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A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications

Author

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  • Mei Zhang
  • Danling Wang
  • Lequan Min
  • Xue Wang

Abstract

Firstly, this study introduces a definition of generalized stability (GST) in discrete-time nonautonomous chaos system (DNCS), which is an extension for chaos generalized synchronization. Secondly, a constructive theorem of DNCS has been proposed. As an example, a GST DNCS is constructed based on a novel 4-dimensional discrete chaotic map. Numerical simulations show that the dynamic behaviors of this map have chaotic attractor characteristics. As one application, we design a chaotic pseudorandom number generator (CPRNG) based on the GST DNCS. We use the SP800-22 test suite to test the randomness of four 100-key streams consisting of 1,000,000 bits generated by the CPRNG, the RC4 algorithm, the ZUC algorithm, and a 6-dimensional CGS-based CPRNG, respectively. The numerical results show that the randomness performances of the two CPRNGs are promising. In addition, theoretically the key space of the CPRNG is larger than 2 1116 . As another application, this study designs a stream avalanche encryption scheme (SAES) in RGB image encryption. The results show that the GST DNCS is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs.

Suggested Citation

  • Mei Zhang & Danling Wang & Lequan Min & Xue Wang, 2015. "A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-12, July.
    • Handle: RePEc:hin:jnlmpe:121359
    DOI: 10.1155/2015/121359
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