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papers/lux-fhe-mpc-hybrid/sections/07-implementation-on-lux.tex
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\section{Implementation on Lux}
\subsection{F-Chain: LiquidFHE Runtime}
The Lux F-Chain provides the FHE computation environment:
\begin{itemize}[leftmargin=2em]
\item TFHE boolean circuits via the \texttt{luxfi/lattice} library.
\item Parameters: $n = 1024$, $q \approx 2^{27}$, NIST Level 1 security (128-bit).
\item Bootstrapping key size: 24 MB per user key.
\item Gate evaluation: 12ms per bootstrapped gate (single core), 3.2ms with 4-way parallelism.
\end{itemize}
\subsection{M-Chain: MPC Threshold Network}
The Lux M-Chain provides the threshold decryption infrastructure:
\begin{itemize}[leftmargin=2em]
\item FROST-based DKG for FHE key generation.
\item $t$-of-$n$ threshold decryption with configurable $(t, n)$.
\item Default configuration: $3$-of-$5$ for application chains, $5$-of-$9$ for the primary network.
\item Decryption latency: 35ms for $3$-of-$5$, 82ms for $5$-of-$9$ (including network round trips).
\end{itemize}
\subsection{End-to-End Benchmarks}
\begin{center}
\begin{tabular}{lrr}
\toprule
\textbf{Operation} & \textbf{Time} & \textbf{Size} \\
\midrule
Order encryption (3 fields) & 0.4ms & 12 KB \\
Price comparison (16-bit) & 38ms & --- \\
Quantity minimum (16-bit) & 41ms & --- \\
Full match (compare + fill) & 47ms & --- \\
Threshold decryption ($3$-of-$5$) & 35ms & 1.2 KB \\
Threshold decryption ($5$-of-$9$) & 82ms & 2.1 KB \\
FROST attestation & 12ms & 64 B \\
\midrule
\textbf{End-to-end match + decrypt} & \textbf{94ms} & --- \\
\bottomrule
\end{tabular}
\end{center}