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papers/lux-cross-chain-security/sections/09-quantitative-security-analysis.tex

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\section{Quantitative Security Analysis}
\subsection{Attack Cost}
\begin{center}
\begin{tabular}{lrr}
\toprule
\textbf{Attack} & \textbf{Requirement} & \textbf{Cost Estimate} \\
\midrule
Consensus override (any chain) & $>1/3$ stake & $>$\$500M at current valuations \\
Warp message forgery & $>1/3$ validator BLS keys & Same as consensus override \\
Finality reversion & Break BLS + ML-DSA + Pulsar & Computationally infeasible \\
Cross-chain replay & Find collision in SHA-256 & $2^{128}$ operations \\
Validator set manipulation & P-Chain consensus attack & $>1/3$ stake \\
\bottomrule
\end{tabular}
\end{center}
\subsection{Comparison with External Bridges}
\begin{center}
\begin{tabular}{lcc}
\toprule
\textbf{Property} & \textbf{External Bridge} & \textbf{Lux Warp} \\
\midrule
Trust assumption & Bridge operators ($M$-of-$N$) & Primary network ($>2/3$ stake) \\
Validator set & Bridge-specific (often small) & Shared with consensus \\
Finality dependency & Source chain only & Triple-proof (both chains) \\
Upgrade risk & Bridge contract upgrades & Protocol-level (hard fork) \\
Historical loss & \$2B+ & \$0 \\
\bottomrule
\end{tabular}
\end{center}