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papers/lux-quasar-benchmarks/sections/08-benchmark-6-dual-certificate-finality.tex

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\section{Benchmark 6: Dual-Certificate Finality}
\label{sec:dual-cert}
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This section quantifies the cost of Quasar's unique dual-certificate mechanism.
\subsection{Latency Decomposition}
\begin{table}[h]
\centering
\begin{tabular}{@{}lrr@{}}
\toprule
\textbf{Phase} & \textbf{Duration (ms)} & \textbf{Critical Path?} \\
\midrule
Block proposal broadcast & 12 & Yes \\
Network propagation (WAN RTT) & 38--62 & Yes \\
BLS partial signing & 0.31 & No (parallel) \\
Pulsar share generation & 0.048 & No (parallel) \\
Vote + share transmission & 38--62 & Yes \\
BLS aggregation & 0.84 & Yes \\
Pulsar combination (15-of-21)& 7.0 & Yes \\
Certificate broadcast & 38--62 & Yes \\
\midrule
\textbf{Total (3 RTT + compute)} & \textbf{$\sim$\,200\,ms} & \\
\bottomrule
\end{tabular}
\caption{Finality latency decomposition for Quasar at $n=21$, 3-datacenter deployment.
The critical path is dominated by network RTT, not cryptographic computation.}
\label{tab:dual-cert-breakdown}
\end{table}
\subsection{Overhead of Dual-Certificate vs. Single-Certificate}
To isolate the cost of dual-certificate finality, we ran Quasar in two modes:
\begin{itemize}
\item \textbf{BLS-only}: Classical single-certificate (no Pulsar).
\item \textbf{Dual-cert}: Full Quasar with both BLS and Pulsar.
\end{itemize}
\begin{table}[h]
\centering
\begin{tabular}{@{}lrrrr@{}}
\toprule
\textbf{Mode} & \textbf{Finality (ms)} & \textbf{TPS} & \textbf{Cert Size (B)} & \textbf{Overhead} \\
\midrule
BLS-only & 192 & 11{,}200 & 144 & baseline \\
Dual-cert & 204 & 10{,}400 & 1{,}168 & +6.3\% latency, $-$7.1\% TPS \\
\bottomrule
\end{tabular}
\caption{Cost of adding Pulsar post-quantum certificate to Quasar at $n=100$.}
\label{tab:dual-overhead}
\end{table}
\textbf{Key finding}: Dual-certificate finality adds only 12\,ms (6.3\%) latency and
reduces throughput by 7.1\%. The cost of quantum security is a $<$10\% performance
penalty---well within operational margin.
\subsection{Why the Overhead is Small}
Three design decisions minimize dual-certificate cost:
\begin{enumerate}
\item \textbf{Piggybacking}: Pulsar shares are sent alongside BLS partial signatures
in the same network message. No additional round trip.
\item \textbf{Threshold vs. multi-sig}: Pulsar combination is a single $\sim$7\,ms
computation, not $n$ individual verifications.
\item \textbf{Parallelism}: BLS aggregation and Pulsar combination run concurrently
on separate CPU cores. The finality deadline is
$\max(\text{BLS}, \text{Pulsar})$, not their sum.
\end{enumerate}
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