Lux Papers -- LLM.md

Post-E2E-PQ State (current)

Papers in this repo are the LaTeX backing for the LP / HIP proposal set. Pulsar (HIP-0084 / LP-171) and Z-Wing (LP-9702 — hybrid PQ secure channel) are the new additions this session.

Recent significant commits

SHA	Impact
`9bae519`	LP-9702: Z-Wing hybrid PQ secure channel
`ee5f6d2`	PQ canonical terminology (FIPS 203/204/205 + Pulsar + Lamport)
`75b2ab8`	Warp 2.0 canonical naming (Beam + ML-DSA + Pulse) + Lux Teleport rebrand
`d747bfe`	lux-nist-mptc-submission: convert .md → .tex (LaTeX-only rule)
`e7b9509`	lp-103: T-Chain (FHE) → F-Chain per LP-134
`78371e8`	M/F/Z-Chain canonical naming per LP-134

Rules

LaTeX only. Per user CLAUDE.md: papers, proofs, audits MUST be .tex (no .md). Translation of any prior .md is a one-shot conversion.
Cross-references between LP-020 (Quasar) and the proofs repo are kept explicit via \cite{qcert-proof}.

LP-020: Quasar Consensus (`lp-020-quasar-consensus.tex`)

Main protocol paper. 19 pages. Sections:

S1 Introduction: Three-layer consensus, algebraic independence of assumptions.
S2 System Model: Partial synchrony, static Byzantine corruption, cryptographic config.
S3 Protocol: Photon (proposal), Wave (FPC voting), Quasar (certificate generation).
S4 Cryptographic Layers: BLS12-381, Pulsar (Module-LWE threshold), ML-DSA-65.
S5 Chain Separation (added 2026-04-13): X=verify, Q=Pulsar consensus, T=all MPC, Z=Groth16 of ML-DSA. Table~2.
S6 QuasarCert (added 2026-04-13): Formal 3-tuple definition. (\sigma_{RT}, \sigma_{BLS}, \pi_{ZK}). Groth16 compresses N ML-DSA sigs to 192 bytes. Def~~6.1, Def~~6.2.
S7 Security Analysis: Safety (Thm~~7.1), Liveness (Thm~~7.2), Unforgeability (Thm~~7.3), Single-Compromise (Thm~~7.4).
- S7.5 QuasarCert Soundness (added 2026-04-13): Thm~7.5. Per-component forgery analysis + composition. Union bound.
- S7.6 Parallel Liveness (added 2026-04-13): Thm~7.6. Three paths parallel; adversary must stall all three.
- S7.7 Post-Quantum Safety (added 2026-04-13): Thm~7.7. If co-CDH falls to Shor, Pulsar + ML-DSA suffice. Explicit hybrid reduction.
S8 Performance: BLS 371us, ML-DSA 504us, Pulsar 2-round, ZAP wire protocol.
S9 Implementation: Go 1.24, luxfi/consensus, SQLite WAL, epoch pruning.
S10 Formal Verification: Lean 4 + Tamarin artifacts.
Appendix A (added 2026-04-13): Why not threshold ML-DSA (rejection sampling circular dependency, hint computation, no NIST standard) or threshold FALCON (distributed Gaussian sampling open problem, O(n^2) rounds, secondary standard).

Companion proof: /Users/z/work/lux/proofs/quasar-cert-soundness.tex (10 pages, 831 lines).

Proof Sketch Appendices (added 2026-04-13)

Appendix B (\ref{app:circuit}): ML-DSA-65 Groth16 circuit analysis. R1CS constraint count: ~1.35M per verification, ~5.77M total (n=21 optimized, ~2^22.5). Proof size 192B (circuit-independent). CPU prover ~400ms, GPU ~5-15ms. Corrects 357us claim.
Appendix C (\ref{app:adaptive}): Adaptive corruption model. Static-only for Thm 7.5. Two corollaries: (1) programmable RO with O(n*Q_H) loss, (2) erasure model with no loss. Cites Canetti 2001, Fischlin 2005, Garay-Kiayias-Leonardos 2015.
Appendix D (\ref{app:setup}): Groth16 trusted setup. Circuit-specific SRS, N-party ceremony (Bowe-Gabizon-Miers 2017), PLONK/Marlin as universal-setup upgrade path (192B -> ~500B).
Appendix E (\ref{app:corona-params}): Pulsar parameter tightness. d=2048, q~~2^48, BKZ beta~~430. Classical 2^142, quantum 2^130.35 via BDGL sieving + Grover. Comparison table with ML-DSA-65 and ML-KEM-768. Four explicit caveats.

LP-020 Thm 7.5 and Thm 7.7 now cross-reference these appendices via \cite{qcert-proof}.

lux-quasar-consensus.tex: Earlier Quasar draft (superseded by LP-020).
lux-triple-proof-consensus.tex: Triple-proof note (superseded by LP-020).
lux-corona-pq.tex: the canonical Corona paper — "Corona: Two-Round Module-LWE Threshold Signatures for Public Permissionless Chains". Module-LWE at module rank 7 (matrix A ∈ R_q^{8×7}, b = A·s + e, R_q = Z_q[X]/(X^256+1), 48-bit q), Module-SIS commitments, leaderless permissionless DKG, ~33 KB sigs (NIST Cat-1), precompile 0x012206 / P3Q kind 0x02, Aurora-profile diversity leg (Pulsar ‖ Corona). Aligns with LP-4440 and the luxfi/corona/Ringtail parameters (N=256/M=8/Nvec=7). The Corona↔Pulsar distinction is parameter regime / lifecycle (Corona = the Ringtail-derived permissionless-DKG leg), not rank-1-vs-rank-k; both are Module-LWE. Pulsar is the ML-DSA-byte-equal sibling at LP-4450 / lp-073-pulsar. (Rewritten 2026-06 from the old mislabeled "Pulsar" body.)
lux-threshold-mpc.tex: FROST + CGGMP21 for M-Chain custody (the MPC chain).
lux-zchain.tex: Z-Chain privacy/ZKP architecture.
lux-mchain-mpc.tex: M-Chain MPC — the threshold/MPC chain (T-Chain was split into M-Chain (MPC) + F-Chain (FHE)).

Build

cd ~/work/lux/papers
/Library/TeX/texbin/pdflatex -interaction=nonstopmode lp-020-quasar-consensus.tex
# Run twice for cross-references

Papers website

site/ is the source for https://papers.lux.network. Its prebuild catalog generator reads the tracked PDF set from Git, copies every tracked artifact into the static export, and combines that complete archive with curated metadata for the featured papers. Do not hand maintain a partial PDF list. .github/workflows/deploy-site.yml verifies and uploads the static export from main, but does not deploy it: the private application repository's GitHub plan does not support Pages. Production is the Cloudflare Pages project lux-papers, whose custom domain is papers.lux.network; publish site/out there from a trusted deployment environment with Pages edit credentials.

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