  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.
