Abstract
In private set intersection (PSI), a set of parties, each holding a private data set, wish to compute the intersection over all data sets in a manner that guarantees both correctness and privacy. This secure computation task is of great importance and usability in many different real-life scenarios. Much research was dedicated to the construction of PSI-tailored concretely efficient protocols for the case of two-party PSI. The case of many parties has been given much less attention, despite probably being a more realistic setting for most applications.
In this work, we propose a new concretely efficient, highly scalable, secure computation protocol for multiparty PSI. Our protocol is an extension of the two-party PSI protocol of Dong et al. [ACM CCS’13] and uses the garbled Bloom filter primitive introduced therein. There are two main variants to our protocol. The first construction provides semi-honest security. The second construction provides (the slightly weaker) augmented semi-honest security, and is substantially more efficient. Furthermore, in the augmented semi-honest protocol all heavy computations can be performed ahead of time, in an offline phase, before the parties ever learn their inputs. This results in an online phase that requires only short interaction. Moreover, in the online phase, interactions are performed over a star topology network. All our constructions tolerate any number of corruptions.
We implemented our protocols and incorporated several optimization techniques. These techniques allow the running time of the protocol to be comparable to that of the two party protocol of Dong et al. and scale linearly with the number of parties. We ran extensive experiments to compare our protocol with the two-party protocol and to demonstrate the effect of the different optimizations.
R. Inbar—Research supported by ISF grant 544/13.
E. Omri—Research supported by ISF grants 544/13 and 152/17.
B. Pinkas—Research supported by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minsters Office, and by ISF grant 1018/16.
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Notes
- 1.
In the original work of [6], this value was x itself, rather than the all-zero string. This change is of no real importance, however, it makes the presentation of our construction simpler.
- 2.
Originally, the hypercube method [2] was used to speed up message propagation replacing a star like propagation scheme with a tree like scheme. We use it in order to aggregate messages sent by all parties to the server.
- 3.
We stress that as we run many instantiations of \(\mathcal{F}_{\text {OT}}\) in parallel, we need to use an \({\text {OT}}\) protocol that is secure under parallel composition.
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Inbar, R., Omri, E., Pinkas, B. (2018). Efficient Scalable Multiparty Private Set-Intersection via Garbled Bloom Filters. In: Catalano, D., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2018. Lecture Notes in Computer Science(), vol 11035. Springer, Cham. https://doi.org/10.1007/978-3-319-98113-0_13
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