Reproducible families of codes and cryptographic applications
Reproducible families of codes and cryptographic applications
复制标题
DOI：
10.1515/jmc-2020-0003
复制
发表时间：
2021-01
影响因子：
1.2
通讯作者：
Paolo Santini;Edoardo Persichetti;M. Baldi
中科院分区：
文献类型：
--
作者：
Paolo Santini;Edoardo Persichetti;M. Baldi
近年来，结构化线性分组码，如循环码、准循环码和准并元码，在差错控制和基于码的密码学中起着越来越重要的作用。一些著名的结构化线性分组码族已经被单独和深入地研究，而没有寻找它们之间可能的桥梁。在这篇文章中，我们从这种类型的著名例子开始，并将它们推广到更广泛的一类代码，我们称之为可重复代码。一些可再生码族具有这样的性质，即它们可以完全从少量的签名向量生成，因此允许可以以非常紧凑的方式描述的矩阵。我们表示这些代码作为companies可再生的代码，并表明它们包括已知的companies可描述的代码，如准循环和准并元码的家庭。然后，我们考虑这种类型的代码的一些加密应用程序，并表明它们的使用可以是有利的，以阻止一些当前的攻击依赖于结构化代码的密码系统。这表明，我们介绍的一般框架可能使未来的发展基于代码的密码学。
Abstract Structured linear block codes such as cyclic, quasi-cyclic and quasi-dyadic codes have gained an increasing role in recent years both in the context of error control and in that of code-based cryptography. Some well known families of structured linear block codes have been separately and intensively studied, without searching for possible bridges between them. In this article, we start from well known examples of this type and generalize them into a wider class of codes that we call ℱ-reproducible codes. Some families of ℱ-reproducible codes have the property that they can be entirely generated from a small number of signature vectors, and consequently admit matrices that can be described in a very compact way. We denote these codes as compactly reproducible codes and show that they encompass known families of compactly describable codes such as quasi-cyclic and quasi-dyadic codes. We then consider some cryptographic applications of codes of this type and show that their use can be advantageous for hindering some current attacks against cryptosystems relying on structured codes. This suggests that the general framework we introduce may enable future developments of code-based cryptography.