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zooqueen 12912be1b5 papers: reconcile Corona to Module-LWE (Ringtail-derived, rank-7), not Ring-LWE rank-1

- canonical lux-corona-pq paper: rank-7 Module-LWE (A in R_q^{8x7}, q=48-bit), Module-SIS
- scrub residual Corona Ring-LWE/R-LWE labels across ethos-of-lux, pqsafe-il5,
  lux-whitepaper, lux-quasar-composition, lp-020; Corona<->Pulsar = parameter regime,
  both Module-LWE (not rank-1-vs-rank-k)
- LLM.md: drop stale 'Corona as rank-1' wobble note; align to code/Ringtail params
- rebuild affected PDFs

2026-06-20 01:59:25 -07:00

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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

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