papers/lux-quasar-horizon/sections/09-related-work.tex

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\section{Related Work}
\label{sec:related-work}
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We compare Quasar Horizon to four neighboring consensus families: Tendermint / HotStuff (linear-chain BFT), Narwhal--Tusk / Bullshark / Aleph (DAG-native BFT), Threshold Raccoon / Hermine (post-quantum threshold primitives), and the lattice-vs-classical hybrid approaches in production research.

\subsection{Tendermint / HotStuff: linear-chain BFT, classical only}

Tendermint \cite{tendermint} and HotStuff \cite{hotstuff} are the canonical linear-chain BFT designs. Both finalize blocks via three rounds (propose / prevote / precommit for Tendermint; the four phases of HotStuff). The signing primitive is conventionally a classical aggregate signature (typically Ed25519 / BLS).

\paragraph{Differences vs Quasar Horizon.} (1) Linear chain vs DAG. Tendermint / HotStuff finalize linear blocks; Quasar Horizon finalizes Nebula DAG bundle roots. (2) Single-lane vs three-lane finality. Tendermint / HotStuff have one signing lane; Quasar Horizon composes a Beam, an ML-DSA cert set, and a Pulse. (3) Classical only vs hybrid PQ. Neither Tendermint nor HotStuff is post-quantum.

A natural question is whether one could ``just bolt'' a PQ threshold sig onto Tendermint / HotStuff. The answer is essentially yes (the threshold-Schnorr family fits in the precommit slot), with two caveats: (a) the lattice-threshold primitives have heavier online phases, which is a poor fit for a synchronous linear-chain hot path, and (b) without the validator-set-rotation lifecycle (LSS), the bolt-on becomes a static-committee scheme rather than a permissionless one. Quasar Horizon's contribution is the bolt-on done correctly, with asynchronous PQ finality and dynamic-resharing, integrated with a DAG substrate that absorbs the Pulse latency without blocking the hot path.

\subsection{Narwhal--Tusk / Bullshark / Aleph: DAG-native BFT, classical only}

Narwhal--Tusk \cite{narwhal} separates mempool / data-availability (Narwhal) from consensus (Tusk), with the consensus layer running over the DAG. Bullshark \cite{bullshark} optimizes the DAG-BFT path with synchronous and asynchronous fallbacks. Aleph \cite{aleph} provides asynchronous atomic broadcast over a DAG.

\paragraph{Differences vs Quasar Horizon.} (1) Classical only. None of these is post-quantum. (2) Single-lane vs three-lane. None composes BLS + ML-DSA + Pulse. (3) Static committees in their default deployments; LSS-style validator rotation is bolt-on work.

The Lux Quasar engine sits in the same DAG-BFT family operationally: Photons / Wave / Focus / Field / Nebula are the DAG-BFT machinery (LP-020 \cite{lp020}; \texttt{protocol/} layout in Section~\ref{sec:implementation}). The novel contribution is the post-quantum hybrid finality wrapper around the DAG-BFT core.

\subsection{Threshold Raccoon / Hermine: PQ threshold primitives, no consensus integration}

Threshold Raccoon \cite{thresholdraccoon} is a two-round Module-LWE threshold signature scheme; Hermine \cite{hermine} is a NIST MPTC-track lattice threshold scheme with DKG and proactive refresh. Both target the cryptographic primitive layer.

\paragraph{Differences vs Quasar Horizon.} The primitives compose into the Pulse lane as kernels; they do not by themselves answer the consensus questions: how does a permissionless validator set rotate without a per-epoch trusted dealer (LSS)? How does the Pulse compose with a fast classical aggregate (Beam) and a per-validator PQ accountability lane (ML-DSA cert set) over a shared transcript (Prism)? How does the Pulse follow the Beam without blocking the hot path (asynchronous PQ finality)? How does grouped deployment scale to large validator sets (Section~\ref{sec:grouped-pulsar})? Threshold Raccoon and Hermine specify the signing primitive; this paper specifies the consensus composition.

