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Bylines, paper authorship, correspondence addresses and the founder blurb under each post named an individual. They name the organisation that published the work instead: the brand on posts and pages, the research byline on papers, and research@ in place of a personal address. Both are what these repositories already used elsewhere — nothing new was coined. Co-authors are untouched. Where a paper named someone else alongside, they stay named; only the one byline changed. Bibliography entries, running heads, PDF metadata and affiliations move with it, so a citation still resolves to whoever the cited paper names. Sample and fixture data uses the placeholder name these tests already use elsewhere, so no assertion changed meaning.
77 lines
2.8 KiB
TeX
77 lines
2.8 KiB
TeX
\documentclass[11pt,a4paper]{article}
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\usepackage{../shared/luxcover}
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\usepackage{amsmath,amssymb,amsthm}
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\DeclareMathOperator*{\argmin}{arg\,min}
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\usepackage{graphicx}
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\usepackage{algorithm,algorithmic}
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\usepackage{hyperref}
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\usepackage{tikz}
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\usepackage{pgfplots}
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\usepackage{booktabs}
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\usepackage{xcolor}
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\usepackage{listings}
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\input{../shared/lstlang}
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\usepackage{float}
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\usetikzlibrary{trees,positioning,calc,shapes.geometric}
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\pgfplotsset{compat=1.17}
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\definecolor{luxblue}{RGB}{0,122,255}
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\definecolor{luxgreen}{RGB}{0,200,83}
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\definecolor{luxgray}{RGB}{128,128,128}
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\lstset{
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basicstyle=\footnotesize\ttfamily,
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keywordstyle=\color{luxblue}\bfseries,
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commentstyle=\color{luxgray}\itshape,
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stringstyle=\color{luxgreen},
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numbers=left,
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numberstyle=\tiny\color{luxgray},
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frame=single,
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breaklines=true,
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captionpos=b
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}
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\theoremstyle{definition}
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\newtheorem{definition}{Definition}
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\newtheorem{theorem}{Theorem}
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\newtheorem{lemma}{Lemma}
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\newtheorem{corollary}{Corollary}
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\title{\textbf{Verkle Trees: Constant-Size Proofs for Stateless Clients on Lux}}
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\author{
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Lux Research\thanks{Corresponding author: [email protected]}\\
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\textit{Lux Industries, Inc.}\\
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\texttt{[email protected]}
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}
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\date{2022}
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\begin{document}
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\luxcoverpage
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\begin{abstract}
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We present the design and implementation of Verkle trees in the Lux blockchain platform, enabling constant-size proofs for stateless clients. Verkle trees utilize polynomial commitments to achieve proof sizes of approximately 150 bytes, independent of tree depth or state size, representing a 4-5x reduction compared to traditional Merkle Patricia trees. Our implementation leverages KZG commitments on the BLS12-381 curve, providing efficient batch verification and enabling practical stateless client operation. We detail the cryptographic foundations, integration with Lux's multi-chain architecture, migration strategy from existing Merkle structures, and performance analysis showing 76\% bandwidth reduction for state proofs while maintaining sub-10ms verification times. This advancement enables light clients to verify state transitions with minimal storage requirements, improving network decentralization and accessibility.
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\end{abstract}
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\input{sections/01-introduction}
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\input{sections/02-merkle-tree-limitations}
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\input{sections/03-verkle-tree-background}
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\input{sections/04-verkle-tree-structure}
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\input{sections/05-polynomial-commitments-kzg}
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\input{sections/06-proof-generation}
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\input{sections/07-lux-implementation}
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\input{sections/08-performance-analysis}
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\input{sections/09-stateless-client-benefits}
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\input{sections/10-cryptographic-primitives}
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\input{sections/11-security-analysis}
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\input{sections/12-comparison-with-alternatives}
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\input{sections/13-economic-impact}
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\input{sections/14-migration-strategy}
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\input{sections/15-future-enhancements}
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\input{sections/99-conclusion}
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\end{document}
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