Ateniese et al. (PKC 2011) introduced the concept of size-hiding private set intersection (SHI-PSI) and proposed a construction for two parties. The SHI-PSI protocol protects the privacy of input set content and better guarantees the privacy of the client set size. However, more practical protocols in multi-party scenarios have remained a research gap. In this paper, we propose a secure and feasible protocol named size-hiding multi-party private set intersection. Based on the Bloom filter, threshold homomorphic encryption and marking technique, the proposed protocol supports the private set intersection among multiple participants. Meanwhile, the set size privacy of the designated participant is preserved. The proposed protocol is proved to be secure against semi-honest participants under the decisional composite residuosity assumption. Finally, the efficiency of our protocol is illustrated through both performance analyses and comparisons of related work.

Ateniese 等人。(PKC 2011) 引入了大小隐藏私有集交集 (SHI-PSI) 的概念，并提出了两方的构造。SHI-PSI协议保护了输入集内容的隐私性，更好地保证了客户端集大小的隐私性。然而，在多方场景中更实用的协议仍然是一个研究空白。在本文中，我们提出了一种安全可行的协议，称为大小隐藏多方私有集交集. 该协议基于布隆过滤器、门限同态加密和标记技术，支持多个参与者之间的私有集交集。同时，指定参与者的设置大小隐私得到保护。在决策复合剩余假设下，所提出的协议被证明对半诚实参与者是安全的。最后，通过性能分析和相关工作的比较来说明我们协议的效率。