多方私有集合相交问题的信息论方法
Multi-Party Private Set Intersection: An Information-Theoretic Approach
摘要：
研究了多方私有集的交集问题。在MP-PSI中，存在$M$方，每个方在$N_i$复制和非共谋数据库上存储数据集$\mathcal{p}_i$，并且我们希望计算数据集$\cap_{i=1}^M \mathcal{p}_i$的交集，而不向任何一方泄漏集合交集之外的任何信息。我们考虑一个特定的通信协议，其中一方，称为领导者党，发起的MP-PSI协议发送查询，其余各方被称为客户端。客户端不允许相互通信。我们提出了一个信息理论的计划，私下计算的交集$\cap_{i=1}^M \mathcal{p}_i$与$D = \min_{t \in \{1, \cdots, M\}} \sum_{i \in \{1, \cdots M\}\setminus {t}} \left\lceil \frac{|\mathcal{p}_t|N_i}{N_i-1}\right\rceil$的下载成本。类似于2方PSI问题，我们的计划建立在PSI问题和多消息对称私有信息检索（MM-SPIR）问题之间的联系。我们的计划是一个非平凡的推广2方PSI计划，因为它需要一个复杂的设计共享的共同随机性。有趣的是，在下载成本方面，我们的计划不会招致任何惩罚，由于更严格的隐私限制的MP-PSI问题相比，2方PSI问题。
英文摘要：
We investigate the problem of multi-party private set intersection (MP-PSI). In MP-PSI, there are $M$ parties, each storing a data set $\mathcal{p}_i$ over $N_i$ replicated and non-colluding databases, and we want to calculate the intersection of the data sets $\cap_{i=1}^M \mathcal{p}_i$ without leaking any information beyond the set intersection to any of the parties. We consider a specific communication protocol where one of the parties, called the leader party, initiates the MP-PSI protocol by sending queries to the remaining parties which are called client parties. The client parties are not allowed to communicate with each other. We propose an information-theoretic scheme that privately calculates the intersection $\cap_{i=1}^M \mathcal{p}_i$ with a download cost of $D = \min_{t \in \{1, \cdots, M\}} \sum_{i \in \{1, \cdots M\}\setminus {t}} \left\lceil \frac{|\mathcal{p}_t|N_i}{N_i-1}\right\rceil$. Similar to the 2-party PSI problem, our scheme builds on the connection between the PSI problem and the multi-message symmetric private information retrieval (MM-SPIR) problem. Our scheme is a non-trivial generalization of the 2-party PSI scheme as it needs an intricate design of the shared common randomness. Interestingly, in terms of the download cost, our scheme does not incur any penalty due to the more stringent privacy constraints in the MP-PSI problem compared to the 2-party PSI problem.
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