In the field of privacy preserving protocols, Private Set Intersection (PSI) plays an important role. In most of the cases, PSI allows two parties to securely determine the intersection of their private input sets, and no other information. In this paper, employing a Bloom filter, we propose a Multiparty Private Set Intersection Cardinality (MPSI-CA), where the number of participants in PSI is not limited to two. The security of our scheme is achieved in the standard model under the Decisional Diffie-Hellman (DDH) assumption against semi-honest adversaries. Our scheme is flexible in the sense that set size of one participant is independent from that of the others. We consider the number of modular exponentiations in order to determine computational complexity. In our construction, communication and computation overheads of each participant is $ O(v_{\sf max}k) $ except that the complexity of the designated party is $ O(v_1) $, where $ v_{\sf max} $ is the maximum set size, $ v_1 $ denotes the set size of the designated party and $ k $ is a security parameter. Particularly, our MSPI-CA is the first that incurs linear complexity in terms of set size, namely $ O(nv_{\sf max}k) $, where $ n $ is the number of participants. Further, we extend our MPSI-CA to MPSI retaining all the security attributes and other properties. As far as we are aware of, there is no other MPSI so far where individual computational cost of each participant is independent of the number of participants. Unlike MPSI-CA, our MPSI does not require any kind of broadcast channel as it uses star network topology in the sense that a designated party communicates with everyone else.

中文翻译：

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安全高效的多方专用集合路口基数

在隐私保护协议领域，私有集交叉点（PSI）扮演着重要角色。在大多数情况下，PSI允许两方安全地确定其私有输入集的交集，而没有其他信息。在本文中，使用布隆过滤器，我们提出了一种多方专用集相交基数（MPSI-CA），其中PSI的参与者数量不限于两个。我们的方案的安全性是在标准Diffie-Hellman（DDH）假设下针对半诚实的对手的标准模型中实现的。我们的方案是灵活的，因为一个参与者的设置大小独立于其他参与者的设置大小。为了确定计算复杂度，我们考虑了模幂的数量。在我们的建筑中 每个参与者的通信和计算开销为$ O（v _ {\ sf max} k）$，除了指定方的复杂度为$ O（v_1）$，其中$ v _ {\ sf max} $为最大集合大小，$ v_1 $表示指定方的设置大小，$ k $是安全参数。特别是，我们的MSPI-CA是首先，这会导致集合大小线性复杂，即$ O（nv _ {\ sf max} k）$，其中$ n $是参与者的数量。此外，我们将MPSI-CA扩展到保留所有安全属性和其他属性的MPSI。据我们所知，到目前为止，没有其他MPSI可以使每个参与者的个人计算成本与参与者的数量无关。与MPSI-CA不同，我们的MPSI不需要任何类型的广播频道，因为它使用星形网络拓扑结构，即指定的一方与其他所有人进行通信。