\paragraph{Pulsar vs Threshold Raccoon vs Hermine.} The Pulsar paper \cite{luxpulsar} discusses primitive-level differences. The composition argument here is kernel-agnostic: any two-round Module-LWE threshold signature satisfying the LP-073 systems contract works in the Pulse slot.

\subsection{FROST / Lens: classical curve threshold, complementary not competing}

FROST (RFC 9591 \cite{rfc9591}) is the canonical Schnorr-family threshold signature. Lens (LP-103 \cite{lp103}) is the Lux instantiation, with key-era lifecycle wrapping identical to Pulsar's (\texttt{proofs/definitions/algorithms.tex} Definition \texttt{def:lens-sign}).

\paragraph{Lens in the Lux stack.} Lens is the curve-side counterpart to Pulsar. It is classical, not post-quantum; it is the right primitive for control-plane operations (governance, parameter updates, validator-set transitions), where compactness and EVM-precompile-cheap verification matter and the ML-DSA cert set / Pulse already provide the PQ root of trust. Lens does not contribute to the Horizon PQ reduction.

\paragraph{LSS as the universal lifecycle.} The LSS lifecycle paper \cite{luxlssmpc} specifies the protocol-agnostic resharing framework that wraps Pulsar, Lens, and ECDSA-CMP under a single contract. The composition contribution of Quasar Horizon is the consensus-level cert; LSS is the orchestration framework underneath.

\subsection{Hybrid classical / PQ approaches in production research}

\paragraph{Replace BLS entirely (\cite{pqfinalitynobls}).} A maximalist position: drop BLS, run only ML-DSA + Pulse. Smaller cert in the common case; operationally simpler. Quasar Horizon takes the conservative position: keep BLS for fast classical finality, add ML-DSA + Pulse for the PQ floor. Defensible under the ``defense-in-depth'' argument: under a quantum break of BLS, the chain falls back to Pulse-sealed / Horizon-final without a chain-level upgrade. The cost is operational complexity; the benefit is graceful degradation.

\paragraph{Z-Chain Groth16 wrapper (LP-307 \cite{lp307}).} A pairing-based SNARK over BLS12-381 compressing the ML-DSA cert set into $\sim 192$ bytes plus a public-inputs hash. Useful for EVM verifier compatibility, useful for compression. Not post-quantum (Remark~\ref{rem:groth16-wrapper-horizon}); not a contribution to the Horizon PQ reduction.

\paragraph{Future PQ-friendly proof systems.} P3Q~\cite{luxp3q} or lattice-based transparent SNARKs replace Groth16 in the wrapper role once they are production-ready (cf.\ \cite{luxwarpv2} for the Warp 2.0 future-work parallel). Until then, the Groth16 wrapper is honest about its classical security limit.

\subsection{Summary table}

\begin{tabular}{@{}p{0.20\textwidth}p{0.18\textwidth}p{0.14\textwidth}p{0.20\textwidth}p{0.16\textwidth}@{}}
  \toprule
  \textbf{Family} & \textbf{Substrate} & \textbf{PQ?} & \textbf{Lifecycle} & \textbf{Lanes} \\
  \midrule
  Tendermint & linear chain & no & static & 1 \\
  HotStuff & linear chain & no & static & 1 \\
  Narwhal--Tusk & DAG & no & static & 1 \\
  Bullshark & DAG & no & static & 1 \\
  Aleph & DAG & no & static & 1 \\
  Threshold Raccoon & primitive only & yes & static & --- \\
  Hermine & primitive only & yes & proactive & --- \\
  FROST & primitive only & no & static & --- \\
  \textbf{Quasar Horizon} & \textbf{DAG (Nebula)} & \textbf{yes (hybrid)} & \textbf{LSS-managed dynamic} & \textbf{3 (Beam + ML-DSA + Pulse)} \\
  \bottomrule
\end{tabular}

The Quasar Horizon row is the only design that combines a DAG substrate, post-quantum threshold finality, dynamic validator-set rotation, and conjunctive multi-lane composition. That combination is the contribution.