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 even larger performance improvements in 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）和恶意四方计算（4PC，含一个腐败方）的新型环上协议。现有研究大多聚焦于改善总通信复杂度，而网络异构性和计算复杂度等实际影响MPC性能的挑战尚未得到充分探索。我们的协议通过容忍参与方之间存在多条任意弱网络连接且不显著降低性能来解决这些问题。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。这些改进使得在均匀网络环境中，协议吞吐量达到最先进方案的两倍，在异构网络环境中性能提升更为显著。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通信复杂度，3PC仅需3个元素，4PC仅需5个元素。我们在一个为高吞吐量优化的新型开源C++框架中实现了我们的协议以及多个最先进协议（Replicated 3PC、ASTRA、Fantastic Four、Tetrad）。在25 Gbit/s局域网环境中，六种已实现的3PC和4PC协议中有五种通过我们的实现实现了每秒超过10亿次32位乘法或超过320亿个AND门运算。这代表了目前3PC和4PC领域达到的最高吞吐量，比现有框架（如MP-SPDZ、ABY3、MPyC和MOTION）高出两到三个数量级。