Maliciously-Secure MrNISC in the Plain Model

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].