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Forked from github.com/luxfi/corona @ d09b2c2. Pulsar inherits the
2-round signing math byte-equal but adds blockchain-grade key
lifecycle and a SHA3-based domain-separated hash profile for
permissionless validator-set rotation.
Inherits from upstream Corona (byte-equal):
- Sign1/Sign2/Combine 2-round signing math
- Lattice ring R_q = Z_q[X]/(X^256+1), q = 0x1000000004A01
- Module-LWE / Module-SIS hardness
- NTT, Discrete-Gaussian Ziggurat, MAC layer
Replaces from upstream:
- Broken Feldman-style DKG (pseudoinverse-recoverable). Replaced
with: (a) one-time foundation MPC ceremony / trusted-dealer
Bootstrap; (b) Pedersen DKG over R_q (research, dkg2/) hiding
under MLWE on B / binding under MSIS on [A | B].
- Trusted-dealer-per-epoch lifecycle (wrong shape for permissionless
rotation). Replaced with Verifiable Secret Resharing (VSR) every
epoch under the persistent group public key.
Key-era lifecycle (KeyEraID / Generation / RollbackFrom):
- KeyEraID bumps only at Reanchor (rare governance event)
- Generation bumps every Refresh / Reshare under the same GroupKey
- RollbackFrom records prior generation reverted from (0 = forward)
- Activation cert (QUASAR-PULSAR-ACTIVATE-v1) gates new generations
under the unchanged GroupKey
Pulsar-SHA3 hash profile (NIST FIPS 202 / SP 800-185):
- Hc: cSHAKE256("PULSAR-HC-v1", transcript) → challenge
- Hu: cSHAKE256("PULSAR-HU-v1", transcript) → XOF stream
- TranscriptHash: TupleHash256("PULSAR-TRANSCRIPT-v1", parts...)
- PRF: KMAC256(key, msg, "PULSAR-PRF-v1")
- MAC: KMAC256(key, msg, "PULSAR-MAC-v1")
- Pairwise: KMAC256(kex, encode(...), "PULSAR-PAIRWISE-v1")
- Default suite is Pulsar-SHA3; Pulsar-BLAKE3 retained as optional
non-normative fast profile. HashSuiteID is bound into transcripts.
- Implementation at pulsar/hash/ with HashSuite interface.
- All KATs regenerated under SHA3 profile; vectors in
luxcpp/crypto/pulsar/test/kat/.
Nebula root binding (TranscriptInputs + ActivationMessage canonical
bytes, all bound under TupleHash256):
chain_id, network_id, group_id,
key_era_id, old_generation, new_generation,
old_epoch_id, new_epoch_id,
old_set_hash, new_set_hash,
threshold_old, threshold_new,
group_public_key_hash,
nebula_root,
hash_suite_id,
implementation_version,
variant.
Packages:
primitives/ Shamir over R_q, Lagrange, hash helpers
sign/ 2-round sign math (byte-equal upstream)
threshold/ GroupKey, KeyShare, Signer types
reshare/ VSR kernel — Refresh (HJKY97 zero-poly), Reshare
(Desmedt-Jajodia), commit (Pedersen R_q), complaint,
transcript, pairwise KEX, activation cert
hash/ HashSuite interface; PulsarSHA3 (default), PulsarBLAKE3
dkg2/ Pedersen DKG over R_q (research, reference only)
keyera/ Lifecycle wrapper: Bootstrap → Reshare → Reanchor
papers/ LP-073-pulsar paper (sections + bibliography)
cmd/*_oracle/ KAT generators (Go ↔ C++ byte-equal validation)
DESIGN.md is the single source of truth:
- The Pulsar metaphor (rotating beam over persistent body)
- Vocabulary stack per LP-105: Nebula / Photon / Lumen / Beam /
Pulsar / Pulse / Prism / Horizon / Quasar
- Pulsar ≠ Lumen (PQ stream is separate, planned)
- Pulsar / Lens / LSS three-layer architecture
- Bootstrap Dealer vs Signature Coordinator
- No-slashing failure ladder (timeout → retry → rollback → reanchor)
- MVP VSR vs Robust VSR phasing
- Borrowed-brand terms ("X-Wing" used casually) replaced with
"hybrid KEM" / "Hybrid Lumen Handshake"; X-Wing cited only as
the IETF combiner primitive name where exact reference matters.
