papers/lux-performance-security-tradeoffs/sections/02-mpc-latency-vs-threshold-size.tex

\section{MPC Latency vs Threshold Size}


Multi-party computation latency is dominated by network round trips. The CGGMP21 (ECDSA) and FROST (Schnorr/BLS) protocols require 2--3 rounds, but each round requires all $t$ participants to respond.

\subsection{Measurements}

All measurements on Lux M-Chain validators (AWS c6g.xlarge, ARM64, inter-node latency 5--15ms within region).

\begin{center}
\begin{tabular}{rrrrr}
\toprule
\textbf{Threshold} & \textbf{Committee} & \textbf{Protocol} & \textbf{Latency (p50)} & \textbf{Latency (p99)} \\
\midrule
2-of-3 & 3 & FROST & 48ms & 72ms \\
3-of-5 & 5 & FROST & 85ms & 135ms \\
5-of-7 & 7 & FROST & 142ms & 218ms \\
5-of-9 & 9 & FROST & 178ms & 290ms \\
7-of-11 & 11 & FROST & 235ms & 410ms \\
10-of-15 & 15 & FROST & 380ms & 620ms \\
15-of-25 & 25 & FROST & 580ms & 890ms \\
20-of-50 & 50 & FROST & 820ms & 1,240ms \\
\midrule
2-of-3 & 3 & CGGMP21 & 95ms & 140ms \\
3-of-5 & 5 & CGGMP21 & 165ms & 260ms \\
5-of-9 & 9 & CGGMP21 & 340ms & 550ms \\
\bottomrule
\end{tabular}
\end{center}

\begin{observation}[MPC Scaling]
FROST latency scales approximately as $O(t \cdot \text{RTT})$ where $\text{RTT}$ is the median round-trip time between participants. CGGMP21 is $\sim$2$\times$ slower than FROST at the same threshold due to additional rounds.
\end{observation}

\subsection{Implications}

\begin{itemize}[leftmargin=2em]
\item \textbf{Bridge signing} (Teleport): 3-of-5 FROST at 85ms is acceptable. Users experience $<$200ms additional latency per cross-chain transfer.
\item \textbf{FHE decryption}: 5-of-9 FROST at 178ms is acceptable for batch decryption (one threshold operation per batch, not per ciphertext).
\item \textbf{Per-block consensus}: MPC at any threshold is too slow for 1ms blocks. This is why BLS aggregation is used per-block and MPC-based mechanisms operate per-epoch.
\end{itemize}