Abstract
Wheeler pointed out that the period of Matthews’ chaotic function (MCF) is often too short to be suitable for cryptographic usage in the manner of computer statistics, but this statement was given only through digital computation. In this paper, we proved by theoretical and practical method that period exists in MCF and analyzed the underlying reason. With two chaotic functions working together we presented a modified MCF (MMCF) that is non-periodic. The simulation tests with reconstruction of phase space showed that our modified MCF is of no period. And we described how to implement a cryptographic usage with MMCF.
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Foundation item: Supported by the National Natural Science Foundation of China (60673071)
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Zhou, X., Zhang, H. A new chaotic function and its cryptographic usage. Wuhan Univ. J. Nat. Sci. 13, 557–561 (2008). https://doi.org/10.1007/s11859-008-0509-2
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DOI: https://doi.org/10.1007/s11859-008-0509-2
Key words
- chaos
- period
- Matthews’ chaotic function (MCF)
- modified Matthews’ chaotic function (MMCF)
- reconstruction of phase space (RPS)
- variable-structure attractor
- invariable-structure attractor