论文标题
恒星产品PIR方案，带有勾结服务器在小领域
Star Product PIR Schemes with Colluding Servers over Small Fields
论文作者
论文摘要
私人信息检索（PIR）是B. Chor，O。Goldreich，E。Kushilevitz和M. Sudan在1995年的论文中提出的。对于MDS编码的分布式存储系统，提出了私人信息检索，并研究了MDS编码分布式存储的PIR方案的能力。从一般编码的分布式存储系统带有勾结服务器的恒星产品PIR方案是在一般有限场上构建的。这些恒星产品方案对字段的大小没有限制，可以在大量服务器上构建用于编码的分布式存储。在本文中，我们首先提出并证明了单型类型上限在存储速率，勾结服务器的比率以及恒星产品PIR方案的检索速率。其次，分析了来自代数几何（AG）代码的编码分布式存储的Star产品PIR方案。我们证明，当服务器的数量转到无穷大时，恒星产品PIR方案带有用于Ag编码的分布式存储的串联服务器的胶结服务器的参数即可接闭到Singleton类型上限，如果该场很大。与星级产品PIR方案进行比较，用于编码和芦苇编码的分布式存储的Reed-Solomon编码和Reed-Muller编码，我们表明，带有AG编码的分布式存储的PIR方案具有其性能优势。讨论了基于Ag代码的星形产品PIR方案，并讨论了串联，拜占庭式和无反应服务器。还研究了基于$ Q $ - 元环代码的星星产品PIR计划，用于复制数据存储。当存储代码是Reed-Muller代码时，检索代码的最佳选择并不总是Reed-Muller代码。
Private Information Retrieval (PIR) was first proposed by B. Chor, O. Goldreich, E. Kushilevitz and M. Sudan in their 1995 FOCS paper. For MDS coded distributed storage system private information retrieval was proposed and the capacity of PIR schemes for MDS coded distributed storage was studied. Star product PIR schemes from general coded distributed storage system with colluding servers were constructed over general finite fields. These star product schemes has no restriction on the sizes of fields and can be constructed for coded distributed storage across large number of servers. In this paper we first propose and prove the Singleton type upper bound on the storage rate, ratio of colluding servers and the retrieval rate of the star product PIR schemes. Secondly star product PIR schemes for coded distributed storage from algebraic geometry (AG) codes are analysed. We prove that when the number of the servers goes to the infinity, star product PIR schemes with colluding servers for AG-coded distributed storage have parameters closing to the Singleton type upper bound if the field is large. Comparing with the star product PIR schemes for Reed-Solomon coded and Reed-Muller coded distributed storage we show that PIR schemes with colluding servers for AG coded distributed storage have their performance advantages. AG-code based star product PIR schemes with colluding, Byzantine and unresponsive servers are discussed. $q$-ary cyclic code based star product PIR schemes for replicated data storage are also studied. When the storage code is the Reed-Muller code, the best choice of the retrieval code is not always the Reed-Muller code.
