and BBS (Blum Blum Shub). NLFSR, linear congruence, nonlinear congruence, and BBS are one-dimensional discrete maps They generate a largeperiod pseudo-random sequence at high computational cost. High-dimensional chaotic systems have a more complex nonlinear dynamic behavior. They have the disadvantages of high resource consumption and lowspeed performance. It is very necessary to design a large-period high-dimensional digital chaotic system with high-speed performance and low resource consumption. A digital pseudo-random sequence generator based on a high-dimensional discrete chaos map is proposed. Compared with the period of other digital chaotic pseudo-random sequence generators, the period of the output sequence of the proposed generator is closer to the upper limit of the maximum period

Sawtooth Chaotic Map

Result

U value

Conclusion