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Mr NISC: Multiparty Reusable Non-Interactive Secure Computation

Part of the Lecture Notes in Computer Science book series (LNSC,volume 12551)

Abstract

Reducing interaction in Multiparty Computation (MPC) is a highly desirable goal in cryptography. It is known that 2-round MPC can be based on the minimal assumption of 2-round Oblivious Transfer (OT) [Benhamouda and Lin, Garg and Srinivasan, EC 2018], and 1-round MPC is impossible in general. In this work, we propose a natural “hybrid” model, called multiparty reusable Non-Interactive Secure Computation (mrNISC). In this model, parties publish encodings of their private inputs \(x_i\) on a public bulletin board, once and for all. Later, any subset I of them can compute on-the-fly a function f on their inputs \(\varvec{x}_I = {\{x_i\}}_{i \in I}\) by just sending a single message to a stateless evaluator, conveying the result \(f(\varvec{x}_I)\) and nothing else. Importantly, the input encodings can be reused in any number of on-the-fly computations, and the same classical simulation security guaranteed by multi-round MPC, is achieved. In short, mrNISC has a minimal yet “tractable” interaction pattern.

We initiate the study of mrNISC on several fronts. First, we formalize the model of mrNISC protocols, and present both a UC security definition and a game-based security definition. Second, we construct mrNISC protocols in the plain model with semi-honest and semi-malicious security based on pairing groups. Third, we demonstrate the power of mrNISC by showing two applications: non-interactive MPC (NIMPC) with reusable setup and a distributed version of program obfuscation.

At the core of our construction of mrNISC is a witness encryption scheme for a special language that verifies Non-Interactive Zero-Knowledge (NIZK) proofs of the validity of computations over committed values, which is of independent interest.

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Fig. 1.
Fig. 2.
Fig. 3.

Notes

  1. 1.

    The message set \(\mathcal {V}\) may depend on the CRS \(\mathsf {crs}\). The only required constraints are that messages in \(\mathcal {V}\) have polynomial size in the security parameter \(\lambda \) and that testing membership to \(\mathcal {V}\) can be done in polynomial-time given \(\mathsf {crs}\). The reason to use messages spaces more complicated than \({\{0,1\}}^{\mathrm {poly}(\lambda )}\) is to allow messages to be elements of some finite field \(\mathbb {Z}_p\) for the definition of bilinear commitments with proofs of quadratic relations.

  2. 2.

    We implicitly systematically assume that \(G\) has input size corresponding to the size of messages in the message set \(\mathcal {V}\).

  3. 3.

    is not a type-1 commitment (using the matrix \(A_1\)) nor a type-2 commitment (using the matrix \(A_2\)) but yet another type of commitment using another matrix B (formally defined in the proof in Eq. (17)). When the CRS is binding, this matrix B is such that the commitment is also binding.

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Acknowledgments

Huijia Lin was supported by NSF grants CNS-1528178, CNS-1514526, CNS-1652849 (CAREER), CNS-2026774, a Hellman Fellowship, a JP Morgan Research Award, the Defense Advanced Research Projects Agency (DARPA) and Army Research Office (ARO) under Contract No. W911NF-15-C-0236, and a subcontract No. 2017-002 through Galois. Part of the work was done while Huijia Lin was visiting the Simons Institute for the Theory of Computing, Berkeley. The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense, the National Science Foundation, or the U.S. Government.

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Benhamouda, F., Lin, H. (2020). Mr NISC: Multiparty Reusable Non-Interactive Secure Computation. In: Pass, R., Pietrzak, K. (eds) Theory of Cryptography. TCC 2020. Lecture Notes in Computer Science(), vol 12551. Springer, Cham. https://doi.org/10.1007/978-3-030-64378-2_13

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  • DOI: https://doi.org/10.1007/978-3-030-64378-2_13

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