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Chapitre D'ouvrage Année : 2015

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

René Lozi

Résumé

We propose a new mechanism for undersampling chaotic numbers obtained by the ring coupling of one-dimensional maps. In the case of 2 coupled maps this mechanism allows the building of a PRNG which passes all NIST Test. This new geometric undersampling is very effective for generating 2 parallel streams of pseudorandom numbers, as we show, computing carefully their properties, up to sequences of 10^12 consecutives iterates of the ring coupled mapping which provides more than 3.35 x 10^10 random numbers in very short time. Both 3 and 4 dimension 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 co-generated sequences can be used at different steps of the ciphering process, since 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 4 mappings are coupled.
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Dates et versions

hal-01333364 , version 1 (17-06-2016)

Identifiants

  • HAL Id : hal-01333364 , version 1

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René Lozi. Cryptography-Based Chaos via Geometric Undersampling of Ring-Coupled Attractors. A. H. Siddiqi, P. Manchanda, R. Bhardwaj. Mathematical Models, Methods and Applications, Springer, pp.1-30, 2015, 978-981-287-971-4. ⟨hal-01333364⟩
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