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Low Rank Parity Check codes and their application to cryptography

Abstract : In this paper we introduce a new family of rank metric codes: the Low Rank Parity Check codes for which we propose an e cient probabilistic decoding algorithm. This family of codes can be seen as the equivalent of classical LDPC codes for the rank metric. We then propose to use these codes for cryptography in the McEliece encryption setting. At the di erence of previous encryption algorithms based on rank metric -especially based on Gabidulin codes -, the codes we use have a very poor structure. Our cryptosystem can be seen as an equivalent to the NTRU cryptosystem [16] (and also to the more recent MDPC[23] cryptosystem) in a rank metric context. Overall our system permits to achieve a very low public key of 1517 bits for a security of 280, moreover our system is very fast, with a decryption failure which can be made arbitrarily small.
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https://hal.archives-ouvertes.fr/hal-00913719
Contributor : Yolande Vieceli <>
Submitted on : Wednesday, December 4, 2013 - 12:12:25 PM
Last modification on : Thursday, January 11, 2018 - 6:26:29 AM

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  • HAL Id : hal-00913719, version 1

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Philippe Gaborit, Gaétan Murat, Olivier Ruatta, Gilles Zemor. Low Rank Parity Check codes and their application to cryptography. The International Workshop on Coding and Cryptography (WCC 13), Apr 2013, Bergen, Norway. 13 p. ⟨hal-00913719⟩

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