Sakkour, Bassem (2007) Decoding of Reed-Muller codes and applications to cryptography. PhD thesis UMA-ENSTA, ENSTA / UMA - Laboratoire de Mathématiques Appliquées, EP/X p.145.
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Alternative Locations: http://www.imprimerie.polytechnique.fr/Theses/Files/Sakkour.pdf
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.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Thesis Supervisor: | Charpin, Pascale |
| Date: | April 2007 |
| Board of examiners: | François, Morain and Grigory, Kabatyanskiy and Sami, Harari and Thierry, Berger and Nicolas, Sendrier and Loidreau, Pierre |
| Ecole Doctorale: | ED 447 ECOLE DOCTORALE DE L'ECOLE POLYTECHNIQUE |
| Discipline: | UMA-ENSTA |
| Collection (Fonds): | EP/X ENSTA |
| Institution: | EP/X |
| Department: | ENSTA / UMA - Laboratoire de Mathématiques Appliquées |
| Subjects: | 2. Information and Communication Sciences and Technologies |
| Uncontrolled Keywords: | Error correcting code, Reed-Muller, Plotkin, Maximum likelihood, Code correcteur d'erreur, Reed-Muller, Plotkin, Maximum de vraisemblance |
Table of content
Introduction à la théorie algébrique des codes codes de Reed-Muller
Décodage des codes de Reed-Muller
Algorithme de Sidel'nikov et Pershakov
Algorithme de Sidel'nikov et Pershakov ModifiéSimulation et résultats expérimentaux
| ID Code: | 2412 |
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| Deposited By: | Laurence Vidament |
| Deposited On: | 02 May 2007 |
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