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zooqueen
b7905739c2
Fix residual mislabels the citation pass missed (no-scheme-key papers): - 'Pulsar (Ring-LWE)' -> 'Pulsar (Module-LWE)' in lux-pq-migration, lux-triple-proof-consensus, lux-master-security-model, quasar-4-activation. - lp-020: reverse mislabel 'Module-LWE for Corona' -> 'Ring-LWE for Corona' (restores the BLS/Corona/Pulsar assumption-diversity point). - lp-203: '(Module-LWE NTT)' -> '(shared lattice NTT)' (Corona is Ring-LWE). - nasua's 'Pulsar lifts Ring-LWE to Module-LWE' left intact (correct rank-1->k). - LLM.md: correct lux-corona-pq description (misnamed Pulsar paper) + M/F-chain. Rebuilt all 6 affected PDFs.
51 lines
2.0 KiB
TeX
51 lines
2.0 KiB
TeX
\section{Phase 1: Hybrid Deployment}
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\textbf{Status: Active (since Lux genesis).}
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In Phase 1, both classical and post-quantum signatures coexist. The security guarantee is: the system is secure if \emph{either} the classical or the post-quantum scheme is unbroken.
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\subsection{Dual Signature Model}
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Every validator registers four keys on the P-Chain:
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\begin{center}
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\begin{tabular}{llrl}
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\toprule
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\textbf{Key Type} & \textbf{Algorithm} & \textbf{Size} & \textbf{Purpose} \\
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\midrule
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EC key & secp256k1 & 33 B (compressed) & EVM address derivation \\
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BLS key & BLS12-381 & 48 B & Per-block consensus aggregation \\
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ML-DSA key & ML-DSA-65 & 1,952 B & Per-epoch PQ identity \\
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Pulsar key & Module-LWE & 2,048 B & Per-epoch PQ anonymous threshold \\
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\bottomrule
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\end{tabular}
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\end{center}
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\subsection{Per-Block Verification (Classical)}
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Each block contains a BLS aggregate signature. Verification:
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$$\text{BLS.Verify}(\text{aggPK}, \text{blockHash}, \sigma_{BLS}) \stackrel{?}{=} \text{true}$$
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This provides sub-millisecond consensus for real-time block production.
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\subsection{Per-Epoch Verification (PQ)}
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Each epoch (1,000 blocks = 1 second) contains a STARK proof compressing $N$ ML-DSA signatures and a Pulsar threshold signature:
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$$\text{STARK.Verify}(\pi, \text{epochDigest}) \stackrel{?}{=} \text{true}$$
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This provides post-quantum finality without per-block overhead.
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\subsection{Hybrid Security Property}
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\begin{theorem}[Hybrid Security]
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If either (a) the BLS discrete logarithm problem is hard, or (b) the Module-LWE problem (ML-DSA) and Module-LWE problem (Pulsar) are hard, then the consensus mechanism is secure.
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\end{theorem}
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\begin{proof}
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The BLS aggregate provides classical security per-block. The STARK-compressed ML-DSA + Pulsar provides post-quantum security per-epoch. An adversary must break both to forge a finalized epoch. Since the two are based on independent mathematical problems (discrete log vs. lattice), compromising one does not help with the other.
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\end{proof}
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