In this work, we present novel protocols over rings for semi-honest secure three-party computation (3PC) and malicious four-party computation (4PC) with one corruption. While most existing works focus on improving total communication complexity, challenges such as network heterogeneity and computational complexity, which impact MPC performance in practice, remain underexplored. Our protocols address these issues by tolerating multiple arbitrarily weak network links between parties without any substantial decrease in performance. Additionally, they significantly reduce computational complexity by requiring up to half the number of basic instructions per gate compared to related work. These improvements lead to up to twice the throughput of state-of-the-art protocols in homogeneous network settings and up to eight times higher throughput in real-world heterogeneous settings. These advantages come at no additional cost: Our protocols maintain the best-known total communication complexity per multiplication, requiring 3 elements for 3PC and 5 elements for 4PC. We implemented our protocols alongside several state-of-the-art protocols (Replicated 3PC, ASTRA, Fantastic Four, Tetrad) in a novel open-source C++ framework optimized for high throughput. Five out of six implemented 3PC and 4PC protocols achieve more than one billion 32-bit multiplications or over 32 billion AND gates per second using our implementation in a 25 Gbit/s LAN environment. This represents the highest throughput achieved in 3PC and 4PC so far, outperforming existing frameworks like MP-SPDZ, ABY3, MPyC, and MOTION by two to three orders of magnitude.

翻译：本文提出了针对半诚实安全三方计算（3PC）及恶意四方计算（4PC，含一个腐败方）的环上新型协议。现有研究大多聚焦于改善总体通信复杂度，然而实际影响MPC性能的网络异构性与计算复杂度等挑战尚未得到充分探索。我们的协议通过容忍参与方之间多条任意弱网络链路而不显著降低性能，有效应对了这些问题。此外，通过将每个逻辑门所需的基本指令数减少至相关工作的一半，这些协议显著降低了计算复杂度。这些改进使得协议在均匀网络环境中达到现有最优协议两倍的吞吐量，在实际异构网络环境中更可实现高达八倍的吞吐量提升。这些优势并未带来额外开销：我们的协议保持了目前已知最优的每次乘法总体通信复杂度，3PC仅需3个元素，4PC仅需5个元素。我们在一个专为高吞吐量优化的新型开源C++框架中实现了我们的协议及多个前沿协议（Replicated 3PC、ASTRA、Fantastic Four、Tetrad）。在25 Gbit/s局域网环境中，六种已实现的3PC与4PC协议中有五种通过我们的实现达到了每秒超过10亿次32位乘法或超过320亿个AND门运算的吞吐量。这代表了目前3PC与4PC领域实现的最高吞吐量，较现有框架（如MP-SPDZ、ABY3、MPyC和MOTION）提升了两到三个数量级。