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Study on Cryptographical Properties of Several Chaotic Pseudorandom Sequences

Chun-Yang Zhang, Xiang Fei, Liwen Zhang

Open publisher page 2 citations

Abstract

The paper presents combining k-error approximate entropy with some tests in NIST's STS randomness test suite to analyze cryptographical properties of several chaotic pseudorandom sequences generated by diverse maps and quantified methods, including Logistic map, Cubic map, Henon map, Sine map, Tent map, Chebyshev map, Piecewise-linear map, Piecewise-square-root map. Simulation results show that the k-error approximate entropy can distinguish the stability of different sequences; that the cryptological properties are influenced by quantified methods; that the sequences generated by Logistic map, Chebyshev map, Piecewise-linear map and Piecewise-square-root map have the best pseudorandom properties, while the sequences generated by Henon map and Tent map have the worst stability.

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What this paper is about

The paper presents combining k-error approximate entropy with some tests in NIST's STS randomness test suite to analyze cryptographical properties of several chaotic pseudorandom sequences generated by diverse maps and quantified methods, including Logistic map, Cubic map, Henon map, Sine map, Tent map, Chebyshev map, Piecewise-linear map, Piecewise-square-root map. Simulation results show that the k-error approximate entropy can distinguish the stability of different sequences; that the cryptological properties are influenced by quantified methods; that the sequences generated by Logistic map, Chebyshev map, Piecewise-linear map and Piecewise-square-root map have the best pseudorandom properties, while the sequences generated by Henon map and Tent map have the worst stability.

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Available abstract

The paper presents combining k-error approximate entropy with some tests in NIST's STS randomness test suite to analyze cryptographical properties of several chaotic pseudorandom sequences generated by diverse maps and quantified methods, including Logistic map, Cubic map, Henon map, Sine map, Tent map, Chebyshev map, Piecewise-linear map, Piecewise-square-root map. Simulation results show that the k-error approximate entropy can distinguish the stability of different sequences; that the cryptological properties are influenced by quantified methods; that the sequences generated by Logistic map, Chebyshev map, Piecewise-linear map and Piecewise-square-root map have the best pseudorandom properties, while the sequences generated by Henon map and Tent map have the worst stability.

Key concepts: Logistic map, Hénon map, Chaotic map, Mathematics, Pseudorandom number generator, Randomness, Tent map, Piecewise linear function

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