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Secure Sampling with Sublinear Communication

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Theory of Cryptography (TCC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13748))

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Abstract

Random sampling from specified distributions is an important tool with wide applications for analysis of large-scale data. In this paper we study how to randomly sample when the distribution is partitioned among two parties’ private inputs. Of course, a trivial solution is to have one party send a (possibly encrypted) description of its weights to the other party who can then sample over the entire distribution (possibly using homomorphic encryption). However, this approach requires communication that is linear in the input size which is prohibitively expensive in many settings. In this paper, we investigate secure 2-party sampling with sublinear communication for many standard distributions. We develop protocols for \(L_1\), and \(L_2\) sampling. Additionally, we investigate the feasibility of sublinear product sampling, showing impossibility for the general problem and showing a protocol for a restricted case of the problem. We additionally show how such product sampling can be used to instantiate a sublinear communication 2-party exponential mechanism for differentially-private data release.

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Notes

  1. 1.

    Of course, if \(\langle \textbf{w}_1, \textbf{w}_2 \rangle = 0\), the probability space is not well-defined, and in this case, we require the protocol to simply output \(\bot \).

  2. 2.

    Throughout the paper, we will describe the round and communication complexities using the asymptotic notation only based on n. That is, all other parameters (e.g., security parameter) independent on n will be suppressed in the asymptotic expressions.

  3. 3.

    Here the assumption that \(\textbf{w}\) are normalized is without loss of generality.

  4. 4.

    Regarding \(\langle \textbf{w}_1, \textbf{w}_2 \rangle \), there is a gap between the lowerbound result (i.e., \(\varOmega (\frac{1}{n^2})\)) and our construction (i.e., \(\omega (\frac{\log n}{n})\)). Resolving the gap is left as an interesting open problem.

  5. 5.

    This can be shown by a simple modification of the lower bound proof from Sect. 4.1.

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Acknowledgments

Seung Geol Choi is supported by NSF grant #CNS-1955319. Dana Dachman-Soled is supported in part by NSF grants #IIS-2147276, #CNS-1933033, #CNS-1453045 (CAREER), and by financial assistance awards 70NANB15H328 and 70NANB19H126 from the U.S. Department of Commerce, National Institute of Standards and Technology. Dov Gordon is supported by NSF grant #CNS-1955264. Arkady Yerukhimovich is supported by NSF grant #CNS-1955620.

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Authors and Affiliations

  1. United States Naval Academy, Annapolis, USA

    Seung Geol Choi

  2. University of Maryland, College Park, USA

    Dana Dachman-Soled

  3. George Mason University, Fairfax City, USA

    S. Dov Gordon

  4. George Washington University, Washington, USA

    Linsheng Liu & Arkady Yerukhimovich

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  1. Seung Geol Choi
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  2. Dana Dachman-Soled
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Correspondence to Seung Geol Choi .

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Editors and Affiliations

  1. Ruhr University Bochum, Bochum, Germany

    Eike Kiltz

  2. Massachusetts Institute of Technology, Cambridge, MA, USA

    Vinod Vaikuntanathan

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Choi, S.G., Dachman-Soled, D., Gordon, S.D., Liu, L., Yerukhimovich, A. (2022). Secure Sampling with Sublinear Communication. In: Kiltz, E., Vaikuntanathan, V. (eds) Theory of Cryptography. TCC 2022. Lecture Notes in Computer Science, vol 13748. Springer, Cham. https://doi.org/10.1007/978-3-031-22365-5_13

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  • DOI: https://doi.org/10.1007/978-3-031-22365-5_13

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