Paper 2024/1670

Statistical Layered MPC

Abstract

The seminal work of Rabin and Ben-Or (STOC'89) showed that the problem of secure $n$-party computation can be solved for $t<n/2$ corruptions with guaranteed output delivery and statistical security. This holds in the traditional static model where the set of parties is fixed throughout the entire protocol execution. The need to better capture the dynamics of large scale and long-lived computations, where compromised parties may recover and the set of parties can change over time, has sparked renewed interest in the proactive security model by Ostrovsky and Yung (PODC'91). This abstraction, where the adversary may periodically uncorrupt and corrupt a new set of parties, is taken even a step further in the more recent YOSO and Fluid MPC models (CRYPTO'21) which allow, in addition, disjoint sets of parties participating in each round. Previous solutions with guaranteed output delivery and statistical security only tolerate $t<n/3$ corruptions, or assume a random corruption pattern plus non-standard communication models. Matching the Rabin and Ben-Or bound in these settings remains an open problem. In this work, we settle this question considering the unifying Layered MPC abstraction recently introduced by David et al. (CRYPTO'23). In this model, the interaction pattern is defined by a layered acyclic graph, where each party sends secret messages and broadcast messages only to parties in the very next layer. We complete the feasibility landscape of layered MPC, by extending the Rabin and Ben-Or result to this setting. Our results imply maximally-proactive MPC with statistical security in the honest-majority setting.