RankSign：一种基于秩度量的高效签名算法
RankSign: an efficient signature algorithm based on the rank metric
摘要：
在本文中，我们提出了一种新的方法，基于代码的签名，特别是利用秩度量码。当经典的方法是通过解码算法找到一个综合征的唯一原像时，我们建议引入擦除和错误的混合解码的概念来构建签名方案。在这种情况下，困难的问题变成了，就像基于格的密码学中的情况一样，找到一个重量高于Gilbert-Varshamov界限的原像（出现许多解的情况），而不是找到一个重量低于Gilbert-Varshamov界限的唯一原像。本文描述了RankSign：针对最近提出的低秩奇偶检验（LRPC）码，基于一种新的纠删纠错混合译码算法，提出了一种新的秩度量签名算法。我们解释它是如何可能的（取决于参数的选择），以获得一个完整的解码算法，这是能够找到一个合理的排名权重的任何随机综合征的一个非常强的概率的原像。我们研究了我们的签名算法的语义安全性，并展示了如何有可能减少不可伪造性直接攻击的公共矩阵，使没有信息泄漏通过签名。最后，我们给出了我们的方案的参数的几个例子，其中一些具有大小为$11,520$位的公钥和大小为$1728$位的签名。此外，该方案可以是非常快速的小基场。
英文摘要：
In this paper we propose a new approach to code-based signatures that makes use in particular of rank metric codes. When the classical approach consists in finding the unique preimage of a syndrome through a decoding algorithm, we propose to introduce the notion of mixed decoding of erasures and errors for building signature schemes. In that case the difficult problem becomes, as is the case in lattice-based cryptography, finding a preimage of weight above the Gilbert-Varshamov bound (case where many solutions occur) rather than finding a unique preimage of weight below the Gilbert-Varshamov bound. The paper describes RankSign: a new signature algorithm for the rank metric based on a new mixed algorithm for decoding erasures and errors for the recently introduced Low Rank Parity Check (LRPC) codes. We explain how it is possible (depending on choices of parameters) to obtain a full decoding algorithm which is able to find a preimage of reasonable rank weight for any random syndrome with a very strong probability. We study the semantic security of our signature algorithm and show how it is possible to reduce the unforgeability to direct attacks on the public matrix, so that no information leaks through signatures. Finally, we give several examples of parameters for our scheme, some of which with public key of size $11,520$ bits and signature of size $1728$ bits. Moreover the scheme can be very fast for small base fields.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
