papers/lp-073-pulsar/references.bib

% --- Lux Improvement Proposals ---

@misc{ringtail,
  author       = {Cecilia Boschini and Darya Kaviani and Russell W. F. Lai and
                  Giulio Malavolta and Akira Takahashi and Mehdi Tibouchi},
  title        = {Ringtail: Practical Two-Round Threshold Signatures from {LWE}},
  year         = {2024},
  howpublished = {Cryptology ePrint Archive, Paper 2024/1113;
                  IEEE Symposium on Security and Privacy (S\&P) 2025},
  url          = {https://eprint.iacr.org/2024/1113},
  note         = {Academic two-round lattice threshold (IACR ePrint 2024/1113, IEEE S\&P 2025).}
}

@misc{lp073,
  title = {LP-073: Pulsar --- Module-LWE Threshold ML-DSA},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LPs/lp-4450-pulsar-threshold-ml-dsa.md}},
  note = {Original Pulsar paper-LP; canonical algorithm spec is now LP-4450.},
}

@misc{lp4450,
  title = {LP-4450: Pulsar --- Boundary-Cleared Module-LWE Threshold
           ML-DSA (FIPS~204, byte-equal)},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LPs/lp-4450-pulsar-threshold-ml-dsa.md}},
  note = {Canonical Pulsar algorithm specification: BCC/CEF no-leak
          threshold, mode restriction, V13 finding, honest status.},
}

@misc{lp019,
  title = {LP-019: Threshold MPC for Bridge Signing},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LP-019-threshold-mpc.md}},
}

@misc{lp020,
  title = {LP-020: Quasar Consensus 3.0},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LP-020-quasar-consensus.md}},
}

@misc{lp022,
  title = {LP-022: ZAP Wire Protocol},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LP-022-zap-wire-protocol.md}},
}

@misc{lp029,
  title = {LP-029: NTT Transform},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LP-029-ntt-transform.md}},
}

@misc{lp070,
  title = {LP-070: FIPS 204 ML-DSA Signatures},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LP-070-mldsa.md}},
}

@misc{lp071,
  title = {LP-071: FIPS 205 SLH-DSA Hash-Based Signatures},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LP-071-slhdsa.md}},
}

@misc{lp072,
  title = {LP-072: FIPS 203 ML-KEM Key Encapsulation},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LP-072-mlkem.md}},
}

@misc{lp074,
  title = {LP-074: FALCON Signature EVM Precompile},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LP-074-falcon.md}},
}

@misc{lp075,
  title = {LP-075: BLS Aggregate Signatures for Warp Messaging},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LP-075-bls-aggregate.md}},
}

@misc{lp077,
  title = {LP-077: Linear Shamir's Secret Sharing},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LP-077-linear-shamir.md}},
}

@misc{lp137,
  title = {LP-137: GPU-Native Crypto Stack},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LP-137.md}},
}

@misc{lp164,
  title = {LP-164: Six-Step NTT and Crossover Thresholds},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lps/blob/main/LP-164-six-step-ntt.md}},
}

% --- Source canonicals ---

@misc{corona,
  author       = {{Lux Industries}},
  title        = {Corona: Two-Round {Ring-LWE} Threshold Signatures},
  year         = {2026},
  howpublished = {\url{https://github.com/luxfi/corona}},
  note         = {Lux's own threshold scheme: {Ring-LWE} (= Module-LWE at
                  rank~1), two-round. Builds on the Ringtail line
                  (\cite{ringtail}); cited via this Lux artifact, never via
                  the academic paper. Q-Chain Feldman/Pedersen DKG.}
}

@misc{lattigov7,
  title = {Lattigo v7: A Lattice-Based Cryptography Library (Lux fork)},
  author = {{Lux Core Team}},
  year = {2026},
  howpublished = {\url{https://github.com/luxfi/lattice}},
  note = {Fork of \texttt{tuneinsight/lattigo}; pinned at v7 for byte-exact reproducibility.},
}

% --- Academic references ---

@misc{fips204,
  title = {FIPS 204: Module-Lattice-Based Digital Signature Standard},
  author = {{NIST}},
  year = {2024},
  howpublished = {\url{https://csrc.nist.gov/pubs/fips/204/final}},
}

@misc{fips203,
  title = {FIPS 203: Module-Lattice-Based Key-Encapsulation Mechanism Standard},
  author = {{NIST}},
  year = {2024},
  howpublished = {\url{https://csrc.nist.gov/pubs/fips/203/final}},
}

@misc{fips205,
  title = {FIPS 205: Stateless Hash-Based Digital Signature Standard},
  author = {{NIST}},
  year = {2024},
  howpublished = {\url{https://csrc.nist.gov/pubs/fips/205/final}},
}

