论文标题
在代码和学习方面学习错误字段的错误
On Codes and Learning With Errors over Function Fields
论文作者
论文摘要
对于线性代码的解码问题的结构化版本，寻找减少决策版本的搜索是一个漫长的开放问题。基于晶格的设置中的此类结果是使用数字字段进行的：多项式lwe，ring-lwe，module-lwe等。我们提出了LWE问题的功能字段版本。这个新的框架导致了关于结构化代码的另一种观点，例如准循环代码，加强了基于晶格和基于代码的密码学之间的联系。特别是，我们获得了第一次搜索结构化代码的决策。遵循基于晶格的密码学中的历史结构，我们将构造与循环磁场的功能场类似物（即Carlitz Extensions）实例化，从而搜索了对RING-LPN的各种版本的决策搜索，这些版本降低了RING-LPN，这些版本具有确保多方计算和人为方案的应用程序。
It is a long standing open problem to find search to decision reductions for structured versions of the decoding problem of linear codes. Such results in the lattice-based setting have been carried out using number fields: Polynomial-LWE, Ring-LWE, Module-LWE and so on. We propose a function field version of the LWE problem. This new framework leads to another point of view on structured codes, e.g. quasi-cyclic codes, strengthening the connection between lattice-based and code-based cryptography. In particular, we obtain the first search to decision reduction for structured codes. Following the historical constructions in lattice-based cryptography, we instantiate our construction with function fields analogues of cyclotomic fields, namely Carlitz extensions, leading to search to decision reductions on various versions of Ring-LPN, which have applications to secure multi party computation and to an authentication protocol.
