papers/lux-performance-security-tradeoffs/sections/09-the-practical-constraint.tex

\section{The Practical Constraint}


The Lux architecture must satisfy simultaneously:

\begin{center}
\begin{tabular}{ll}
\toprule
\textbf{Requirement} & \textbf{Constraint} \\
\midrule
Sub-second finality & Block time $\leq$ 1ms, epoch = 1s \\
Post-quantum security & ML-DSA + Pulsar (lattice-based) \\
Commodity hardware & No GPU or FPGA required for validators \\
Compact proofs & Epoch proof $\leq$ 300 bytes \\
Scalable validation & $O(1)$ or $O(\log N)$ verification \\
\bottomrule
\end{tabular}
\end{center}

No single primitive satisfies all requirements:

\begin{center}
\begin{tabular}{lccccc}
\toprule
\textbf{Primitive} & \textbf{Speed} & \textbf{PQ} & \textbf{Compact} & \textbf{Scalable} & \textbf{Commodity} \\
\midrule
BLS aggregate & \checkmark & $\times$ & \checkmark & \checkmark & \checkmark \\
ML-DSA (individual) & \checkmark & \checkmark & $\times$ & $\times$ & \checkmark \\
STARK (alone) & $\times$ & \checkmark & \checkmark & \checkmark & $\times$$^*$ \\
MPC threshold & $\times$ & Varies & \checkmark & $\times$ & \checkmark \\
FHE & $\times$ & \checkmark & N/A & $\times$ & $\times$ \\
\bottomrule
\end{tabular}
\end{center}

$^*$STARK proof generation requires significant CPU/memory, but verification runs on commodity hardware.

The solution is temporal composition:

\begin{enumerate}[leftmargin=2em]
\item \textbf{Per-block (1ms)}: BLS aggregation. Fast, compact, scalable, not PQ.
\item \textbf{Per-epoch (1s)}: STARK-compressed ML-DSA + Pulsar. PQ, compact, scalable, but too slow for per-block.
\item \textbf{Per-operation (on demand)}: FHE for privacy, MPC for threshold trust. Neither is fast enough for consensus.
\end{enumerate}