@inproceedings{dilithium,
  title = {{CRYSTALS-Dilithium}: A Lattice-Based Digital Signature Scheme},
  author = {Ducas, L\'{e}o and Kiltz, Eike and Lepoint, Tancr\`{e}de and Lyubashevsky, Vadim and Schwabe, Peter and Seiler, Gregor and Stehl\'{e}, Damien},
  booktitle = {IACR Transactions on Cryptographic Hardware and Embedded Systems},
  year = {2018},
  volume = {2018},
  number = {1},
  pages = {238--268},
}

@article{mlwe,
  title = {On Ideal Lattices and Learning with Errors over Rings},
  author = {Lyubashevsky, Vadim and Peikert, Chris and Regev, Oded},
  journal = {Journal of the ACM},
  volume = {60},
  number = {6},
  pages = {1--35},
  year = {2013},
  publisher = {ACM},
}

@inproceedings{drijvers2019,
  title = {On the Security of Two-Round Multi-Signatures},
  author = {Drijvers, Manu and Edalatnejad, Kasra and Ford, Bryan and Neven, Gregory and Stadler, Igors},
  booktitle = {IEEE Symposium on Security and Privacy (S\&P)},
  year = {2019},
  publisher = {IEEE},
  pages = {1084--1101},
}

@misc{frost,
  title = {{FROST}: {Flexible} Round-Optimized Schnorr Threshold Signatures},
  author = {Komlo, Chelsea and Goldberg, Ian},
  howpublished = {RFC 9591},
  year = {2024},
}

@misc{cggmp21,
  title = {{UC} Non-Interactive, Proactive, Threshold {ECDSA} with Identifiable Aborts},
  author = {Canetti, Ran and Gennaro, Rosario and Goldfeder, Steven and Makriyannis, Nikolaos and Peled, Udi},
  howpublished = {Cryptology ePrint Archive, Paper 2021/060},
  year = {2021},
}

@inproceedings{boneh2018,
  title = {Threshold Cryptosystems from Threshold Fully Homomorphic Encryption},
  author = {Boneh, Dan and Gennaro, Rosario and Goldfeder, Steven and Jain, Aayush and Kim, Sam and Rasmussen, Peter and Sahai, Amit},
  booktitle = {CRYPTO},
  year = {2018},
  publisher = {Springer},
  pages = {565--596},
}

@inproceedings{damgard2021,
  title = {Two-Round $n$-out-of-$n$ and Multi-Signatures and Trapdoor Commitment from Lattices},
  author = {Damg\aa{}rd, Ivan and Orlandi, Claudio and Takahashi, Akira and Tibouchi, Mehdi},
  booktitle = {PKC},
  year = {2021},
  publisher = {Springer},
}

@inproceedings{dttf2024,
  title = {Two-Round Threshold Signature from Algebraic One-More Learning with Errors},
  author = {Anonymous},
  booktitle = {EUROCRYPT},
  year = {2024},
  publisher = {Springer},
  note = {Concrete two-round threshold Dilithium analogue cited for comparison.},
}

@inproceedings{cosmin2021,
  title = {Threshold {SPHINCS+}: A Hash-Based Threshold Signature},
  author = {Cosmin, Andrei and Khovratovich, Dmitry},
  booktitle = {SAC},
  year = {2021},
  publisher = {Springer},
}

@misc{bls,
  title = {{BLS12-381}: New {zk-SNARK} Elliptic Curve Construction},
  author = {Bowe, Sean},
  year = {2017},
  howpublished = {\url{https://electriccoin.co/blog/new-snark-curve/}},
}

@misc{falcon,
  title = {{FALCON}: Fast-Fourier Lattice-Based Compact Signatures over {NTRU}},
  author = {Fouque, Pierre-Alain and Hoffstein, Jeffrey and Kirchner, Paul and Lyubashevsky, Vadim and Pornin, Thomas and Prest, Thomas and Ricosset, Thomas and Seiler, Gregor and Whyte, William and Zhang, Zhenfei},
  year = {2020},
  howpublished = {\url{https://falcon-sign.info}},
}

@misc{sphincs,
  title = {{SPHINCS+}: Submission to the {NIST} Post-Quantum Project},
  author = {Bernstein, Daniel J. and H\"{u}lsing, Andreas and K\"{o}lbl, Stefan and Niederhagen, Ruben and Rijneveld, Joost and Schwabe, Peter},
  year = {2022},
}

@misc{blake2,
  title = {{BLAKE2}: Simpler, Smaller, Fast as {MD5}},
  author = {Aumasson, Jean-Philippe and Neves, Samuel and Wilcox-O'Hearn, Zooko and Winnerlein, Christian},
  howpublished = {RFC 7693},
  year = {2015},
}

