Chapter

Cryptography and Coding

Volume 2260 of the series Lecture Notes in Computer Science pp 205-221

Date:

Statistical Properties of Digital Piecewise Linear Chaotic Maps and Their Roles in Cryptography and Pseudo-Random Coding

  • Shujun LiAffiliated withInstitute of Image Processing, School of Electronics and Information Engineering, Xi’an Jiaotong University
  • , Qi LiAffiliated withDepartment of Electrical Engineering and Electronics, The University of Liverpool
  • , Wenmin LiAffiliated withDepartment of Electircal and Electronic Engeering, Imperial College
  • , Xuanqin MouAffiliated withInstitute of Image Processing, School of Electronics and Information Engineering, Xi’an Jiaotong University
  • , Yuanlong CaiAffiliated withInstitute of Image Processing, School of Electronics and Information Engineering, Xi’an Jiaotong University

* Final gross prices may vary according to local VAT.

Get Access

Abstract

The applications of digital chaotic maps in discrete-time chaotic cryptography and pseudo-random coding are widely studied recently. However, the statistical properties of digital chaotic maps are rather different from the continuous ones, which impedes the theoretical analyses of the digital chaotic ciphers and pseudo-random coding. This paper detailedly investigates the statistical properties of a class of digital piecewise linear chaotic map (PLCM), and rigorously proves some useful results. Based on the proved results, we further discuss some notable problems in chaotic cryptography and pseudo-random coding employing digital PLCM-s. Since the analytic methods proposed in this paper can essentially extended to a large number of PLCM-s, they will be valuable for the research on the performance of such maps in chaotic cryptography and pseudo-random coding.