papers/zoo-threshold-signatures/sections/08-gpu-acceleration.tex

\section{GPU Acceleration}

\label{sec:gpu}

\subsection{FHE Operations in T-Chain}

Threshold FHE decryption is the most computationally intensive operation in \TChain{}. Each validator holds a share of the FHE decryption key and must perform partial decryption on ciphertexts that may encode vectors of thousands of elements. \TChain{} offloads these operations to GPU:

\begin{itemize}
\item \textbf{NTT (Number Theoretic Transform)}: Polynomial multiplication in RLWE-based FHE uses NTT, which parallelizes across GPU cores. We observe $47\times$ speedup over CPU for degree-$2^{16}$ polynomials.
\item \textbf{Batch partial decryption}: Multiple ciphertexts are decrypted in a single GPU kernel launch, amortizing launch overhead.
\item \textbf{ZK proof generation}: Range proofs and commitment verification for CGGMP21 presignatures leverage GPU-parallel multi-scalar multiplication (MSM).
\end{itemize}

\subsection{Performance}

\begin{table}[h]
\centering
\begin{tabular}{lccc}
\toprule
\textbf{Operation} & \textbf{CPU (ms)} & \textbf{GPU (ms)} & \textbf{Speedup} \\
\midrule
FROST 2-round sign ($t{=}10, n{=}15$) & 12 & 3 & $4\times$ \\
CGGMP21 presignature ($t{=}10, n{=}15$) & 840 & 58 & $14.5\times$ \\
TFHE partial decrypt (degree $2^{16}$) & 2,350 & 50 & $47\times$ \\
ZK range proof (Bulletproofs) & 180 & 22 & $8.2\times$ \\
\bottomrule
\end{tabular}
\caption{GPU acceleration benchmarks (NVIDIA A100, single GPU)}
\label{tab:gpu}
\end{table}

These benchmarks demonstrate that GPU acceleration makes threshold FHE decryption practical at consensus timescales. See \cite{zoo-fhe} for the full FHE architecture.

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