Abstract. 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 pseudo-random 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 3.35×10 10 random numbers in very short time.Keywords: Cryptography, Chaos, Randomness, Under-sampling, Pseudo-random number generator.Résumé. Nous proposons un nouveau mécanisme de sous-échantillonnage de nombres chaotiques obtenus par couplage en anneau de fonctions unidimensionnelles. Dans le cas de 2 fonctions couplées, ce mécanisme permet de construire un Générateur de Nombres Pseudo-Aléatoires (GNPA) qui satisfait tous les tests NIST. Ce nouveau sous-échantillonnage géométrique est très efficace pour générer deux séries parallèles de nombres pseudo-aléatoires, comme nous le montrons enétudiant très soigneusement leurs propriétés pour des suites de nombres allant jusqu'à 10 12 nombres consécutifs de l'application couplée en anneau, ce qui fournit plus de 3.35 × 10 10 nombres aléatoires en un temps très court. AMSC: 9A20, 11K45, 37H10, 65P20 Mots-clefs: Cryptographie, Chaos, Aléatoire, Sous-échantillonnage, Générateurs de nombres pseudoaléatoires. Article published online by EDP Sciences and available at http://www.esaim-proc.org or http://dx
Contents
This paper is devoted to the design of new chaotic Pseudo Random Number Generator (CPRNG). Exploring several topologies of network of 1-D coupled chaotic mapping, we focus first on two dimensional networks. Two coupled maps are studied: T T L RC non-alternative, and T T L SC alternative. The primary idea of the novel maps has been based on an original coupling of the tent and logistic maps to achieve excellent random properties and homogeneous /uniform/ density in the phase plane, thus guaranteeing maximum security when used for chaos base cryptography. In this aim a new nonlinear CPRNG: MT T L SC 2 is proposed. In addition, we explore higher dimension and the proposed ring coupling with injection mechanism enables us to achieve the strongest security requirements.
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