论文标题
与勾结服务器的PIR方案中的存储和检索代码
Storage and Retrieval Codes in PIR Schemes with Colluding Servers
论文作者
论文摘要
已经为现实的编码分布式数据存储系统提出了私人信息检索（PIR）方案（带有或不使用碰撞服务器）。 Star Product Pir方案与R. Freij-Hollanti，O。W。Gnilke，C。Hollanti和A. Karpuk在一般有限的田地上建造了一般编码的分布式存储系统。这些明星产品PIR配件与胶合服务器的构造服务器适用于在小型字段中存储在小型字段上的存储和构造的分布系统，并构建了较大的分布系统。在本文有关有效的存储代码中，考虑了良好检索代码的问题。通常，如果存储代码是二进制芦苇 - 毛刺代码，则检索代码一般不需要是二进制芦苇 - 毛刺代码。事实证明，当存储代码包含一些特殊的代码字时，与勾结服务器的非零检索速率恒星产品PIR方案只能防止少量的串联服务器。我们还举例说明，当存储代码是一个良好的循环代码时，检索代码的最佳选择通常不是循环的。因此，在与勾结服务器的恒星产品PIR方案的设计中，使用存储代码和同一代数代码家族中的检索代码的方案并不总是有效的。
Private information retrieval (PIR) schemes (with or without colluding servers) have been proposed for realistic coded distributed data storage systems. Star product PIR schemes with colluding servers for general coded distributed storage system were constructed over general finite fields by R. Freij-Hollanti, O. W. Gnilke, C. Hollanti and A. Karpuk in 2017. These star product PIR schemes with colluding servers are suitable for the storage of files over small fields and can be constructed for coded distributed storage system with large number of servers. In this paper for an efficient storage code, the problem to find good retrieval codes is considered. In general if the storage code is a binary Reed-Muller code the retrieval code needs not to be a binary Reed-Muller code in general. It is proved that when the storage code contains some special codewords, nonzero retrieval rate star product PIR schemes with colluding servers can only protect against small number of colluding servers. We also give examples to show that when the storage code is a good cyclic code, the best choice of the retrieval code is not cyclic in general. Therefore in the design of star product PIR schemes with colluding servers, the scheme with the storage code and the retrieval code in the same family of algebraic codes is not always efficient.
