International Association
for Cryptologic Research

In this work, we study the communication complexity of constant-round secure multiparty computation (MPC) against a fully malicious adversary and consider both the honest majority setting and the dishonest majority setting. In the (strong) honest majority setting (where $t=(1/2-\epsilon)n$ for a constant $\epsilon$), the best-known result without relying on FHE is given by Beck et al. (CCS 2023) based on the LPN assumption that achieves $O(|C|\kappa)$ communication, where $\kappa$ is the security parameter and the achieved communication complexity is independent of the number of participants. In the dishonest majority setting, the best-known result is achieved by Goyal et al. (ASIACRYPT 2024), which requires $O(|C|n\kappa)$ bits of communication and is based on the DDH and LPN assumptions. In this work, we achieve the following results: (1) For any constant $\epsilon<1$, we give the first constant-round MPC in the dishonest majority setting for corruption threshold $t<(1-\epsilon)n$ with $O(|C|\kappa+D (n+\kappa)^2\kappa+n^3)$ communication assuming random oracles and oblivious transfers, where $D$ is the circuit depth. (2) We give the first constant-round MPC in the standard honest majority setting (where $t=(n-1)/2$) with $O(|C|\kappa+D (n+\kappa)^2\kappa+n^3)$ communication only assuming random oracles. Unlike most of the previous constructions of constant-round MPCs that are based on multiparty garbling, we achieve our result by letting each party garble his local computation in a non-constant-round MPC that meets certain requirements. We first design a constant-round MPC that achieves $O(|C|\kappa + Dn^2\kappa)$ communication assuming random oracles in the strong honest majority setting of $t=n/4$. Then, we combine the party virtualization technique and the idea of MPC-in-the-head to boost the corruption threshold to $t<(1-\epsilon)n$ for any constant $\epsilon<1$ assuming oblivious transfers to achieve our first result. Finally, our second result is obtained by instantiating oblivious transfers using a general honest-majority MPC and the OT extension technique built on random oracles.

Secure multiparty computation (MPC) allows a set of $n$ parties to jointly compute a function on their private inputs. In this work, we focus on the information-theoretic MPC in the \emph{asynchronous network} setting with optimal resilience ($t<n/3$). The best-known result in this setting is achieved by Choudhury and Patra [J. Cryptol '23], which requires $O(n^4\kappa)$ bits per multiplication gate, where $\kappa$ is the size of a field element. An asynchronous complete secret sharing (ACSS) protocol allows a dealer to share a batch of Shamir sharings such that all parties eventually receive their shares. ACSS is an important building block in AMPC. The best-known result of ACSS is due to Choudhury and Patra [J. Cryptol '23], which requires $O(n^3\kappa)$ bits per sharing. On the other hand, in the synchronous setting, it is known that distributing Shamir sharings can be achieved with $O(n\kappa)$ bits per sharing. There is a gap of $n^2$ in the communication between the synchronous setting and the asynchronous setting. Our work closes this gap by presenting the first ACSS protocol that achieves $O(n\kappa)$ bits per sharing. When combined with the compiler from ACSS to AMPC by Choudhury and Patra [IEEE Trans. Inf. Theory '17], we obtain an AMPC with $O(n^2\kappa)$ bits per sharing, improving the previously best-known result by a factor of $n^2$. Moreover, with a concurrent work that improves the compiler by Choudhury and Patra by a factor of $n$, we obtain the first AMPC with $O(n\kappa)$ bits per multiplication gate.

In this work, we study constant round multiparty computation (MPC) for Boolean circuits against a fully malicious adversary who may control up to $n-1$ out of $n$ parties. Without relying on fully homomorphic encryption (FHE), the best-known results in this setting are achieved by Wang et al. (CCS 2017) and Hazay et al. (ASIACRYPT 2017) based on garbled circuits, which require a quadratic communication in the number of parties $O(|C|\cdot n^2)$. In contrast, for non-constant round MPC, the recent result by Rachuri and Scholl (CRYPTO 2022) has achieved linear communication $O(|C|\cdot n)$. In this work, we present the first concretely efficient constant round MPC protocol in this setting with linear communication in the number of parties $O(|C|\cdot n)$. Our construction can be based on any public-key encryption scheme that is linearly homomorphic for public keys. Our work gives a concrete instantiation from a variant of the El-Gamal Encryption Scheme assuming the DDH assumption. The analysis shows that when the computational security parameter $\lambda=128$ and statistical security parameter $\kappa=80$, our protocol achieves a smaller communication than Wang et al. (CCS 2017) when there are $16$ parties for AES circuit, and $8$ parties for general Boolean circuits (where we assume that the numbers of AND gates and XOR gates are the same). When comparing with the recent work by Beck et al. (CCS 2023) that achieves constant communication complexity $O(|C|)$ in the strong honest majority setting ($t<(1/2-\epsilon)n$ where $\epsilon$ is a constant), our protocol is better as long as $n<3500$ (when $t=n/4$ for their work).