mirror of
https://github.com/lux-apps/papers.git
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zeekay
dd93cb41f7
Sweep across the non-Tier-1 paper catalogue (Tier-1 owned by parallel
agent and excluded). All 113 processed papers already had luxcover
wired up; this commit fixes 14 build breakers and produces fresh
PDFs across the catalogue.
Fixes:
- lux-blockchain-scaling-laws: em-dash inside lstlisting -> --
- lux-corona-pq: stale \input pointing at 03-the-corona-scheme renamed
to 03-the-corona-scheme (file already renamed on disk)
- lux-lattice-cryptography-primer: same Corona->Corona rename
- lux-formal-verification-lean4: Lean source uses unicode (×, ∀, ∃, ∈,
∧, ∨, ∩, ≠, ⟨, ⟩, ·, ¬) inside lstlistings. Added a literate map
so listings render the math glyphs without UTF-8 fault.
- lux-id-did-specification: ✓/✗ in tabular replaced with \ding{51}
/ \ding{55} (pifont). Added pifont package.
- lux-ntt-simd-implementation: middle-dot in Go assembly listings;
added literate {·}{\textperiodcentered}.
- lux-ntt-transform: μ, ×, –, — in regular text (no T1 fontenc).
Replaced with $\mu$/$\times$/--/--- via unicode->latex sweep.
- lux-perpetuals-derivatives, lux-quantum-consensus,
lux-quasar-consensus, lux-tee-computing-mesh: same unicode->latex
sweep across body text. Also fixed broken math segment
`$L_{avg} = 10$\times$$` -> `$L_{avg} = 10\times$`.
- lux-zchain: emoji glyphs in roadmap table replaced with
parenthetical text.
- lux-triple-proof-consensus: dropped duplicate \usepackage{geometry}
that clashed with luxcover (geometry option clash).
- pq: defined missing \Rq macro.
PDFs rebuilt for the full Tier-2/3 set.
Excluded (Tier-1, parallel agent): lp-073-pulsar, lp-stricte2epq,
dag-evm-formal, lp-010-quasar-stm-{3,4}, lp-020-quasar-consensus,
lux-institutional-custody, lux-nist-mptc-submission, pqsafe-il5,
pq-rns, plus shared/ and lps/.
73 lines
3.9 KiB
TeX
73 lines
3.9 KiB
TeX
\documentclass[11pt]{article}
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\usepackage{../shared/luxcover}
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\usepackage{amsmath, amssymb, amsthm}
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\usepackage{mathtools}
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\usepackage{bm}
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\usepackage{graphicx}
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\usepackage{booktabs}
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\usepackage{hyperref}
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\usepackage{enumitem}
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\usepackage{algorithm}
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\usepackage{algpseudocode}
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\usepackage{listings}
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\usepackage{xcolor}
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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{proposition}[theorem]{Proposition}
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\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{definition}{Definition}
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\title{LSS: A Universal Lifecycle Framework\\for Threshold Cryptographic Protocols\\\large{Dynamic share lifecycle for ECDSA, FROST/Lens, and lattice/Pulsar schemes}}
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\author{
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Vishnu J. Seesahai\thanks{Corresponding author: [email protected]}
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\quad
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Zach Kelling\\
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\textit{Lux Industries, Inc.}\\
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\texttt{[email protected]}
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}
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\date{2024}
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\begin{document}
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\luxcoverpage
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\begin{abstract}
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\noindent Lux is not merely adding post-quantum signatures to a chain; it defines a hybrid finality architecture for DAG-native consensus, with protocol-agnostic threshold lifecycle, post-quantum threshold sealing, and cross-chain propagation of Horizon finality. LSS is the protocol-agnostic lifecycle framework that powers that systems layer.
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We present \textbf{LSS} (Linear Shamir Secret Sharing), a universal dynamic-resharing extension for threshold cryptographic protocols. LSS is \emph{not} a signature scheme; it is the lifecycle / orchestration framework that manages share generations, snapshot history, rollback, dealer/coordinator role separation, and live-resharing wire protocol --- across multiple threshold-kernel families.
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The principal innovation is coordinator-driven verifiable resharing via Joint Verifiable Secret Sharing (JVSS), enabling transition from $(t, n)$ to $(t', n \pm k)$ without reconstructing the master key or interrupting signing operations. LSS solves three operational challenges that the underlying signature schemes leave open:
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(1)~\emph{dynamic resharing} --- live expansion and contraction of the signing group without downtime or key reconstruction;
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(2)~\emph{automated fault tolerance} --- node eviction, state rollback to previously certified shard generations, and persistence-backed recovery;
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(3)~\emph{multi-kernel adaptation} --- a unified adapter pattern that gives the same lifecycle to ECDSA-CMP, FROST/Schnorr, and lattice threshold schemes.
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The framework's adapters cover three kernel families:
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\begin{itemize}
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\item \texttt{lss\_cmp.go}: ECDSA-CMP adapter (Protocol~I localized nonce blinding, Protocol~II collaborative nonce blinding; sub-25ms signing).
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\item \texttt{lss\_lens.go}: classical curve threshold via Lens, replacing the placeholder \texttt{lss\_frost.go} stub.
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\item \texttt{lss\_pulsar.go}: lattice threshold via Pulsar; Generation/RollbackFrom/KeyEraID lineage; activation cert under unchanged group public key; 10/10 acceptance tests pass.
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\end{itemize}
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The classical foundations are HJKY proactive secret sharing, Desmedt--Jajodia secret redistribution, and Wong--Wang--Wing verifiable redistribution. The novel work is the unified adapter architecture: \emph{one lifecycle framework, multiple threshold kernels}.
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Production-deployed in the Lux Teleport omnichain bridge securing cross-chain assets across 270+ connected blockchains, and adopted by Quasar consensus for dynamic post-quantum threshold finality with rotating validator sets.
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\end{abstract}
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\tableofcontents
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%% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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\input{sections/01-introduction}
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\input{sections/02-preliminaries}
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\input{sections/03-lss-protocol}
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\input{sections/04-multi-chain-adaptation}
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\input{sections/05-post-quantum-extension}
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\input{sections/06-security-analysis}
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\input{sections/07-performance}
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\input{sections/08-deployment}
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\input{sections/99-conclusion}
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\end{document}
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