papers/lux-quasar-composition/lux-quasar-composition.tex

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\title{Quasar: Composing Threshold Post-Quantum Signatures\\
for Blockchain Finality}

\author{
Zach Kelling\thanks{Corresponding author: [email protected]}\\
\textit{Lux Industries, Inc.}\\
\texttt{[email protected]}
}

\date{2026-05-18}

\begin{document}

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\begin{abstract}
\noindent
Quasar is the Lux Network's post-quantum (PQ) consensus suite.
Per-round finality is asserted via a single wire-format certificate,
the \emph{QuasarCert}, that composes up to five independent
cryptographic legs: a BLS12-381 aggregate signature (classical fast
path, discrete logarithm), a Pulsar threshold ML-DSA-65 signature
(Module-LWE), an optional Corona threshold signature (Module-LWE), an
optional Magnetar threshold SLH-DSA signature (hash-based), and a
Z-Chain Groth16 proof rolling up $N$ per-validator ML-DSA-65 identity
signatures into a 192-byte SNARK. Three cert profiles ---
\textbf{Pulsar} (BLS + Pulsar + Z-Chain Groth16; PQ floor),
\textbf{Aurora} (adds Corona; intra-lattice diversity), and
\textbf{Polaris} (adds Magnetar; cross-family) --- select which legs
are populated. Each profile is independently selectable per Lux
chain.

This paper formalizes the QuasarCert wire format, the three cert
profile compositions, and the cross-primitive composition theorems.
The central security claim is conjunctive hardness diversification:
forging a profile-$\mathcal{P}$ cert requires forging \emph{every}
populated leg, each backed by an independent hardness assumption.
We document the production deployment topology on Lux primary
network's Q-Chain finality and the gating from the current Pulsar
profile to the Aurora and Polaris profiles as the underlying
Corona and Magnetar primitives reach Tier A audit status. The
Pulsar profile is currently production-deployed; Aurora and
Polaris are operationally ready and gated on primitive maturity.

\textbf{Scope.} This is the umbrella paper for the Quasar suite.
The per-primitive papers --- LP-020 (Quasar consensus), LP-073
(Pulsar), Corona, Magnetar, and the Lean-mechanized soundness proof
at \texttt{quasar-cert-soundness.tex} --- own the per-leg security
arguments. This paper owns the cross-primitive composition: the wire
format that binds the legs into a single envelope, the verifier that
enforces the conjunction, and the theorems that bound forgery by the
minimum advantage across populated legs.
\end{abstract}

\tableofcontents
\newpage

\input{sections/01-introduction}
\input{sections/02-preliminaries}
\input{sections/03-wire-format}
\input{sections/04-profiles}
\input{sections/05-composition}
\input{sections/06-binding}
\input{sections/07-implementation}
\input{sections/08-evaluation}
\input{sections/09-threat-model}
\input{sections/10-production}
\input{sections/11-conclusion}

\bibliographystyle{plain}
\bibliography{references}

\appendix
\section*{Reproducibility}
\textbf{Source code.}
\texttt{github.com/luxfi/quasar} (umbrella spec, profile registry,
composition proofs);
\texttt{github.com/luxfi/consensus} (consensus engine, QuasarCert wire
implementation, \texttt{protocol/quasar/types.go} canonical);
\texttt{github.com/luxfi/pulsar} (threshold ML-DSA-65 primitive,
v1.0.9);
\texttt{github.com/luxfi/corona} (threshold Module-LWE primitive, v0.6.0);
\texttt{github.com/luxfi/magnetar} (threshold SLH-DSA primitive,
v0.2.0);
\texttt{github.com/luxfi/crypto} (BLS / ML-DSA / SLH-DSA primitives);
\texttt{github.com/luxfi/threshold} (threshold MPC protocol library);
\texttt{github.com/luxfi/chains/quantumvm} (Z-Chain Groth16 rollup VM).

\noindent\textbf{Build.}
\texttt{GOWORK=off go build ./...} and
\texttt{GOWORK=off go test ./...} in
\texttt{luxfi/consensus}; per-primitive build and KAT vectors are
documented in each repo's \texttt{README.md} and \texttt{SPEC.md}.

\noindent\textbf{Hardware tested.}
Apple M1 Max (10 cores, darwin/arm64) for the measurements in
Section~\ref{sec:eval}; commodity x86\_64 Linux validators
for production deployment.

\noindent\textbf{Standards referenced.}
FIPS 203 (ML-KEM), FIPS 204 (ML-DSA), FIPS 205 (SLH-DSA),
IETF \texttt{draft-irtf-cfrg-bls-signature}, RFC 9591 (FROST),
NIST IR 8214C (MPTC).

\noindent\textbf{Mechanized proofs.}
Lean proofs at \texttt{luxfi/proofs/lean/Consensus/Quasar.lean}
(triple-mode composition, BFT quorum intersection, single-round
uniqueness). LaTeX proof at
\texttt{luxfi/proofs/quasar-cert-soundness.tex}
(Theorems 7.5--7.8). TLA+ specifications at
\texttt{luxfi/proofs/tla/}. Tamarin protocol verification at
\texttt{luxfi/proofs/tamarin/}.

\noindent\textbf{Contact.}
\texttt{[email protected]}.

\end{document}