English

Using Reed-Solomon codes in the $\left( U\mid U+V\right)$ construction and an application to cryptography

Cryptography and Security 2016-02-01 v1 Information Theory math.IT

Abstract

In this paper we present a modification of Reed-Solomon codes that beats the Guruwami-Sudan 1R1-\sqrt{R} decoding radius of Reed-Solomon codes at low rates RR. The idea is to choose Reed-Solomon codes UU and VV with appropriate rates in a (UU+V)\left( U\mid U+V\right) 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 performances as the (UU+V)\left( U\mid U+V\right)-construction) for 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, their structure seems to avoid the Sidelnikov-Shestakov attack which broke a previous McEliece proposal based on generalized Reed-Solomon codes.

Keywords

Cite

@article{arxiv.1601.08227,
  title  = {Using Reed-Solomon codes in the $\left( U\mid U+V\right)$ construction and an application to cryptography},
  author = {Irene Márquez-Corbella and Jean-Pierre Tillich},
  journal= {arXiv preprint arXiv:1601.08227},
  year   = {2016}
}
R2 v1 2026-06-22T12:39:40.391Z