papers/lightspeed-dex/sections/04-cross-chain-swaps.tex

\section{Cross-Chain Swaps}


\subsection{Atomic Swap Protocol}

We implement \textbf{light client bridges} for instant cross-chain verification:

\begin{algorithm}
\caption{Lux $\leftrightarrow$ Ethereum Atomic Swap}
\begin{algorithmic}
\STATE \textbf{Setup}:
\STATE Lux validator set: $V_L = \{v_1, \ldots, v_n\}$
\STATE Ethereum light client on Lux: $LC_{ETH}$
\STATE Lux light client on Ethereum: $LC_{LUX}$

\STATE \textbf{User initiates swap} (100 LUX $\to$ 2 ETH):
\STATE Lock 100 LUX in escrow contract on Lux
\STATE Emit event: $E_L = \text{SwapInitiated}(user, 100 LUX)$

\STATE \textbf{Relayers observe event} (50ms):
\STATE Submit Merkle proof of $E_L$ to Ethereum
\STATE $LC_{LUX}$ verifies proof against Lux block header

\STATE \textbf{Ethereum executes swap} (12 seconds):
\STATE If proof valid, release 2 ETH to user
\STATE Emit event: $E_E = \text{SwapCompleted}(user, 2 ETH)$

\STATE \textbf{Lux finalizes} (200ms):
\STATE Relayers submit proof of $E_E$ to Lux
\STATE $LC_{ETH}$ verifies, marks swap complete
\STATE Burn 100 LUX (or keep in liquidity pool)

\STATE \textbf{Total Time}: 12.25 seconds (dominated by Ethereum)
\end{algorithmic}
\end{algorithm}

\textbf{Optimization for HFT}: Pre-stage liquidity on both chains, settle later.

\subsection{Sub-500ms Settlement}

For Lux $\leftrightarrow$ Lux appchain swaps:

\begin{enumerate}
    \item Both chains share validator set
    \item Atomic transaction executed in single block
    \item Settlement: 10ms (single GPU BLS consensus round)
\end{enumerate}

\begin{lstlisting}[language=Go]
type AtomicSwap struct {
    ChainA   string  // Source chain
    ChainB   string  // Dest chain
    AmountA  uint64
    AmountB  uint64
    Timeout  uint64  // Revert if not settled
}

func (s *AtomicSwap) Execute() error {
    // Lock assets on both chains simultaneously
    lockA := s.ChainA.Lock(s.AmountA, s.Timeout)
    lockB := s.ChainB.Lock(s.AmountB, s.Timeout)
    
    // Validators sign both state transitions
    sig := ValidatorSet.SignAtomic(lockA, lockB)
    
    // Finalize in single block
    return Consensus.FinalizeAtomic(sig)
}
\end{lstlisting}