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a1f77cacc9
Ringtail (Boschini et al., ePrint 2024/1113) is third-party prior art; Lux's Corona (Ring-LWE = Module-LWE rank-1) builds on it; Pulsar is Module-LWE rank-k. Retired the conflated boschini2024corona/corona2024/coronago/... bib keys to the single canonical ringtail/corona/pulsar/magnetar keys, rewrote \cite + \bibitem by context, and fixed 'Pulsar (Ring-LWE)' mislabels (Corona where corona.metal/ single-ring/Ringtail-derived; Pulsar where Module-LWE rank-k/ML-DSA). Cryptographer-led.
57 lines
2.5 KiB
TeX
57 lines
2.5 KiB
TeX
\section{Concrete Security Analysis (2025 Revision)}
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\subsection{Forgery Probability}
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We compute concrete security margins for the deployed MPC configurations. For a $(t, n)$-threshold scheme, the forgery probability depends on the underlying hardness assumption:
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\begin{table}[h]
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\centering
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\begin{tabular}{@{}llll@{}}
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\toprule
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\textbf{Scheme} & \textbf{Configuration} & \textbf{Hardness} & \textbf{$\Pr[\text{Forge}]$} \\
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\midrule
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CGG21 & 11-of-15 (ETH) & ECDLP + Paillier & $< 2^{-127}$ \\
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MuSig2 & 11-of-15 (BTC) & OMDL in ROM & $< 2^{-128}$ \\
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FROST & 7-of-10 (XRPL) & OMDL in ROM & $< 2^{-128}$ \\
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Corona & 15-of-21 (PQ) & LWE ($n=630$, $q=2^{32}$) & $< 2^{-128}$ \\
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Dual-sig & CGG21 + Corona & ECDLP $\times$ LWE & $< 2^{-255}$ \\
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\bottomrule
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\end{tabular}
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\label{tab:concrete-security}
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\end{table}
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\subsection{Liveness at Scale}
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For $n = 100$ validators, $t = 67$ threshold, individual uptime $p = 0.999$:
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\begin{equation}
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\Pr[\text{unavailable}] = \Pr[\text{Binomial}(100, 0.999) < 67] < 2^{-139.6}
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\end{equation}
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This is computed via the exact binomial CDF. The expected available nodes $\mu = 99.9$ exceeds the threshold by $32.9$ nodes, providing substantial headroom. See Appendix of the companion Lux Bridge paper \cite{lux-bridge-2025} for the full derivation.
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\subsection{Contract-Level Security Fixes}
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Four critical vulnerabilities were identified in the bridge smart contracts that interact with M-Chain:
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\begin{enumerate}
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\item \textbf{C-01}: \texttt{bridgeMint()} in LRC20B lacked daily limits. Fixed: configurable \texttt{dailyMintLimit} with automatic period reset.
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\item \textbf{C-02}: \texttt{MINTER\_ROLE} was conflated with \texttt{DEFAULT\_ADMIN\_ROLE}. Fixed: separate role with explicit grant/revoke.
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\item \textbf{C-03}: MPC-signed messages used \texttt{block.timestamp} as nonce. Fixed: monotonic counter nonce per bridge contract.
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\item \textbf{C-04}: Withdraw nonce used predictable hash. Fixed: sequential per-user counter nonce.
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\end{enumerate}
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All fixes verified by Halmos symbolic proofs (68 \texttt{check\_} functions across the ecosystem).
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\subsection{Formal Verification}
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The M-Chain threshold cryptography is backed by Lean~4 proofs at \texttt{github.com/luxfi/formal}:
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\begin{itemize}
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\item \texttt{Crypto/FROST.lean}: FROST correctness and threshold unforgeability
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\item \texttt{Crypto/BLS.lean}: BLS aggregation soundness from bilinearity
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\item \texttt{Crypto/Corona.lean}: LWE security with concrete parameters ($n=630$, $q=2^{32}$, $\sigma=13744$)
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\item \texttt{Consensus/BFT.lean}: $2f+1$ quorum safety for SwapSigTx validation
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\end{itemize}
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