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papers/lux-zchain/sections/03-zk-evm-architecture.tex
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\section{zk-EVM Architecture}
\subsection{zkEVM Design}
Z-Chain implements a \textbf{Type-3 zkEVM} (EVM-equivalent bytecode):
\begin{enumerate}
\item User submits shielded transaction $T$
\item Sequencer executes $T$ off-chain, generates witness $w$
\item Prover generates zk-SNARK proof $\pi$:
\begin{equation}
\pi \leftarrow \text{Prove}\left(\text{ValidExec}(T, w, \text{state}_{\text{old}}, \text{state}_{\text{new}})\right)
\end{equation}
\item L1 verifier checks $\pi$ and updates state commitment
\end{enumerate}
\textbf{Privacy Guarantee}: L1 sees only state commitment $C = \text{Hash}(\text{state}_{\text{new}})$, not transaction details.
\subsection{Proof System}
\textbf{Circuit Constraints}:
\begin{itemize}[leftmargin=1.1em]
\item EVM opcode execution: 2.1M constraints
\item Merkle proof verification: 850k constraints
\item Signature verification (ECDSA): 1.5M constraints
\item Total: \textbf{4.45M constraints}
\end{itemize}
\textbf{Performance}:
\begin{itemize}[leftmargin=1.1em]
\item Proof generation: 6.8s per transaction
\item Proof size: 288 bytes (Groth16)
\item Verification time: 12ms on-chain
\item Gas cost: 280k per proof
\end{itemize}