papers/lux-mchain-mpc/sections/01-introduction.tex

\section{Introduction}


Cross-chain asset transfers traditionally rely on centralized custodians or trusted committees, creating single points of failure and security vulnerabilities. Recent bridge exploits have resulted in losses exceeding \$2B \cite{bridge-exploits-2022}, primarily due to compromised private keys, malicious insiders, or centralized infrastructure failures.

\subsection{The Bridge Trilemma}

Existing bridge architectures face three conflicting requirements:

\begin{enumerate}
\item \textbf{Security}: No single point of compromise
\item \textbf{Performance}: Sub-second finality for user experience
\item \textbf{Decentralization}: Permissionless participation
\end{enumerate}

Most bridges sacrifice one or more of these properties:
\begin{itemize}
\item \textbf{Centralized bridges}: Fast but trusted (e.g., centralized exchanges)
\item \textbf{Multi-sig bridges}: Decentralized but slow and quantum-vulnerable
\item \textbf{Light client bridges}: Trustless but expensive and limited cross-chain support
\end{itemize}

\subsection{M-Chain's Solution}

M-Chain solves the bridge trilemma through:

\begin{enumerate}
\item \textbf{Threshold Custody}: $t$-of-$n$ signatures required, no single point of compromise
\item \textbf{On-Chain Coordination}: SwapSigTx provides transparent, auditable proof of authorization
\item \textbf{Economic Security}: Staking, rewards, and slashing align validator incentives
\item \textbf{Quantum Resistance}: Dual signatures (classical + post-quantum) for future-proofing
\item \textbf{Sub-Second Finality}: Optimized MPC protocols achieve <200ms signature generation
\end{enumerate}