papers/zoo-fhe/sections/06-integration-with-t-chain.tex

\section{Integration with T-Chain}

\label{sec:tchain}
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\Zoo{} \TChain{} (Threshold Chain) combines threshold signing~\cite{zoo-threshold-signatures} with FHE in a unified VM execution environment.

\subsection{FHE Opcodes}

The \TChain{} VM extends the EVM with FHE-specific opcodes:

\begin{table}[h]
\centering
\small
\begin{tabular}{lll}
\toprule
\textbf{Opcode} & \textbf{Operation} & \textbf{Gas Cost} \\
\midrule
\texttt{FHE\_ENC} & Encrypt plaintext to \TFHE{}/\CKKS{} ciphertext & 50{,}000 \\
\texttt{FHE\_ADD} & Homomorphic addition & 10{,}000 \\
\texttt{FHE\_MUL} & Homomorphic multiplication (+ relin) & 200{,}000 \\
\texttt{FHE\_BOOT} & Programmable bootstrap (\TFHE{}) & 500{,}000 \\
\texttt{FHE\_RESCALE} & Rescale \CKKS{} ciphertext & 80{,}000 \\
\texttt{FHE\_ROTATE} & Rotate \CKKS{} slots & 150{,}000 \\
\texttt{FHE\_DEC\_REQ} & Request threshold decryption & 1{,}000{,}000 \\
\bottomrule
\end{tabular}
\caption{FHE opcodes added to the \TChain{} VM}
\label{tab:opcodes}
\end{table}

Gas costs reflect computational load. \texttt{FHE\_DEC\_REQ} is the most expensive because it triggers a multi-round threshold decryption protocol across 67+ validators.

\subsection{GPU Acceleration Configuration}

Validators configure GPU FHE acceleration in their node configuration:

\begin{itemize}
  \item \texttt{fhe.gpu.enabled}: boolean, default \texttt{true} for \TChain{} validators.
  \item \texttt{fhe.gpu.device}: CUDA device index (supports multi-GPU).
  \item \texttt{fhe.gpu.max\_batch}: maximum bootstrap batch size (default 4096).
  \item \texttt{fhe.gpu.memory\_limit}: GPU memory reserved for FHE (default 40\,GB).
\end{itemize}

Validators without GPU support may still participate in consensus and threshold decryption but cannot execute FHE opcodes. Block producers for FHE-heavy blocks are selected preferentially from the GPU-enabled validator subset.

\subsection{Ciphertext Storage}

\TFHE{} ciphertexts (LWE, $\sim$5\,KB each) and \CKKS{} ciphertexts ($\sim$3.75\,MB at full level) are stored in a dedicated ciphertext trie separate from the account state trie. Content-addressing (Blake3 hash) enables deduplication. State rent is charged per ciphertext per epoch to bound storage growth.

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