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zooqueen
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.
51 lines
1.6 KiB
TeX
51 lines
1.6 KiB
TeX
\section{Security Considerations}
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\subsection{Byzantine Fault Tolerance}
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Q-Chain maintains safety under standard Byzantine assumptions:
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\begin{theorem}[Safety]
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If $f < n/3$ validators are Byzantine and the network delay $\Delta < \Delta_{max}$, then no two honest validators finalize conflicting blocks.
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\end{theorem}
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\begin{proof}
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For a block to finalize, it requires:
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\begin{enumerate}
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\item BLS signatures from $\geq 2n/3$ validators
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\item Corona shares from $\geq 2n/3$ validators
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\item Confidence $\geq \beta$ in Lux voting
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\end{enumerate}
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With $f < n/3$ Byzantine nodes, at least $n - f > 2n/3$ honest nodes exist. Two conflicting blocks cannot both obtain $2n/3$ signatures from honest validators.
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\end{proof}
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\subsection{Liveness}
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\begin{theorem}[Liveness]
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If $f < n/3$ validators are Byzantine and network delay $\Delta < \Delta_{max}$, then all valid transactions eventually finalize.
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\end{theorem}
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\begin{proof}
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Honest validators always prefer valid transactions. With $>2n/3$ honest validators and bounded network delay, the Lux consensus mechanism guarantees that valid preferences reach confidence threshold $\beta$ within finite rounds.
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\end{proof}
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\subsection{Slashing Conditions}
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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{Reason} & \textbf{Evidence} & \textbf{Penalty} \\
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\midrule
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Double Sign & Two conflicting block sigs & 100\% stake \\
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Missing PQ Cert & No Corona signature & 50\% stake \\
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Invalid Signature & Malformed signature & 75\% stake \\
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Extended Downtime & >99\% missed blocks & 25\% stake \\
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\bottomrule
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\end{tabular}
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\label{tab:slashing}
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\end{table}
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