@misc{blake3,
  title = {{BLAKE3}: One Function, Fast Everywhere},
  author = {O'Connor, Jack and Aumasson, Jean-Philippe and Neves, Samuel and Wilcox-O'Hearn, Zooko},
  year = {2020},
  howpublished = {\url{https://github.com/BLAKE3-team/BLAKE3}},
}

@article{ziggurat,
  title = {The Ziggurat Method for Generating Random Variables},
  author = {Marsaglia, George and Tsang, Wai Wan},
  journal = {Journal of Statistical Software},
  volume = {5},
  number = {8},
  pages = {1--7},
  year = {2000},
}

@inproceedings{hjky97,
  author    = {Amir Herzberg and Stanislaw Jarecki and Hugo Krawczyk and Moti Yung},
  title     = {Proactive Secret Sharing or: How to Cope With Perpetual Leakage},
  booktitle = {CRYPTO},
  year      = {1995},
  note      = {Updated 1997}
}

@inproceedings{desmedtjajodia97,
  author    = {Yvo Desmedt and Sushil Jajodia},
  title     = {Redistributing Secret Shares to New Access Structures and Its Applications},
  booktitle = {Technical Report ISSE TR-97-01, George Mason University},
  year      = {1997}
}

@inproceedings{wongwangwing02,
  author    = {Theodore M. Wong and Chenxi Wang and Jeannette M. Wing},
  title     = {Verifiable Secret Redistribution for Archive Systems},
  booktitle = {SISW},
  year      = {2002}
}

@misc{thresholdraccoon,
  author       = {Rafael del Pino and Shuichi Katsumata and Mary Maller and Fabrice Mouhartem and Thomas Prest and Mark{-}Henry Servera},
  title        = {Threshold Raccoon: Practical Threshold Signatures from Standard Lattice Assumptions},
  howpublished = {Eurocrypt},
  year         = {2024}
}

@misc{hermine,
  author       = {NIST Multi-Party Threshold Cryptography Project},
  title        = {Hermine: Threshold Lattice Signatures with DKG and Proactive Refresh},
  howpublished = {NIST MPTC presentation},
  year         = {2025}
}

@misc{rfc9591,
  author       = {Deirdre Connolly and Chelsea Komlo and Ian Goldberg and Christopher A. Wood},
  title        = {{RFC 9591}: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures},
  howpublished = {RFC Editor},
  year         = {2024}
}

@inproceedings{komlogoldberg20,
  author    = {Chelsea Komlo and Ian Goldberg},
  title     = {{FROST}: Flexible Round-Optimized {S}chnorr Threshold Signatures},
  booktitle = {SAC},
  year      = {2020}
}

@misc{lp103,
  author       = {{Lux Industries}},
  title        = {{LP-103}: Lens --- Curve-Based Threshold Signatures with Dynamic Resharing},
  howpublished = {Lux Improvement Proposal},
  year         = {2026}
}

@misc{luxlssmpc,
  author       = {Vishnu J. Seesahai and Zach Kelling},
  title        = {{LSS}: A Pragmatic Framework for Dynamic and Resilient Threshold Signatures with Live Secret Resharing},
  howpublished = {Lux Industries, Inc.},
  year         = {2025}
}

@misc{nistir8214c,
  author       = {{NIST}},
  title        = {{NIST IR 8214C}: Multi-Party Threshold Cryptography Schemes},
  howpublished = {NIST Internal Report},
  year         = {2024}
}

@misc{lp105,
  author       = {{Lux Industries}},
  title        = {{LP-105}: The Lux Finality Stack --- Public Vocabulary and Internal Names},
  howpublished = {Lux Improvement Proposal},
  year         = {2026}
}

@misc{quasarcertsoundness,
  author       = {Zach Kelling},
  title        = {{QuasarCert} Soundness: Canonical Formal Specification, {Quasar 3.0}},
  howpublished = {Lux Industries; \texttt{lux/proofs/quasar-cert-soundness.tex}},
  year         = {2026}
}

@misc{leancrypto,
  author       = {{Lux Industries}},
  title        = {Lean4 Cryptographic Proof Tree},
  howpublished = {\url{https://github.com/luxfi/proofs/tree/main/lean/Crypto}},
  year         = {2026},
  note         = {Mechanised companion to \texttt{quasar-cert-soundness.tex}; canonical theorem names cited verbatim from this tree.}
}

@inproceedings{bdgl2016,
  author       = {Anja Becker and L\'{e}o Ducas and Nicolas Gama and Thijs Laarhoven},
  title        = {New Directions in Nearest Neighbor Searching with Applications to Lattice Sieving},
  booktitle    = {SODA},
  year         = {2016}
}

