Abstract
A private set membership (PSM) protocol allows a “receiver” to learn whether its input x is contained in a large database \(\textsf{DB} \) held by a “sender”. In this work, we define and construct credible private set membership (C-PSM) protocols: in addition to the conventional notions of privacy, C-PSM provides a soundness guarantee that it is hard for a sender (that does not know x) to convince the receiver that \(x \in \textsf{DB} \). Furthermore, the communication complexity must be logarithmic in the size of \(\textsf{DB} \).
We provide 2-round (i.e., round-optimal) C-PSM constructions based on standard assumptions:
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We present a black-box construction in the plain model based on DDH or LWE.
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Next, we consider protocols that support predicates f beyond string equality, i.e., the receiver can learn if there exists \(w \in \textsf{DB} \) such that \(f(x,w) = 1\). We present two results with transparent setups: (1) A black-box protocol, based on DDH or LWE, for the class of NC\(^1\) functions f which are efficiently searchable. (2) An LWE-based construction for all bounded-depth circuits. The only non-black-box use of cryptography in this construction is through the bootstrapping procedure in fully homomorphic encryption.
As an application, our protocols can be used to build enhanced round-optimal leaked password notification services, where unlike existing solutions, a dubious sender cannot fool a receiver into changing its password.
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Acknowledgments
Sanjam Garg is supported in part by DARPA under Agreement No. HR00112020026, AFOSR Award FA9550-19-1-0200, NSF CNS Award 1936826, and research grants by the Sloan Foundation, and Visa Inc. Omkant Pandey is supported in part by DARPA SIEVE Award HR00112020026, NSF CAREER Award 2144303, NSF grants 2028920, 2106263, and 2128187. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Government, DARPA, Sloan Foundation, Visa Inc., or NSF.
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Garg, S., Hajiabadi, M., Jain, A., Jin, Z., Pandey, O., Shiehian, S. (2023). Credibility in Private Set Membership. In: Boldyreva, A., Kolesnikov, V. (eds) Public-Key Cryptography – PKC 2023. PKC 2023. Lecture Notes in Computer Science, vol 13941. Springer, Cham. https://doi.org/10.1007/978-3-031-31371-4_6
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