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/.
95 lines
3.4 KiB
TeX
95 lines
3.4 KiB
TeX
\documentclass[11pt,twocolumn]{article}
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\usepackage{../shared/luxcover}
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% Packages
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\usepackage[utf8]{inputenc}
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\usepackage[T1]{fontenc}
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\usepackage{amsmath,amssymb,amsthm}
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\usepackage{graphicx}
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\usepackage{hyperref}
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\usepackage{algorithm}
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\usepackage{algpseudocode}
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\usepackage{booktabs}
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\usepackage{multirow}
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\usepackage{array}
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\usepackage{xcolor}
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\usepackage{float}
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\usepackage{enumitem}
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\usepackage{mathtools}
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\usepackage{tikz}
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\usetikzlibrary{arrows.meta,positioning,shapes.geometric}
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% Theorem environments
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\newtheorem{theorem}{Theorem}[section]
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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}[section]
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\newtheorem{remark}{Remark}[section]
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\hypersetup{
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colorlinks=true,
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linkcolor=blue,
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citecolor=blue,
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urlcolor=blue
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}
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% ============================================================
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% Title
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% ============================================================
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\title{\textbf{Unified Threshold Cryptography for\\Omnichain Asset Custody:\\FROST, CGGMP21, and Taproot Integration}}
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\author{
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Zach Kelling\thanks{Corresponding author: [email protected]}
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\quad
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Vishnu Seesahai\\
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\textit{Lux Industries, Inc.}\\
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\texttt{[email protected]}
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}
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\date{2021 (Revised August 2025)}
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\begin{document}
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\luxcoverpage
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\begin{abstract}
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We present a unified threshold cryptographic framework for omnichain asset custody
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deployed in the Lux Teleport bridge protocol. The framework integrates two complementary
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threshold signature schemes---FROST (Flexible Round-Optimized Schnorr Threshold) for
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Ed25519 and BIP-340 Taproot chains, and CGGMP21 for threshold ECDSA on secp256k1
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chains---to provide native signature verification on every major blockchain without
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on-chain multisig overhead. FROST covers 12 chain families (Solana, TON, Sui, Aptos,
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Cosmos, Polkadot, NEAR, Stellar, Cardano, Algorand, Tezos, Bitcoin Taproot) with
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2-round signing producing standard 64-byte Schnorr signatures. CGGMP21 covers 5 chain
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families (Ethereum and all EVM chains, TRON, XRPL, StarkNet, legacy Bitcoin) with
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identifiable abort producing standard 65-byte ECDSA signatures. Both protocols share a
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common distributed key generation (DKG) phase with no trusted dealer, a proactive key
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refresh mechanism that rotates shares without changing the public key, and a 7-day
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timelocked signer rotation with on-chain visibility. We prove unforgeability under
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$t-1$ static corruption for both protocols in the random oracle model, give a formal
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composition theorem establishing that the dual-protocol system maintains security when
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sharing infrastructure, and present gas cost measurements for signature verification
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across 17 chain families. The system is implemented in Go at
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\texttt{github.com/luxfi/threshold} and \texttt{github.com/luxfi/mpc}, deployed in
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production securing cross-chain assets on Lux Teleport.
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\end{abstract}
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% ============================================================
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\input{sections/01-introduction}
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\input{sections/02-system-model-and-definitions}
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\input{sections/03-frost-protocol}
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\input{sections/04-cggmp21-protocol}
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\input{sections/05-bitcoin-taproot-integration}
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\input{sections/06-key-management}
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\input{sections/07-security-analysis}
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\input{sections/08-gas-cost-analysis}
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\input{sections/09-comparison-with-alternatives}
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\input{sections/10-implementation}
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\input{sections/11-formal-security-proofs}
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\input{sections/12-related-work}
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\input{sections/99-conclusion}
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\end{document}
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