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Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications

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Listed:
  • Wafaa S. Sayed
  • Ahmed G. Radwan
  • Ahmed A. Rezk
  • Hossam A. H. Fahmy

Abstract

Chaotic systems appear in many applications such as pseudo-random number generation, text encryption, and secure image transfer. Numerical solutions of these systems using digital software or hardware inevitably deviate from the expected analytical solutions. Chaotic orbits produced using finite precision systems do not exhibit the infinite period expected under the assumptions of infinite simulation time and precision. In this paper, digital implementation of the generalized logistic map with signed parameter is considered. We present a fixed-point hardware realization of a Pseudo-Random Number Generator using the logistic map that experiences a trade-off between computational efficiency and accuracy. Several introduced factors such as the used precision, the order of execution of the operations, parameter, and initial point values affect the properties of the finite precision map. For positive and negative parameter cases, the studied properties include bifurcation points, output range, maximum Lyapunov exponent, and period length. The performance of the finite precision logistic map is compared in the two cases. A basic stream cipher system is realized to evaluate the system performance for encryption applications for different bus sizes regarding the encryption key size, hardware requirements, maximum clock frequency, NIST and correlation, histogram, entropy, and Mean Absolute Error analyses of encrypted images.

Suggested Citation

  • Wafaa S. Sayed & Ahmed G. Radwan & Ahmed A. Rezk & Hossam A. H. Fahmy, 2017. "Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications," Complexity, Hindawi, vol. 2017, pages 1-21, February.
  • Handle: RePEc:hin:complx:8692046
    DOI: 10.1155/2017/8692046
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    References listed on IDEAS

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    1. Kanso, Ali & Smaoui, Nejib, 2009. "Logistic chaotic maps for binary numbers generations," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2557-2568.
    2. Persohn, K.J. & Povinelli, R.J., 2012. "Analyzing logistic map pseudorandom number generators for periodicity induced by finite precision floating-point representation," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 238-245.
    3. Hsieh, David A, 1991. "Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-1877, December.
    4. Basalto, N. & Bellotti, R. & De Carlo, F. & Facchi, P. & Pascazio, S., 2005. "Clustering stock market companies via chaotic map synchronization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 196-206.
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    Cited by:

    1. Chunlei Fan & Qun Ding, 2019. "Effects of Limited Computational Precision on the Discrete Chaotic Sequences and the Design of Related Solutions," Complexity, Hindawi, vol. 2019, pages 1-10, January.
    2. Valle, João & Bruno, Odemir M., 2024. "Dynamics and patterns of the least significant digits of the infinite-arithmetic precision logistic map orbits," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Elmanfaloty, Rania A. & Abou-Bakr, Ehab, 2019. "Random property enhancement of a 1D chaotic PRNG with finite precision implementation," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 134-144.
    4. Nardo, Lucas G. & Nepomuceno, Erivelton G. & Arias-Garcia, Janier & Butusov, Denis N., 2019. "Image encryption using finite-precision error," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 69-78.

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