Paper 2024/2071 Original: eprint.iacr.org/2024/2071 ↗

Perfectly Secure Fluid MPC with Abort and Linear Communication Complexity

Abstract

The \emph{Fluid} multiparty computation (MPC) model, introduced in (Choudhuri \emph{et al.} CRYPTO 2021), addresses dynamic scenarios where participants can join or leave computations between rounds. Communication complexity initially stood at $\Omega(n^2)$ elements per gate, where $n$ is the number of parties in a committee online at a time. This held for both statistical security (honest majority) and computational security (dishonest majority) in (Choudhuri \emph{et al.}~CRYPTO'21) and (Rachuri and Scholl, CRYPTO'22), respectively. The work of Bienstock \emph{et al.}~CRYPTO'23) improved communication to $O(n)$ elements per gate. However, it's important to note that the perfectly secure setting with one-third corruptions per committee has only recently been addressed in the work of (David \emph{et al.}~CRYPTO'23). Notably, their contribution marked a significant advancement in the Fluid MPC literature by introducing guaranteed output delivery. However, this achievement comes at the cost of prohibitively expensive communication, which scales to $\Omega(n^9)$ elements per gate. In this work, we study the realm of perfectly secure Fluid MPC under one-third active corruptions. Our primary focus lies in proposing efficient protocols that embrace the concept of security with abort. Towards this, we design a protocol for perfectly secure Fluid MPC that requires only \emph{linear} communication of $O(n)$ elements per gate, matching the communication of the non-Fluid setting. Our results show that, as in the case of computational and statistical security, perfect security with abort for Fluid MPC comes "for free (asymptotically linear in $n$) with respect to traditional non-Fluid MPC, marking a substantial leap forward in large scale dynamic computations, such as Fluid MPC.