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Pseudo-random bit generator based on multi-modal maps

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Abstract

In this work we present a pseudo-random Bit Generator via unidimensional multi-modal discrete dynamical systems called k-modal maps. These multi-modal maps are based on the logistic map and are useful to yield pseudo-random sequences with longer period, i.e., in order to attend the problem of periodicity. In addition the pseudo-random sequences generated via multi-modal maps are evaluated with the statistical suite of test from NIST and satisfactory results are obtained when they are used as key stream. Furthermore, we show the impact of using these sequences in a stream cipher resulting in a better encryption quality correlated with the number of modals of the chaotic map. Finally, a statistical security analysis applied to cipher images is given. The proposed algorithm to encrypt is able to resist the chosen-plaintext attack and differential attack because the same set of encryption keys generates a different cipher image every time it is used.

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Acknowledgments

M. García-Martínez is doctoral fellow of the CONACYT in the Graduate Program on control and dynamical systems at DMAp-IPICYT. E. Campos-Cantón acknowledges the CONACYT financial support through project No. 181002.

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Authors and Affiliations

  1. División de Matemáticas Aplicadas, Instituto Potosino de Investigación Cientfica y Tecnológica, Camino a la Presa San José 2055, 78216, San Luis Potosí, S.L.P., México

    M. García-Martínez & E. Campos-Cantón

  2. Colegio de la Frontera Sur CHETUMAL, Av. del Centenario Km. 5.5, 77900, Chetumal, Q. Roo, México

    M. García-Martínez

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  1. M. García-Martínez
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  2. E. Campos-Cantón
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Correspondence to M. García-Martínez.

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García-Martínez, M., Campos-Cantón, E. Pseudo-random bit generator based on multi-modal maps. Nonlinear Dyn 82, 2119–2131 (2015). https://doi.org/10.1007/s11071-015-2303-y

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