标题： 在$\left( U\mid U+V\right)$构造中使用里德-所罗门码及其在密码学中的应用 显示英文标题

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

摘要： 在本文中，我们提出了一种对Reed-Solomon码的修改，该修改在低速率下超过了Reed-Solomon码的Guruwami-Sudan$1-\sqrt{R}$解码半径$R$。 其思路是选择适当的Reed-Solomon码$U$和$V$，在$\left( U\mid U+V\right)$构造中使用合适的速率，并用Koetter-Vardy软信息解码器进行解码。 我们建议使用这些码的一个稍微更通用的版本（但其解码性能与$\left( U\mid U+V\right)$构造相同）用于基于码的密码学，即构建McEliece方案。 这里的关键是，这些码不仅在性能上几乎与Reed-Solomon码相当（甚至在低速率情况下表现更好），它们的结构似乎可以避免Sidelnikov-Shestakov攻击，该攻击破坏了基于广义Reed-Solomon码的先前McEliece提案。 显示英文摘要

摘要： 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.