papers/lux-fraud-proofs/sections/07-lux-implementation-details.tex

\section{Lux Implementation Details}


Lux's fraud proof implementation leverages the network's unique architecture to provide enhanced functionality and performance.

\subsection{C-Chain Integration}

The fraud proof contracts deploy on the C-Chain, Lux's EVM-compatible chain:

\begin{lstlisting}[language=Solidity, caption=Lux Fraud Proof Manager]
contract LuxFraudProofManager {
    mapping(bytes32 => Challenge) public challenges;
    mapping(address => uint256) public stakes;
    
    function initiateChallenge(
        bytes32 assertionId,
        bytes calldata disputedState
    ) external payable {
        require(msg.value >= minStake, "Insufficient stake");
        // Create challenge with Lux-specific parameters
        challenges[challengeId] = Challenge({
            challenger: msg.sender,
            assertion: assertionId,
            stake: msg.value,
            deadline: block.timestamp + challengePeriod,
            bisectionRound: 0
        });
    }
}
\end{lstlisting}

\subsection{Bridge Rollup Support}

Lux bridges can leverage fraud proofs for secure cross-chain communication:

\begin{equation}
\text{BridgeProof} = \langle \text{SourceChain}, \text{DestChain}, \text{Message}, \text{StateProof} \rangle
\end{equation}

This enables verification of cross-chain messages without trusting bridge operators.

\subsection{Multi-Rollup Coordination}

Multiple rollups can share security through coordinated fraud proofs:

\begin{proposition}[Shared Security]
If rollups $R_1, R_2, ..., R_n$ share a common fraud proof contract, the security of the system is:
\begin{equation}
\text{Security}_{\text{total}} = 1 - \prod_{i=1}^{n}(1 - \text{Security}_i)
\end{equation}
where $\text{Security}_i$ is the probability that rollup $i$ has at least one honest challenger.
\end{proposition}

\subsection{Appchain as Execution Environment}

Lux appchains can serve as specialized rollup execution environments:

\begin{enumerate}
    \item \textbf{Dedicated Resources}: Appchain validators provide computational resources
    \item \textbf{Custom VM}: Specialized virtual machines for specific workloads
    \item \textbf{Native Integration}: Direct integration with Lux consensus
    \item \textbf{Flexible Parameters}: Customizable gas costs and execution rules
\end{enumerate}