Abstract
We study strong versions of round-optimal MPC. A recent work of Benhamouda and Lin (TCC ’20) identified a version of secure multiparty computation (MPC), termed Multiparty reusable Non-Interactive Secure Computation (MrNISC), that combines at the same time several fundamental aspects of secure computation with standard simulation security into one primitive: round-optimality, succinctness, concurrency, and adaptivity. In more detail, MrNISC is essentially a two-round MPC protocol where the first round of messages serves as a reusable commitment to the private inputs of participating parties. Using these commitments, any subset of parties can later compute any function of their choice on their respective inputs by broadcasting one message each. Anyone who sees these parties’ commitments and evaluation messages (even an outside observer) can learn the function output and nothing else. Importantly, the input commitments can be computed without knowing anything about other participating parties (neither their identities nor their number) and they are reusable across any number of computations.
By now, there are several known MrNISC protocols from either (bilinear) group-based assumptions or from LWE. They all satisfy semi-malicious security (in the plain model) and require trusted setup assumptions in order to get malicious security. We are interested in maliciously secure MrNISC protocols in the plain model, without trusted setup. Since the standard notion of polynomial simulation is un-achievable in less than four rounds, we focus on security with super-polynomial-time simulation (SPS).
Our main result is the first maliciously secure SPS MrNISC in the plain model. The result is obtained by generically compiling any semi-malicious MrNISC and the security of our compiler relies on several well-studied assumptions of an indistinguishability obfuscator, DDH over \({\mathbb Z} ^*_{p}\) and asymmetric pairing groups, and a time-lock puzzle (all of which need to be sub-exponentially hard). As a special case, we obtain the first 2-round maliciously secure SPS MPC based on well-founded assumptions. This MPC is also concurrently self-composable and its first message is short (i.e., its size is independent of the number of the participating parties) and reusable throughout any number of computations. Prior to our work, for two round maliciously secure MPC, neither concurrent MPC nor reusable MPC nor MPC with first message independent in the number of parties was known from any set of assumptions. Of independent interest is one of our building blocks: the first construction of a one-round non-malleable commitment scheme from well-studied assumptions, avoiding keyless hash functions and non-standard hardness amplification assumptions. The full version of this paper can be found at [26].
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Notes
- 1.
By quasi-non-interactive we refer to “non-interactive” protocols that require a trusted setup such as a common reference string.
- 2.
We discuss this work further in Sect. 1.3.
- 3.
Semi-malicious security allows the adversary to choose arbitrary randomness for the parties, but otherwise requires honest behavior.
- 4.
DDH assumption over asymmetric pairing groups is also referred to as the SXDH assumption. We will interchangeably use SXDH wherever we specifically require DDH over assymetric pairing groups.
- 5.
An adaptive one-way function is a non-falsifiable hardness assumption postulating the existence of a one-way function f that is hard to invert on a random point \(y = f(x)\) even if you get access to an inversion oracle that inverts it on every other point \(y'\ne y\).
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Acknowledgement
Rex Fernando is supported in part by a Simons Investigator Award, DARPA SIEVE award, NTT Research, NSF Frontier Award 1413955, BSF grant 2012378, a Xerox Faculty Research Award, a Google Faculty Research Award, and an Okawa Foundation Research Grant. This material is based upon work supported by the Defense Advanced Research Projects Agency through Award HR00112020024. Ilan Komargodski is the incumbent of the Harry & Abe Sherman Senior Lectureship at the School of Computer Science and Engineering at the Hebrew University, supported in part by an Alon Young Faculty Fellowship, by a grant from the Israel Science Foundation (ISF Grant No. 1774/20), and by a grant from the US-Israel Binational Science Foundation and the US National Science Foundation (BSF-NSF Grant No. 2020643).
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Fernando, R., Jain, A., Komargodski, I. (2023). Maliciously-Secure MrNISC in the Plain Model. In: Hazay, C., Stam, M. (eds) Advances in Cryptology – EUROCRYPT 2023. EUROCRYPT 2023. Lecture Notes in Computer Science, vol 14005. Springer, Cham. https://doi.org/10.1007/978-3-031-30617-4_4
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