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Title:
Perfectly Secure Fluid MPC with Abort and Linear Communication Complexity
Authors: Alexander Bienstock, Daniel Escudero, Antigoni Polychroniadou
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.
ePrint: https://eprint.iacr.org/2024/2071
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