papers/lux-corona-pq/sections/99-conclusion.tex

\section{Conclusion}

\label{sec:conclusion}

Corona is the foundational member of the Lux lattice threshold-signature family: a
two-round Module-LWE threshold scheme over the module $R_q^{N'}$ (with
$\mathbf{A} \in R_q^{8 \times 7}$, $R_q = \mathbb{Z}_q[X]/(X^{256}+1)$,
$q = \texttt{0x1000000004A01}$), with Module-SIS commitments and Category~1 security
($\sim$128-bit classical, $\sim$130-bit quantum). It produces $\sim$33--35\,KB signatures
that verify in $\sim$1.6\,ms via the native precompile at \texttt{0x012206}. Its
distinguishing contribution is engineering rather than a new hardness assumption: Corona
takes the Ringtail two-round lattice threshold construction and makes it run on a public,
permissionless validator set through leaderless distributed key generation with no trusted
dealer, dynamic resharing across a changing set, and on-chain ceremony binding anchored to
the Lux Q-Chain. Under Quasar, Corona is the intra-lattice diversity leg of the Aurora
profile (Pulsar $\|$ Corona) and Polaris profile (Pulsar $\|$ Corona $\|$ Magnetar); the
production-tuned, FIPS~204-byte-equal Module-LWE sibling is Pulsar~\cite{pulsar}
(LP-4450), and the cross-family hash leg is Magnetar~\cite{magnetar} (LP-4540). The
reference implementation is \texttt{github.com/luxfi/corona}~\cite{corona} (a fork of
\texttt{luxfi/ringtail}), with machine-checked correctness in
\texttt{proofs/lean/Crypto/Corona.lean}.

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