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A digital pseudo-random number generator based on sawtooth chaotic map with a guaranteed enhanced period

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Abstract

In this paper, a very low complexity method is proposed to achieve a guaranteed substantial extension in the period of a popular class of chaos-based digital pseudo-random number generators (PRNGs). To this end, the relation between the chaotic PRNG and multiple recursive generators is investigated and some theorems are provided to show that how a simple recursive structure and an additive piecewise-constant perturbation inhibit unpredictable short period trajectories and ensure an a priori known long period for the chaotic PRNG. The statistical performance of the proposed PRNG is evaluated, and the results show that it is a good candidate for applications in which long-period secure pseudo-random sequence generators at a low complexity level are required.

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Notes

  1. Also called Bernoulli shift or Rényi map.

  2. The period of a recursion modulo \(2^r\) cannot be smaller than its period modulo 2 [36].

  3. Choosing other values for \(a_i\) rather than 1 or 0 does not have any effect on the period length if the feedback polynomial satisfies the conditions of Theorem 1, yet it may change the trajectory.

  4. It is the period of a conventional linear feedback shift register with primitive feedback polynomial.

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Acknowledgements

The authors would like to thank Dr. J. Lahtonen for helpful comments on some proofs.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran

    Mohammad A. Dastgheib & Mahmoud Farhang

Authors
  1. Mohammad A. Dastgheib
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  2. Mahmoud Farhang
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Correspondence to Mahmoud Farhang.

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This work was supported in part by Iran National Elites Foundation (INEF) and Iran National Science Foundation (INSF).

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Dastgheib, M.A., Farhang, M. A digital pseudo-random number generator based on sawtooth chaotic map with a guaranteed enhanced period. Nonlinear Dyn 89, 2957–2966 (2017). https://doi.org/10.1007/s11071-017-3638-3

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