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Cryptography-Based Chaos via Geometric Undersampling of Ring-Coupled Attractors

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Mathematical Models, Methods and Applications

Part of the book series: Industrial and Applied Mathematics ((INAMA))

Abstract

We propose a new mechanism for undersampling chaotic numbers obtained by the ring coupling of one-dimensional maps. In the case of two coupled maps, this mechanism allows the building of a PRNG which passes all NIST tests. This new geometric undersampling is very effective for generating two parallel streams of pseudo-random numbers, as we show, computing carefully their properties, up to sequences of 1012 consecutives iterates of the ring-coupled mapping which provides more than 3.35 × 1010 random numbers in very short time. Both three- and four-dimensional cases can be managed in the same way. In addition, we recall a novel method of noise-resisting ciphering. The originality lies in the use of a chaotic pseudo-random number generator: several cogenerated sequences can be used at different steps of the ciphering process, as they present the strong property of being uncorrelated. Each letter of the initial alphabet of the plain text is encoded as a subinterval of [−1, 1]. The bounds of each interval are defined in function of the known bound of the additive noise. A pseudo-random sequence is used to enhance the complexity of the ciphering. The transmission consists of a substitution technique inside a chaotic carrier, depending on another cogenerated sequence. This novel noise-resisting ciphering method can be used with geometric undersampling when four mappings are coupled.

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Authors and Affiliations

  1. Université de NICE Sophia-Antipolis, Laboratoire J. A. Dieudonné, UMR CNRS 7351, Parc Valrose, 06108, Nice, Cedex 02, France

    René Lozi

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  1. René Lozi
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Correspondence to René Lozi .

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Editors and Affiliations

  1. School of Basic Sciences and Research, Sharda University, Greater Noida, Uttar Pradesh, India

    Abul Hasan Siddiqi

  2. Guru Nanak Dev University, Amritsar, Punjab, India

    Pammy Manchanda

  3. University, Guru Gobind Singh Indraprastha, Dwarka, India

    Rashmi Bhardwaj

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Lozi, R. (2015). Cryptography-Based Chaos via Geometric Undersampling of Ring-Coupled Attractors. In: Siddiqi, A., Manchanda, P., Bhardwaj, R. (eds) Mathematical Models, Methods and Applications. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-287-973-8_1

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