New Enciphering Algorithm Based on Chaotic Generalized Hénon Map

Octaviana Datcu 1 Jean-Pierre Barbot 2, 3 Adriana Vlad 4
1 ECS-lab EA 3649
ECS-Lab - Électronique et Commande des Systèmes Laboratoire
3 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : The paper belongs to the field of chaotic based cryptography. It relies on some ideas from classical fundamentals as mixing functions suggested by C.E. Shannon for secrecy systems, and on the known publication of M.S. Baptista, a paper essentially implying the ergodicity assumption of the chaotic signal in cipher design. In this paper, the first step was to choose a chaotic system of a higher dimension than Baptista used, aiming to obtain a more complex system having a hyperchaotic behavior. The proposed algorithm is based on Generalized Hénon Map (3D), stated in literature as hyperchaotic for a number of bifurcation parameters. The paper advances a new mixing enciphering scheme based on the Generalized Hénon Map (GHM), which may be used as an inner element in a cipher, providing a good practical diffusion and confusion. A random variable transform is applied on the state of the chaotic system at each iteration in order to obtain a new random variable of a quasi uniform law. This new random variable is further transformed, through a series of other functions containing elements of the secret key, into a discrete random variable. The discrete values - which are ASCII numbers - are combined by a simple relation with the plain message, also in ASCII format. It is obtained a first mask of the original message, involving the GHM. On this result (in its binary representation form) other simple transformations that depend on the state of the GHM are applied. That finally allows getting a transformed version of the message that can be included in one of the states of the GHM without disturbing its chaotic behavior. The results, including a perception of the diffusion and the confusion involved, are illustrated on natural text and jpeg image.
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Submitted on : Thursday, January 10, 2013 - 10:24:54 PM
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Octaviana Datcu, Jean-Pierre Barbot, Adriana Vlad. New Enciphering Algorithm Based on Chaotic Generalized Hénon Map. CHAOS 2010, 3rd Chaotic Modeling and Simulation International Conference, Jun 2010, Chania, Crete, Greece. 2010. 〈hal-00772660〉



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