Tests: full suite green
hash 5+/5+, keyera 5/5, reshare 45+/45+, threshold, sign, dkg,
dkg2, primitives, networking, utils, corona_oracle_v2 KAT —
all pass.
Honest claim: the crypto primitives are not new (HJKY97,
Desmedt-Jajodia97, Wong-Wang-Wing02, Corona, Hermine, Threshold
Raccoon all exist). The novel contribution is the systems
composition: a permissionless-consensus deployment architecture that
turns static two-round PQ threshold signatures into a dynamic,
leaderless, validator-rotation-tolerant finality layer.
Companion docs: papers/lp-073-pulsar/ (academic paper); LP-073 +
LP-103 + LP-105 in github.com/luxfi/lps; threshold/protocols/lss/
lss_pulsar.go (LSS adapter wrapping this kernel).
73 lines
2.6 KiB
TeX
73 lines
2.6 KiB
TeX
% Standalone wrapper to compile the resharing section.
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% The full LP-073-pulsar paper is composed at ~/work/lux/papers/lp-073-pulsar/
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% (parent directory under lux/papers/); this minimal wrapper exists so
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% the section can be typechecked in isolation during development.
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%
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% Compile with: pdflatex lp-073-pulsar-resharing.tex (twice, for refs).
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\documentclass[11pt,a4paper]{article}
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\usepackage[utf8]{inputenc}
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\usepackage[T1]{fontenc}
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\usepackage{amsmath,amssymb,amsfonts,amsthm}
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\usepackage{graphicx}
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\usepackage{hyperref}
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\usepackage{booktabs}
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\usepackage{algorithm}
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\usepackage{algpseudocode}
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\usepackage{enumitem}
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\usepackage{cleveref}
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\hypersetup{colorlinks=true,linkcolor=black,citecolor=blue,urlcolor=blue}
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\newtheorem{theorem}{Theorem}
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{remark}{Remark}
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\title{LP-073-pulsar: Proactive Secret Resharing for Pulsar Lattice Threshold Signatures}
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\author{Lux Industries Inc}
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\date{\today}
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\begin{document}
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\maketitle
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\begin{abstract}
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We adapt the Herzberg-Jakobsson-Jarecki-Krawczyk-Yung 1997 proactive
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secret-sharing protocol to the lattice ring $R_q = \mathbb{Z}_q[X]/(X^{256}+1)$
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used by Pulsar lattice threshold signatures, allowing the validator-set
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rotation problem of Quasar consensus to be solved without re-running
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trusted-dealer key generation at every epoch boundary. The master secret
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$s$ is preserved across rotations; only the share distribution changes.
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The genesis-time public key $\tilde b$ is unchanged, so signatures from
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any future epoch verify under the same public anchor.
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\end{abstract}
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\input{sections/06-resharing}
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\begin{thebibliography}{99}
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\bibitem{hjky97}
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Amir Herzberg, Markus Jakobsson, Stanis\l{}aw Jarecki, Hugo Krawczyk, Moti Yung.
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``Proactive secret sharing or: How to cope with perpetual leakage.''
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\emph{CRYPTO 1995/1997}.
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\bibitem{desmedt-jajodia97}
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Yvo Desmedt, Sushil Jajodia.
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``Redistributing secret shares to new access structures and its applications.''
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Technical Report ISSE TR-97-01, George Mason University, 1997.
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\bibitem{shamir79}
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Adi Shamir.
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``How to share a secret.''
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\emph{Communications of the ACM} 22(11):612--613, 1979.
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\bibitem{wong02}
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Theodore M.\ Wong, Chenxi Wang, Jeannette M.\ Wing.
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``Verifiable secret redistribution for archive systems.''
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In \emph{Proceedings of the First International IEEE Security in Storage Workshop}, 2002.
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\bibitem{lp020}
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LP-020. ``Quasar Consensus: Triple-Sign with BLS, Corona, and ML-DSA.''
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\bibitem{lp070}
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LP-070. ``ML-DSA-65 Identity Layer for Quasar Validators.''
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\bibitem{lp073}
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LP-073. ``Corona: A Two-Round MAC-Authenticated Lattice-Based Threshold Signature.''
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\end{thebibliography}
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\end{document}
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