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Statistical complexity measure of pseudorandom bit generators

Author

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  • González, C.M.
  • Larrondo, H.A.
  • Rosso, O.A.

Abstract

Pseudorandom number generators (PRNG) are extensively used in Monte Carlo simulations, gambling machines and cryptography as substitutes of ideal random number generators (RNG). Each application imposes different statistical requirements to PRNGs. As L’Ecuyer clearly states “the main goal for Monte Carlo methods is to reproduce the statistical properties on which these methods are based whereas for gambling machines and cryptology, observing the sequence of output values for some time should provide no practical advantage for predicting the forthcoming numbers better than by just guessing at random”. In accordance with different applications several statistical test suites have been developed to analyze the sequences generated by PRNGs. In a recent paper a new statistical complexity measure [Phys. Lett. A 311 (2003) 126] has been defined. Here we propose this measure, as a randomness quantifier of a PRNGs. The test is applied to three very well known and widely tested PRNGs available in the literature. All of them are based on mathematical algorithms. Another PRNGs based on Lorenz 3D chaotic dynamical system is also analyzed. PRNGs based on chaos may be considered as a model for physical noise sources and important new results are recently reported. All the design steps of this PRNG are described, and each stage increase the PRNG randomness using different strategies. It is shown that the MPR statistical complexity measure is capable to quantify this randomness improvement. The PRNG based on the chaotic 3D Lorenz dynamical system is also evaluated using traditional digital signal processing tools for comparison.

Suggested Citation

  • González, C.M. & Larrondo, H.A. & Rosso, O.A., 2005. "Statistical complexity measure of pseudorandom bit generators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 281-300.
    • Handle: RePEc:eee:phsmap:v:354:y:2005:i:c:p:281-300
    DOI: 10.1016/j.physa.2005.02.054
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    Citations

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    Cited by:

    1. Zunino, L. & Pérez, D.G. & Garavaglia, M. & Rosso, O.A., 2007. "Wavelet entropy of stochastic processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 503-512.
    2. Valle, João & Machicao, Jeaneth & Bruno, Odemir M., 2022. "Chaotical PRNG based on composition of logistic and tent maps using deep-zoom," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Avaroğlu, Erdinç, 2020. "The implementation of ring oscillator based PUF designs in Field Programmable Gate Arrays using of different challenge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 546(C).
    4. Etem, Taha & Kaya, Turgay, 2020. "A novel True Random Bit Generator design for image encryption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    5. Eduarda T. C. Chagas & Marcelo Queiroz‐Oliveira & Osvaldo A. Rosso & Heitor S. Ramos & Cristopher G. S. Freitas & Alejandro C. Frery, 2022. "White Noise Test from Ordinal Patterns in the Entropy–Complexity Plane," International Statistical Review, International Statistical Institute, vol. 90(2), pages 374-396, August.

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