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Etude du décodage des codes de Reed-Muller et application à la cryptographie.

Abstract : In this thesis, we study the Reed-Muller codes which constitute one of the classes of error correcting codes the most studied, and most used in numerical communications. Thanks to their speed of encoding and decoding, they were in particular used for the satellite transmissions. They also have a strong bond with the concepts of Boolean functions. The study of Boolean functions constitutes the heart of the realization and the safety of secret key cryptography. Since the introduction of these codes, many decoding algorithms were introduced, and even today the study of their structure! in order to build decoding algorithms constitutes an interested field of research in coding theory and in cryptography for finding good linear, quadratic etc approximations to Boolean functions used in cryptography We expose a unifying point of view to all known decoding algorithms of this codes, this point of view is that of the discrete derivative. We expose a powerful algorithm for the decoding of the codes of order two, which we analyze then. We discuss the results of simulations of the algorithms studied for the small and average lengths of code. Simulation results show that the proposed algorithm decodes in practice much further that the other algorithms.
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Contributor : Ecole Polytechnique <>
Submitted on : Wednesday, July 28, 2010 - 3:08:07 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:04 AM
Long-term archiving on: : Friday, October 29, 2010 - 10:13:19 AM


  • HAL Id : pastel-00002412, version 1



Bassem Sakkour. Etude du décodage des codes de Reed-Muller et application à la cryptographie.. Informatique [cs]. Ecole Polytechnique X, 2007. Français. ⟨pastel-00002412⟩



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