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An algebraic state estimation approach for the recovery of chaotically encrypted messages

Hebertt Sira-Ramirez 1 Michel Fliess 2, 3
3 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
Abstract : In this article we use a variant of recently introduced algebraic state estimation method obtained from a fast output signal time derivatives computation process. The fast time derivatives calculations are entirely based on the consequences of using the "algebraic approach" in linear system description. Here we demonstrate, through computer simulations, the effectiveness of the proposed algebraic approach in the accurate and fast (i.e. non asymptotic) estimation of the chaotic states in some of the most popular chaotic systems. The propsed state estimation method can then be used in a coding-decoding process of a secret message transmission using the message modulated chaotic system states and the reliable transmission of the chaotic system output. Simulation examples, using Chen's chaotic system output and the Rossler system, demonstrate the importance of the proposed fast state estimation method in the accurate extraction of a chaotically encrypted message. In our simulation results, the proposed approach is shown to be quite robust with respect to (computer generated) transmission noise perturbations. We also propose a way to evade computational singularities associated with the local lack of observability of certain chaotic system outputs and still carry out the encrypting and decoding of secret messages in a reliable manner.
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https://hal.inria.fr/inria-00001247
Contributor : Michel Fliess <>
Submitted on : Thursday, April 13, 2006 - 9:50:24 PM
Last modification on : Friday, April 2, 2021 - 11:09:14 AM
Long-term archiving on: : Saturday, April 3, 2010 - 9:08:08 PM

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Hebertt Sira-Ramirez, Michel Fliess. An algebraic state estimation approach for the recovery of chaotically encrypted messages. International journal of bifurcation and chaos in applied sciences and engineering , World Scientific Publishing, 2006, 16 (2), pp.295-309. ⟨10.1142/S0218127406014812⟩. ⟨inria-00001247⟩

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