Using Reed-Solomon codes in the $\left( U\mid U+V\right)$ construction and an application to cryptography
Abstract
In this paper we present a modification of Reed-Solomon codes that beats the Guruwami-Sudan $1-\sqrt{R}$ 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 $\left( U\mid U+V\right)$ 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 $\left( U\mid U+V\right)$-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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2016
- DOI:
- 10.48550/arXiv.1601.08227
- arXiv:
- arXiv:1601.08227
- Bibcode:
- 2016arXiv160108227M
- Keywords:
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- Computer Science - Cryptography and Security;
- Computer Science - Information Theory