papers/lux-bridge/lux-bridge.tex

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\title{Lux Bridge: Threshold-Secured Cross-Chain Communication\\with MPC Custody, Post-Quantum Verification,\\and Formally Verified Contract Invariants}
\author{
Zach Kelling\thanks{Corresponding author: [email protected]}
\quad
Vishnu Seesahai\\
\textit{Lux Industries, Inc.}\\
\texttt{[email protected]}
}
\date{2023}

\begin{document}

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\begin{abstract}
We present \textbf{Lux Bridge}, a trustless cross-chain communication protocol enabling atomic transfers between Lux L1, L2 appchains, L3 app-chains, and external blockchains (Ethereum, Bitcoin, Cosmos). In this revised edition we formalize the MPC security model that underpins the bridge's threshold custody layer. Specifically, we analyze the CGGMP21 and FROST threshold signature protocols deployed in production, proving a forgery probability of $2^{-139.6}$ for a $t = 67$-of-$n = 100$ committee on \texttt{secp256k1}. We introduce the \textbf{Quasar hybrid verification} layer, which combines BLS12-381 aggregate signatures with Corona post-quantum lattice signatures for quantum-resilient finality. We describe the integration of TFHE (threshold fully homomorphic encryption) for private bridge operations, enabling confidential cross-chain transfers where amounts and recipients are encrypted. We detail four critical security hardening measures (C-01 through C-04) applied to the bridge smart contracts and verified by 68 Halmos symbolic proofs. Formal proofs in Lean~4 cover the cryptographic primitives (BLS aggregation, FROST correctness, Corona LWE security). Lux Bridge achieves \textbf{sub-500ms cross-chain finality} on native routes, \textbf{$< \$0.001$} bridge costs through batch verification, and \textbf{99.99\% uptime} via a decentralized relayer network. Deployed on mainnet with zero bridge exploits.
\end{abstract}

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\input{sections/01-introduction}
\input{sections/02-architecture}
\input{sections/03-zk-light-client-protocol}
\input{sections/04-atomic-swap-protocol}
\input{sections/05-fraud-proof-system}
\input{sections/06-mpc-threshold-signature-security}
\input{sections/07-quasar-hybrid-verification}
\input{sections/08-tfhe-bridge-privacy}
\input{sections/09-contract-security-hardening}
\input{sections/10-formal-verification}
\input{sections/11-ibc-integration}
\input{sections/12-security-analysis}
\input{sections/13-performance-evaluation}
\input{sections/14-deployment}
\input{sections/15-future-work}
\input{sections/16-conclusion}
\input{sections/17-zk-circuit-specifications}
\input{sections/18-solidity-interfaces}
\input{sections/99-cggmp21-failure-probability-derivation}

\end{document}