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}.

\begin{thebibliography}{99}
\bibitem{shor1997polynomial} P. Shor, ``Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,'' \emph{SIAM J. Computing}, 1997.
\bibitem{boldyreva2003threshold} A. Boldyreva, ``Threshold signatures, multisignatures and blind signatures based on the gap-Diffie-Hellman-group signature scheme,'' in \emph{PKC}, 2003.
\bibitem{komlo2020frost} C. Komlo and I. Goldberg, ``FROST: Flexible round-optimized Schnorr threshold signatures,'' in \emph{SAC}, 2020.
\bibitem{canetti2021uc} R. Canetti et al., ``UC non-interactive, proactive, threshold ECDSA with identifiable aborts,'' in \emph{CCS}, 2021.
\bibitem{bendlin2013semi} R. Bendlin, S. Krehbiel, C. Peikert, and A. Rosen, ``Semi-homomorphic encryption and multiparty computation,'' in \emph{EUROCRYPT}, 2013.
\bibitem{boneh2018threshold} D. Boneh et al., ``Threshold cryptosystems from threshold fully homomorphic encryption,'' in \emph{CRYPTO}, 2018.
\bibitem{cozzo2023sharing} D. Cozzo and N. Smart, ``Sharing the LUOV: Threshold post-quantum signatures,'' in \emph{IMA}, 2023.
\bibitem{espitau2024fiat} T. Espitau, M. Tibouchi, and A. Wallet, ``Practical Fiat-Shamir with aborts threshold signatures from lattices,'' 2024.
\bibitem{ringtail} G. Boschini, A. Kaviani, R. W. F. Lai, G. Malavolta, A. Takahashi, and M. Tibouchi, ``Ringtail: Practical two-round threshold signatures from LWE,'' IACR ePrint 2024/1113; IEEE S\&P 2025.
\bibitem{lyubashevsky2010ideal} V. Lyubashevsky, C. Peikert, and O. Regev, ``On ideal lattices and learning with errors over rings,'' in \emph{EUROCRYPT}, 2010.
\bibitem{langlois2015module} A. Langlois and D. Stehl\'e, ``Worst-case to average-case reductions for module lattices,'' \emph{Designs, Codes and Cryptography}, 2015.
\bibitem{regev2009lattices} O. Regev, ``On lattices, learning with errors, random linear codes, and cryptography,'' \emph{JACM}, 2009.
\bibitem{pulsar} Lux Core Team, ``Pulsar: Module-LWE threshold ML-DSA-65 (FIPS~204 byte-equal),'' Lux Proposal LP-4450.
\bibitem{magnetar} Lux Core Team, ``Magnetar: hash-based threshold SLH-DSA (FIPS~205),'' Lux Proposal LP-4540.
\bibitem{corona} Lux Core Team, ``Corona reference implementation,'' \texttt{github.com/luxfi/corona} (v0.10.x); Lux Proposal LP-4440.
\bibitem{raccoon} R. del Pino, T. Espitau, S. Katsumata, M. Maller, F. Mouhartem, T. Prest, and M.-J. Saarinen, ``Raccoon: A side-channel-secure signature scheme,'' \texttt{raccoonfamily.org}, 2023 (NIST additional-signatures Round-1 submission).
\bibitem{traccoon} R. del Pino, S. Katsumata, M. Maller, F. Mouhartem, T. Prest, and M.-J. Saarinen, ``Threshold Raccoon: Practical threshold signatures from standard lattice assumptions,'' in \emph{EUROCRYPT}, 2024.
\bibitem{musigl} C. Boschini, A. Takahashi, and M. Tibouchi, ``MuSig-L: Lattice-based multi-signature with single-round online phase,'' in \emph{CRYPTO}, 2022.
\bibitem{ekt} T. Espitau, S. Katsumata, and K. Takemure, ``Two-round threshold signature from algebraic one-more learning with errors,'' in \emph{CRYPTO}, 2024.
\bibitem{hintmlwe} D. Kim, D. Lee, J. Seo, and Y. Song, ``Toward practical lattice-based proof of knowledge from Hint-MLWE,'' in \emph{CRYPTO}, 2023.
\end{thebibliography}