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91 lines
3.8 KiB
TeX
91 lines
3.8 KiB
TeX
\section{Conclusion}
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Security requires explicit threat models, not vague assertions. This document
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provides such a model for the Lux Network, covering four adversary classes, four
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protocol layers, three cryptographic assumption families, and their interactions.
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The key structural property is defense in depth: any two of the three cryptographic
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assumption families (discrete log, lattice, hash) suffice for security. No single
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breakthrough---quantum computers, lattice attacks, hash function weaknesses---is
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sufficient to compromise the system. Only a simultaneous failure of two independent
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mathematical hardness assumptions could break the security guarantees.
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The key process property is the machine-checkable invariant: every security claim is
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either formally proven, empirically tested, or explicitly marked as an assumption.
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This eliminates the most dangerous category of security claims---those that nobody
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has checked.
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Triple-proof quantum finality achieves the practical synthesis: 248 bytes per epoch,
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${\sim}2$--$5$\,ms CPU verification~\cite{lux-benchmarks}, 1\,ms blocks, and security
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against classical, quantum, and economic adversaries simultaneously.
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%% ========================================================================
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%% BIBLIOGRAPHY
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%% ========================================================================
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\begin{thebibliography}{20}
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\bibitem{boneh2001bls}
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D. Boneh, B. Lynn, and H. Shacham, ``Short Signatures from the Weil Pairing,''
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\emph{Journal of Cryptology}, vol.~17, no.~4, pp.~297--319, 2004.
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\bibitem{fips204}
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NIST, ``Module-Lattice-Based Digital Signature Standard (FIPS 204),''
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National Institute of Standards and Technology, August 2024.
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\bibitem{fips203}
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NIST, ``Module-Lattice-Based Key-Encapsulation Mechanism Standard (FIPS 203),''
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National Institute of Standards and Technology, August 2024.
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\bibitem{fips205}
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NIST, ``Stateless Hash-Based Digital Signature Standard (FIPS 205),''
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National Institute of Standards and Technology, August 2024.
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\bibitem{canetti2021uc}
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R. Canetti, R. Gennaro, S. Goldfeder, N. Makriyannis, and U. Peled, ``UC
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Non-Interactive, Proactive, Threshold ECDSA with Identifiable Aborts,''
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\emph{ACM CCS 2020}, pp.~1769--1787, 2020.
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\bibitem{komlo2020frost}
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C.~Komlo and I.~Goldberg, ``FROST: Flexible Round-Optimized Schnorr Threshold
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Signatures,'' \emph{SAC 2020}, pp.~34--65, Springer, 2020.
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\bibitem{rocket2020scalable}
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Team Rocket, M. Yin, K. Sekniqi, R. van Renesse, and E.~G. Sirer, ``Scalable and
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Probabilistic Leaderless BFT Consensus through Metastability,'' arXiv:1906.08936, 2020.
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\bibitem{shor1997}
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P.~W. Shor, ``Polynomial-Time Algorithms for Prime Factorization and Discrete
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Logarithms on a Quantum Computer,'' \emph{SIAM Journal on Computing}, vol.~26,
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no.~5, pp.~1484--1509, 1997.
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\bibitem{grover1996}
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L.~K. Grover, ``A Fast Quantum Mechanical Algorithm for Database Search,''
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\emph{Proceedings of the 28th Annual ACM Symposium on Theory of Computing},
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pp.~212--219, 1996.
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\bibitem{wood2014ethereum}
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G.~Wood, ``Ethereum: A Secure Decentralised Generalised Transaction Ledger,''
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Ethereum Project Yellow Paper, 2014.
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\bibitem{nakamoto2008bitcoin}
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S.~Nakamoto, ``Bitcoin: A Peer-to-Peer Electronic Cash System,'' 2008.
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\bibitem{buterin2020combining}
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V.~Buterin, D.~Hernandez, T.~Kamphefner, et al., ``Combining GHOST and Casper,''
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arXiv:2003.03052, 2020.
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\bibitem{lyubashevsky2010ideal}
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V.~Lyubashevsky, C.~Peikert, and O.~Regev, ``On Ideal Lattices and Learning with
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Errors over Rings,'' \emph{EUROCRYPT 2010}, pp.~1--23, Springer, 2010.
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\bibitem{mosca2018}
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M.~Mosca, ``Cybersecurity in an Era with Quantum Computers: Will We Be Ready?''
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\emph{IEEE Security \& Privacy}, vol.~16, no.~5, pp.~38--41, 2018.
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\bibitem{lux-benchmarks}
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Lux Industries, ``Quasar Consensus --- Measured Benchmarks,'' 2026. Apple M1 Max, darwin/arm64, Go 1.26.1. \url{https://github.com/luxfi/consensus/blob/main/BENCHMARKS.md}.
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\end{thebibliography}
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