In this work, we introduce the Gulliver multi-party computation model (GMPC). The GMPC model considers a single highly powerful party, called the server or Gulliver, that is connected to $n$ users over a star topology network (alternatively formulated as a full network, where the server can block any message). The users are significantly less powerful than the server, and, in particular, should have both computation and communication complexities that are polylogarithmic in $n$. Protocols in the GMPC model should be secure against malicious adversaries that may corrupt a subset of the users and/or the server. Designing protocols in the GMPC model is a delicate task, since users can only hold information about polylog(n) other users (and, in particular, can only communicate with polylog(n) other users). In addition, the server can block any message between any pair of honest parties. Thus, reaching an agreement becomes a challenging task. Nevertheless, we design generic protocols in the GMPC model, assuming that at most $\alpha<1/6$ fraction of the users may be corrupted (in addition to the server). Our main contribution is a variant of Feige's committee election protocol [FOCS 1999] that is secure in the GMPC model. Given this tool we show: 1. Assuming fully homomorphic encryption (FHE), any computationally efficient function with $O\left(n\cdot polylog(n)\right)$-size output can be securely computed in the GMPC model. 2. Any function that can be computed by a circuit of $O(polylog(n))$ depth, $O\left(n\cdot polylog(n)\right)$ size, and bounded fan-in and fan-out can be securely computed in the GMPC model without assuming FHE. 3. In particular, sorting can be securely computed in the GMPC model without assuming FHE. This has important applications for the shuffle model of differential privacy, and resolves an open question of Bell et al. [CCS 2020].

翻译：本文提出了格列佛多方计算模型（GMPC）。该模型考虑一个功能强大的单一参与方（称为服务器或格列佛），通过星型拓扑网络（亦可表述为全连接网络，其中服务器可阻断任意消息）与n个用户相连。用户的计算能力显著弱于服务器，尤其需要满足计算复杂度和通信复杂度均为n的多对数规模。GMPC模型中的协议需能够抵抗可能腐败部分用户和/或服务器的恶意对手。设计GMPC协议是一项精细任务，因为用户只能持有关于polylog(n)个其他用户的信息（并仅能与polylog(n)个其他用户通信）。此外，服务器可阻断任意诚实方之间的消息，使得达成共识成为挑战。尽管如此，我们假设最多α<1/6比例的用户可能被腐败（服务器除外），并设计了GMPC模型下的通用协议。主要贡献是Feige委员会选举协议[FOCS 1999]的一个变体，该变体在GMPC模型中安全。基于此工具，我们证明：1. 假设存在全同态加密（FHE），任何具有O(n·polylog(n))规模输出的计算高效函数均可在GMPC模型中安全计算。2. 任何可由深度为O(polylog(n))、规模为O(n·polylog(n))且扇入扇出有界的电路计算的函数，无需FHE即可在GMPC模型中安全计算。3. 特别地，排序可在无需FHE的情况下在GMPC模型中安全计算。这对差分隐私的混洗模型具有重要应用，并解决了Bell等人[CCS 2020]提出的公开问题。