We consider the problem of Private Information Retrieval with Private Side Information (PIR-PSI), wherein a user wants to retrieve a file from replication based non-colluding databases by using the prior knowledge of a subset of the files stored on the databases. The PIR-PSI framework ensures that the privacy of the demand and the side information are jointly preserved, thereby finding potential applications when multiple files have to be downloaded spread across different time-instants. Although the capacity of the PIR-PSI setting is known, we observe that the underlying capacity achieving code construction uses Maximum Distance Separable (MDS) codes thereby contributing to high computational complexity when retrieving the demand. Pointing at this drawback of MDS-based PIR-PSI codes, we propose XOR-based PIR-PSI codes for a simple yet non-trivial setting of two non-colluding databases and two side information files at the user. While our codes offer substantial reduction in complexity when compared to MDS based codes, the code-rate marginally falls short of the capacity of the PIR-PSI setting. Nevertheless, we show that our code-rate is strictly higher than that of XOR-based codes for PIR with no side information, thereby implying that our codes can be useful when downloading multiple files in a sequential manner, instead of applying XOR-based PIR codes on each file.
翻译:我们考虑了私隐信息检索私隐侧信息(PIR-PSI)问题,用户希望通过使用数据库中储存的一组文件的先前知识,从基于复制的非污染数据库检索基于非污染数据库的文件。PIR-PSI框架确保联合保存需求隐私和侧面信息,从而在多个文件必须下载在不同时间用户之间时找到潜在的应用程序。虽然PIR-PSI设置的能力是众所周知的,但我们看到,实现代码构建的基本能力使用最大距离代码,从而在检索需求时导致高计算复杂性。指出基于MDS的PIR-PSI代码的这一退出,我们建议以XOR为基础的PIR-PSI代码编码用于简单但非三边设置的两个非循环数据库和用户的两个侧面信息文件。虽然与基于MDS的代码相比,我们的代码的复杂程度大大降低,但代码在重现PIR-PSI文件设定能力方面略短于PIR的计算能力。然而,我们提出,在应用基于MSIR的多级代码时,我们的代码可以严格地将我们的X的代码用于下载。