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Pseudo-random number generator based on a generalized conservative Sprott-A system

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Abstract

Pseudo-random number generator (PRNG) has been widely used in digital image encryption and secure communication. This paper reports a novel PRNG based on a generalized Sprott-A system that is conservative. To validate whether the system can produce high quality chaotic signals, we numerically investigate its conservative chaotic dynamics and the complexity based on the approximate entropy algorithm. In this PRNG, we first select an initial value as a key to generate conservative chaotic sequence, then a scrambling operation is introduced into the process to enhance the complexity of the sequence, which is quantified by the binary quantization method. The national institute of standards and technology statistical test suite is used to test the randomness of the scrambled sequence, and we also analyze its correlation, keyspace, key sensitivity, linear complexity, information entropy and histogram. The numerical results show that the binary random sequence produced by the PRNG algorithm has the advantages of the large keyspace, high sensitivity, and good randomness. Moreover, an improved finite precision period calculation (FPPC) algorithm is proposed to calculate the repetition rate of the sequence and further discuss the relationship between the repetition rate and fixed-point accuracy; the proposed FPPC algorithm can be used to set the fixed-point notation for the proposed PRNG and avoid the degradation of the chaotic system due to the data precision.

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Acknowledgements

This work is partly supported by the National Natural Science Foundation of China (Grant No. 61873186), South African National Research Foundation (Grant Nos. 112142 and 112108), South African National Research Foundation Incentive Grant (No. 114911), and South African Eskom Tertiary Education Support Programme.

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Authors and Affiliations

  1. Department of Product Design, Tianjin University of Science and Technology, Tianjin, 300222, People’s Republic of China

    Shijian Cang

  2. School of Electronic Information and Automation, Tianjin University of Science and Technology, Tianjin, 300222, People’s Republic of China

    Zhijun Kang

  3. Department of Electrical and Mining Engineering, University of South Africa, Florida, 1710, South Africa

    Zenghui Wang

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  1. Shijian Cang
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  2. Zhijun Kang
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  3. Zenghui Wang
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Correspondence to Shijian Cang.

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Cang, S., Kang, Z. & Wang, Z. Pseudo-random number generator based on a generalized conservative Sprott-A system. Nonlinear Dyn 104, 827–844 (2021). https://doi.org/10.1007/s11071-021-06310-9

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