Secure and efficient multiparty private set intersection cardinality

Abstract

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(vmaxk) except that the complexity of the designated party is O(v 1), where vmax 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(nvmaxk), 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.

Quantum Bloom Filter and Its Applications

“…What's more, we focus on its applications. The further results show that quantum Bloom filter is a nearly perfect tool to solve the privacy-preserving issues with private sets, e.g., Oblivious Set-member Decision [12] and Multiparty Private Set Intersection Cardinality [13].…”

“…In classical settings, a Bloom filter is a space-efficient probabilistic data structure [14], firstly presented by B. H. Bloom in 1970 [15], which is utilized to decide whether an element belongs to a set. It uses a bit array of size to represent a set of elements and employs independent collision-resistant hash functions {ℎ 1 , ℎ 2 , … , ℎ } to add elements into the bit array [13], where ℎ : {0,1} * → {1,2, … , } for = 1,2, … , .…”

“…Private Set Intersection Cardinality (PSI-CA) is another private issue widely concerned, in which two parties jointly compute the intersection cardinality without revealing their respective private sets [20]. Multiparty Private Set Intersection Cardinality (MPSI-CA) [13,25] is a natural extension of Two-party Private Set Intersection Cardinality, in which there are parties ( ≥ 2), each with a private set , to privately compute | 1 ∩ 2 ∩ ⋯ |. The MPSI-CA has wide applications in real life, e.g., privacypreserving data statistics about friendship-determining in social networks.…”

“…To the best our knowledge, the communicational complexity of the best classical algorithm [13] is ( ). Clearly, the proposed MPSI-CA protocol indeed achieves the linear round, where the communicational complexity is ( 2 ) (note.…”

An Efficient and Robust System for Vertically Federated Random Forest

“…In the initialization stage, the encrypted label will be broadcasted to all participating parties, and ID alignment will be performed. Specifically, Diffie-Hellman algorithm (Li, 2010) will be used to perform private set intersection (Debnath et al, 2021) (PSI) and fulfill the ID alignment task. During the training process, Alg.…”