papers/zoo-fhe/sections/09-benchmarks.tex

\section{Benchmarks}

\label{sec:bench}
%----------------------------------------------------------------------

All benchmarks run on \Zoo{} testnet validators equipped with NVIDIA H100 80\,GB GPUs, AMD EPYC 9654 CPUs (96 cores), and 512\,GB DDR5.

\subsection{Bootstrap Latency}

\begin{table}[h]
\centering
\begin{tabular}{lrrr}
\toprule
\textbf{Operation} & \textbf{CPU (ms)} & \textbf{GPU (ms)} & \textbf{Speedup} \\
\midrule
Single TFHE bootstrap & 12.0 & 0.30 & 40$\times$ \\
8-bit integer comparison & 96.0 & 4.10 & 23$\times$ \\
256-bit comparison circuit & 3{,}072 & 52.0 & 59$\times$ \\
Batch 4096 bootstraps & 49{,}152 & 62.0 & 793$\times$ \\
\bottomrule
\end{tabular}
\caption{TFHE bootstrap latency: CPU vs GPU}
\label{tab:bootstrap}
\end{table}

Batch amortization yields superlinear speedup because GPU occupancy increases with batch size until the 4096-element sweet spot.

\subsection{CKKS Multiplication Throughput}

\begin{table}[h]
\centering
\begin{tabular}{lrr}
\toprule
\textbf{Metric} & \textbf{CPU} & \textbf{GPU} \\
\midrule
Single ciphertext multiply + relin (ms) & 8.5 & 0.6 \\
Throughput (multiplications/sec) & 118 & 1{,}667 \\
Rescale (ms) & 2.1 & 0.15 \\
Slot rotation (ms) & 6.2 & 0.45 \\
\bottomrule
\end{tabular}
\caption{CKKS operation throughput at $N = 16384$, $L = 15$}
\label{tab:ckks}
\end{table}

\subsection{Threshold Decryption Latency}

\begin{table}[h]
\centering
\begin{tabular}{lr}
\toprule
\textbf{Phase} & \textbf{Latency (ms)} \\
\midrule
Partial decryption (per validator) & 0.8 \\
Network collection (67 shares, p95) & 180 \\
Lagrange aggregation & 2.1 \\
Smudging noise verification & 0.3 \\
\textbf{Total end-to-end} & \textbf{$\sim$183} \\
\bottomrule
\end{tabular}
\caption{Threshold decryption latency for LWE ciphertext (67-of-100)}
\label{tab:threshold}
\end{table}

The dominant cost is network latency for collecting 67 partial decryptions. Computation is negligible relative to communication.

\subsection{End-to-End Application Benchmarks}

\begin{table}[h]
\centering
\begin{tabular}{lrr}
\toprule
\textbf{Application} & \textbf{Latency (ms)} & \textbf{Gas Cost} \\
\midrule
Encrypted order match (2 orders) & 48 & 1.8M \\
Sealed-bid auction (64 bids) & 312 & 42M \\
4-layer NN inference (CKKS) & 580 & 68M \\
\bottomrule
\end{tabular}
\caption{End-to-end application benchmarks on GPU-enabled validators}
\label{tab:e2e}
\end{table}

%----------------------------------------------------------------------