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Auto-fixes from the paper accuracy swarm: unambiguous build-breakers, broken \ref/\cite/\input targets, and prose typos. Substantive accuracy findings (dates, contradictory numbers, LP numbering) reported separately for review.
64 lines
2.2 KiB
TeX
64 lines
2.2 KiB
TeX
\section{Security Analysis}
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\subsection{Quantum Attack Surface}
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\begin{table}[h]
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\centering
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\begin{tabular}{lll}
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\toprule
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\textbf{Component} & \textbf{Classical Security} & \textbf{Quantum Security} \\
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\midrule
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Validator signatures & ECDSA (128-bit) & ML-DSA (128-bit) \\
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Block finality proofs & BLS (128-bit) & zk-STARK (256-bit) \\
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Key exchange (P2P) & ECDH (128-bit) & ML-KEM (128-bit) \\
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Long-term checkpoints & ECDSA (128-bit) & SLH-DSA (FIPS 205, formerly SPHINCS+) (192-bit) \\
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Cross-chain bridges & Multi-sig (96-bit) & Threshold ML-DSA (128-bit) \\
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\bottomrule
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\end{tabular}
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\caption{Security comparison: Classical vs Quantum}
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\end{table}
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\subsection{Threat Model}
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\textbf{Adversary capabilities}:
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\begin{enumerate}
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\item \textbf{Quantum computer}: 10,000+ logical qubits (sufficient for Shor's algorithm)
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\item \textbf{Network control}: Can delay/reorder messages (Byzantine)
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\item \textbf{Stake control}: Controls up to 33\% of validator stake
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\end{enumerate}
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\textbf{Security guarantees}:
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\begin{itemize}
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\item \textbf{Liveness}: Network progresses as long as $>$66\% honest validators
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\item \textbf{Safety}: No conflicting blocks finalized (even with quantum computer)
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\item \textbf{Censorship resistance}: Transactions eventually included
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\end{itemize}
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\subsection{Cryptographic Assumptions}
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\textbf{Theorem 1} (Quantum-Safe Consensus):
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\begin{quote}
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If MLWE problem is $(T, \epsilon)$-hard for quantum algorithms, then Lux Quantum Consensus achieves $(T', \epsilon')$-security where $T' = T / poly(n)$ and $\epsilon' = \epsilon \cdot n$.
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\end{quote}
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\textbf{Proof sketch}: Security reduces to breaking ML-DSA signatures, which requires solving MLWE. With $n$ validators, union bound gives factor-$n$ security loss. $\square$
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\subsection{Hybrid Security Transition}
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During migration, we use \textbf{dual signatures}:
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\begin{equation}
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\text{Sig}_{\text{hybrid}}(m) = (\text{ECDSA}(sk_1, m), \text{ML-DSA}(sk_2, m))
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\end{equation}
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\textbf{Validation}: Block is valid if \emph{both} signatures verify.
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\textbf{Timeline}:
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\begin{itemize}
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\item \textbf{Phase 1} (2025): Hybrid mode (ECDSA + ML-DSA)
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\item \textbf{Phase 2} (2027): ML-DSA primary, ECDSA optional
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\item \textbf{Phase 3} (2030): ML-DSA only (ECDSA deprecated)
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\end{itemize}
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