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Etudes de systèmes cryptographiques construits à l'aide de codes correcteurs, en métrique de Hamming et en métrique rang.

Abstract : This thesis explores two different approaches to reduce the size of the public key cryptosystems based on error correcting codes. One idea that meaning is the use of families of codes with high correction capability, such as geometric codes. Since the attack Sidelnikov and Shestakov, we know that an attacker can find the structure of a Reed-Solomon code used in the public key. We have managed to adapt to the hyperelliptic curves attack method developed by cons Minder elliptic codes. We are particularly able to attack in polynomial time system Janwa and Moreno on codes developed geometric genus 2 or more. A second idea is the use of error correcting codes for the rank metric. This enormously complicates the decoding attacks, which can no longer use a window of information to try to decode. We can thus protect themselves against attacks decoding using a public key of Bollywood. In this context, we present a public key cryptosystem based on the problem of reconstruction of linear polynomials. We show that our system is fast, uses keys of reasonable size, and resists all known attacks in the state of the art.
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Submitted on : Wednesday, July 21, 2010 - 10:31:15 AM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM
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Cédric Faure. Etudes de systèmes cryptographiques construits à l'aide de codes correcteurs, en métrique de Hamming et en métrique rang.. Sciences de l'information et de la communication. Ecole Polytechnique X, 2009. Français. ⟨pastel-00005288⟩

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