Using Reed-Solomon codes in the (U | U + V ) construction and an application to cryptography

Abstract : —In this paper we present a modification of Reed-Solomon codes that beats the Guruswami-Sudan 1 − √ R decoding radius of Reed-Solomon codes at low rates R. The idea is to choose Reed-Solomon codes U and V with appropriate rates in a (U | U + V) construction and to decode them with the Koetter-Vardy soft information decoder. We suggest to use a slightly more general version of these codes (but which has the same decoding performance as the (U | U + V)-construction) for being used in code-based cryptography , namely to build a McEliece scheme. The point is here that these codes not only perform nearly as well (or even better in the low rate regime) as Reed-Solomon codes, but also that their structure seems to avoid the Sidelnikov-Shestakov attack which broke a previous McEliece proposal based on generalized Reed-Solomon codes.
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Submitted on : Tuesday, December 6, 2016 - 3:08:31 PM
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Irene Márquez-Corbella, Jean-Pierre Tillich. Using Reed-Solomon codes in the (U | U + V ) construction and an application to cryptography. International Symposium on Information Theory, Jul 2016, Barcelona, Spain. ⟨hal-01410201⟩

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