Using Reed-Solomon codes in the (U | U + V ) construction and an application to cryptography
Irene Márquez-Corbella, Jean–Pierre Tillich · 2016
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.