In this work, we present novel protocols over rings for semi-honest secure three-party computation (3-PC) and malicious four-party computation (4-PC) with one corruption. Compared to state-of-the-art protocols in the same setting, our protocols require fewer low-latency and high-bandwidth links between the parties to achieve high throughput. Our protocols also reduce the computational complexity by requiring up to 50 percent fewer basic instructions per gate. Further, our protocols achieve the currently best-known communication complexity (3, resp. 5 elements per multiplication gate) with an optional preprocessing phase to reduce the communication complexity of the online phase to 2 (resp. 3) elements per multiplication gate. In homogeneous network settings, i.e. all links between the parties share similar network bandwidth and latency, our protocols achieve up to two times higher throughput than state-of-the-art protocols. In heterogeneous network settings, i.e. all links between the parties share different network bandwidth and latency, our protocols achieve even larger performance improvements. We implemented our protocols and multiple other state-of-the-art protocols (Replicated 3-PC, Astra, Fantastic Four, Tetrad) in a novel open-source C++ framework optimized for achieving high throughput. Five out of six implemented 3-PC and 4-PC protocols achieve more than one billion 32-bit multiplication or more than 32 billion AND gates per second using our implementation in a 25 Gbit/s LAN environment. This is the highest throughput achieved in 3-PC and 4-PC so far and between two and three orders of magnitude higher than the throughput MP-SPDZ achieves in the same settings.

翻译：本文提出针对半诚实安全三方计算（3-PC）与恶意安全四方计算（4-PC）的新型环上协议（允许单方腐败）。与同等设定下的最优协议相比，本协议通过减少参与方间低延迟高带宽链路需求实现高吞吐量，同时将每门电路的基础指令数降低最多50%，显著降低计算复杂度。此外，本协议在实现当前最优通信复杂度（每个乘法门分别需3个及5个元素）的同时，支持可选的预处理阶段，可将在线阶段通信复杂度分别降至每个乘法门2个及3个元素。在同构网络（参与方间所有链路共享相近网络带宽与延迟）中，本协议吞吐量可达现有最优协议的两倍；在异构网络（参与方间链路具有不同网络带宽与延迟）中，性能提升更为显著。我们在新型开源C++框架中实现了本协议及多种现有最优协议（Replicated 3-PC、Astra、Fantastic Four、Tetrad），该框架专为高吞吐量优化。在25 Gbit/s局域网环境下，六个已实现的3-PC与4-PC协议中有五个每秒可执行超过十亿次32位乘法运算或超过320亿个AND门操作。这是目前3-PC与4-PC领域实现的最高吞吐量，在相同设定下较MP-SPDZ的吞吐量高出两到三个数量级。