论文标题
在任意勾结和窃听模式下取回对称私人信息的能力
The Capacity of Symmetric Private Information Retrieval under Arbitrary Collusion and Eavesdropping Patterns
论文作者
论文摘要
我们在任意勾结和复制数据库的窃听模式下研究对称私人信息检索（SPIR）问题。我们找到了其容量，与原始SPIR问题的容量相同，其数据库数量$ n $被数字$ f^*$代替。数字$ f^*$是线性编程问题的最佳解决方案，该问题是关节模式的函数，即勾结和窃听模式的结合。这是第一个结果表明，两个任意模式如何共同影响PIR问题的能力。我们得出一个结论，即对于肺活问题，勾结和窃听的约束在容量方面是可以互换的。作为我们结果的特殊情况，还发现了在任意勾结模式下的肺活问题的能力以及在任意窃听模式下PIR问题的能力。
We study the symmetric private information retrieval (SPIR) problem under arbitrary collusion and eavesdropping patterns for replicated databases. We find its capacity, which is the same as the capacity of the original SPIR problem with the number of databases $N$ replaced by a number $F^*$. The number $F^*$ is the optimal solution to a linear programming problem that is a function of the joint pattern, which is the union of the collusion and eavesdropping pattern. This is the first result that shows how two arbitrary patterns collectively affect the capacity of the PIR problem. We draw the conclusion that for SPIR problems, the collusion and eavesdropping constraints are interchangeable in terms of capacity. As special cases of our result, the capacity of the SPIR problem under arbitrary collusion patterns and the capacity of the PIR problem under arbitrary eavesdropping patterns are also found.
