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On Adaptively Secure Multiparty Computation with a Short CRS

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Security and Cryptography for Networks (SCN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9841))

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Abstract

In the setting of multiparty computation, a set of mutually distrusting parties wish to securely compute a joint function of their private inputs. A protocol is adaptively secure if honest parties might get corrupted after the protocol has started. Recently (TCC 2015) three constant-round adaptively secure protocols were presented [10, 11, 15]. All three constructions assume that the parties have access to a common reference string (CRS) whose size depends on the function to compute, even when facing semi-honest adversaries. It is unknown whether constant-round adaptively secure protocols exist, without assuming access to such a CRS.

In this work, we study adaptively secure protocols which only rely on a short CRS that is independent on the function to compute.

  • First, we raise a subtle issue relating to the usage of non-interactive non-committing encryption within security proofs in the UC framework, and explain how to overcome it. We demonstrate the problem in the security proof of the adaptively secure oblivious-transfer protocol from [8] and provide a complete proof of this protocol.

  • Next, we consider the two-party setting where one of the parties has a polynomial-size input domain, yet the other has no constraints on its input. We show that assuming the existence of adaptively secure oblivious transfer, every deterministic functionality can be computed with adaptive security in a constant number of rounds.

  • Finally, we present a new primitive called non-committing indistinguishability obfuscation, and show that this primitive is complete for constructing adaptively secure protocols with round complexity independent of the function.

R. Cohen—Work supported by the European Research Council under the ERC consolidators grant agreement n. 615172 (HIPS), by a grant from the Israel Ministry of Science, Technology and Space (grant 3-10883) and by the National Cyber Bureau of Israel.

C. Peikert—This material is based upon work supported by the National Science Foundation under CAREER Award CCF-1054495 and CNS-1606362, the Alfred P. Sloan Foundation, and by a Google Research Award. The views expressed are those of the authors and do not necessarily reflect the official policy or position of the National Science Foundation, the Sloan Foundation, or Google.

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Notes

  1. 1.

    In this work we do not assume the existence secure erasures, meaning that we do not rely on the ability of an honest party to erase specific parts of its memory.

  2. 2.

    An adaptively well-formed functionality is a functionality that reveals its random input in case all parties are corrupted [8].

  3. 3.

    Since the protocol of [8] is designed in the UC framework of Canetti [5], security against malicious adversaries requires some form of a trusted-setup assumption, see [6, 9, 27].

  4. 4.

    The input of \(P_1\) is \({\mu }\), the output of \(P_2\) is \({\mu }\), and all other parties have no input nor output.

  5. 5.

    The idea of using OT over domain which is of polynomial size first appeared in Poupard and Stern [30].

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Acknowledgements

We would like to thank Yehuda Lindell for helpful discussions on the topic and to the anonymous referees for pointing to the work of [30] regarding OT over polynomial-size domain and for pointing out a problem in an earlier version of Definition 4.

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Authors and Affiliations

  1. Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel

    Ran Cohen

  2. Computer Science and Engineering, University of Michigan, Ann Arbor, USA

    Chris Peikert

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Correspondence to Ran Cohen .

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  1. Rensselaer Polytechnic Institute, Troy, New York, USA

    Vassilis Zikas

  2. University of Salerno, Fisciano, Italy

    Roberto De Prisco

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Cohen, R., Peikert, C. (2016). On Adaptively Secure Multiparty Computation with a Short CRS. In: Zikas, V., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2016. Lecture Notes in Computer Science(), vol 9841. Springer, Cham. https://doi.org/10.1007/978-3-319-44618-9_7

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  • DOI: https://doi.org/10.1007/978-3-319-44618-9_7

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