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.
翻译:私人信息检索( PIR) 计划( 与或不与串通服务器一起) 是为现实的编码分布式数据存储系统而提议的。 由 R. Freij- Hollanti、 O. W. Gnilke、 C. Hollanti 和 A. Karpuk 于2017年在一般限域内建造了带有普通编码分布式存储系统串通服务器的星产品 PIR 计划。 这些带有串通服务器的恒星产品 PIR 计划适合在小域内存储文件, 并且可以为大量服务器的编码分布式共享存储系统建造。 在本文中, 考虑找到良好检索代码的问题。 一般来说, 如果存储代码是一个二元 Reed- Muller 代码, 则检索代码不必是普通的双元Reed- Muller 代码。 当存储代码包含一些特殊代码时, 非零检索率恒星 PIR 产品 PIR 计划与串通服务器只能保护少量的编码。 我们还举例子, 显示当存储代码不是存储代码是一个好的系统, 与普通存储周期规则的系统中, 最佳选择是普通的存储码。