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Mathematical Problems in Engineering
Volume 2016, Article ID 1496329, 14 pages
Research Article

A Chaos Robustness Criterion for 2D Piecewise Smooth Map with Applications in Pseudorandom Number Generator and Image Encryption with Avalanche Effect

1Schools of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
2School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Received 28 August 2015; Revised 3 January 2016; Accepted 24 January 2016

Academic Editor: Jonathan N. Blakely

Copyright © 2016 Dandan Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study proposes a chaos robustness criterion for a kind of 2D piecewise smooth maps (2DPSMs). Using the chaos robustness criterion, one can easily determine the robust chaos parameter regions for some 2DPSMs. Combining 2DPSM with a generalized synchronization (GS) theorem, this study introduces a novel 6-dimensional discrete GS chaotic system. Based on the system, a 216-word chaotic pseudorandom number generator (CPRNG) is designed. The key space of the CPRNG is larger than 2996. Using the FIPS 140-2 test suit/generalized FIPS 140-2 test suit tests the randomness of the 1000 key streams consists of 20,000 bits generated by the CPRNG, the RC4 algorithm, and the ZUC algorithm, respectively. The numerical results show that the three algorithms do not have significant differences. The CPRNG and a stream encryption scheme with avalanche effect (SESAE) are used to encrypt an image. The results demonstrate that the CPRNG is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs. The SESAE with one-time-pad scheme makes any attackers have to use brute attacks to break our cryptographic system.