A new framework for interference alignment in secure and private information retrieval (PIR) from colluding servers is proposed, generalizing the original cross-subspace alignment (CSA) codes proposed by Jia, Sun, and Jafar. The general scheme is built on algebraic geometry codes and explicit constructions with replicated storage are given over curves of genus zero and one. It is shown that the proposed scheme offers interesting tradeoffs between the field size, file size, number of colluding servers, and the total number of servers. When the field size is fixed, this translates in some cases to higher retrieval rates than those of the original scheme. In addition, the new schemes exist also in cases where the original ones do not.

翻译：本文提出了一种用于从合谋服务器进行安全私有信息检索（PIR）的干扰对齐新框架，该框架推广了Jia、Sun和Jafar最初提出的跨子空间对齐（CSA）码。该通用方案建立在代数几何码之上，并在亏格为零和一的曲线上给出了具有复制存储的显式构造。研究表明，所提方案在域大小、文件大小、合谋服务器数量以及服务器总数之间提供了有意义的权衡。当域大小固定时，在某些情况下这转化为比原始方案更高的检索率。此外，新方案在原始方案不存在的某些情况下同样适用。