@inproceedings{laarhoven2015,
  author       = {Thijs Laarhoven},
  title        = {Sieving for Shortest Vectors in Lattices Using Angular Locality-Sensitive Hashing},
  booktitle    = {CRYPTO},
  year         = {2015}
}

@misc{albrechtestimator,
  author       = {Martin R.~Albrecht and Rachel Player and Sam Scott},
  title        = {On the Concrete Hardness of Learning with Errors},
  journal      = {Journal of Mathematical Cryptology},
  volume       = {9},
  number       = {3},
  pages        = {169--203},
  year         = {2015}
}

@inproceedings{boneh2001short,
  author       = {Dan Boneh and Ben Lynn and Hovav Shacham},
  title        = {Short Signatures from the {Weil} Pairing},
  booktitle    = {ASIACRYPT},
  year         = {2001},
  publisher    = {Springer}
}

@inproceedings{canetti2001uc,
  author       = {Ran Canetti},
  title        = {Universally Composable Security: A New Paradigm for Cryptographic Protocols},
  booktitle    = {FOCS},
  year         = {2001},
  publisher    = {IEEE}
}

@inproceedings{garaybackbone,
  author       = {Juan A.~Garay and Aggelos Kiayias and Nikos Leonardos},
  title        = {The Bitcoin Backbone Protocol: Analysis and Applications},
  booktitle    = {EUROCRYPT},
  year         = {2015},
  publisher    = {Springer}
}

@inproceedings{fischlin2005,
  author       = {Marc Fischlin},
  title        = {Communication-Efficient Non-Interactive Proofs of Knowledge with Online Extractors},
  booktitle    = {CRYPTO},
  year         = {2005},
  publisher    = {Springer}
}

@techreport{pulsar,
  author      = {Zach Kelling},
  title       = {{LP-073}: Pulsar --- Module-{LWE} Rank-$k$ Threshold {ML-DSA}
                 for Permissionless Validator Sets},
  number      = {LP-073},
  institution = {Lux Industries, Inc.},
  year        = {2026},
  howpublished = {\url{https://github.com/luxfi/pulsar}},
  note        = {Lux's own threshold {ML-DSA} (FIPS~204) over Module-{LWE} at
                 general rank~$k$; canonical {LP-073}. Distinct from Corona
                 (rank~1) and from Ringtail (\cite{ringtail}).}
}

@misc{bowe2017,
  author       = {Sean Bowe and Ariel Gabizon and Ian Miers},
  title        = {Scalable Multi-Party Computation for {zk-SNARK} Parameters in the Random Beacon Model},
  howpublished = {IACR ePrint 2017/1050},
  year         = {2017}
}

@inproceedings{groth2016,
  author       = {Jens Groth},
  title        = {On the Size of Pairing-Based Non-Interactive Arguments},
  booktitle    = {EUROCRYPT},
  year         = {2016},
  publisher    = {Springer}
}

@inproceedings{regev2009,
  author       = {Oded Regev},
  title        = {On Lattices, Learning with Errors, Random Linear Codes, and Cryptography},
  journal      = {Journal of the ACM},
  volume       = {56},
  number       = {6},
  pages        = {1--40},
  year         = {2009},
  publisher    = {ACM}
}

@inproceedings{tmldsa2025,
  author       = {Andrea Celi and Rafa\"el del Pino and Thomas Espitau and Guilhem Niot and Thomas Prest},
  title        = {Efficient Threshold {ML-DSA}},
  booktitle    = {USENIX Security},
  year         = {2025}
}

@inproceedings{gks24,
  author       = {Gennaro, Rosario and Krawczyk, Hugo and Sahai, Amit},
  title        = {Lattice-Based GJKR Distributed Key Generation with NIZK},
  booktitle    = {ACNS},
  year         = {2024}
}

@inproceedings{krt24,
  author       = {Katsumata, Shuichi and Reichle, Markus and Takemure, Kaoru},
  title        = {Lattice-Based Joint-Feldman Distributed Key Generation},
  booktitle    = {ASIACRYPT},
  year         = {2024}
}

@inproceedings{bdlop18,
  author       = {Baum, Carsten and Damg\aa{}rd, Ivan and Lyubashevsky, Vadim and Oechsner, Sabine and Peikert, Chris},
  title        = {More Efficient Commitments from Structured Lattice Assumptions},
  booktitle    = {SCN},
  year         = {2018}
}

@misc{red-dkg-review,
  author       = {Lux Industries Inc.},
  title        = {RED-DKG-REVIEW: Internal Red Review of the Corona Feldman DKG},
  howpublished = {luxcpp/crypto/corona/RED-DKG-REVIEW.md},
  year         = {2026}
}