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f4ee7a0525
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.
83 lines
4.3 KiB
TeX
83 lines
4.3 KiB
TeX
\documentclass[11pt,a4paper]{article}
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\usepackage{../shared/luxcover}
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\usepackage[utf8]{inputenc}
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\usepackage[T1]{fontenc}
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\usepackage{amsmath,amssymb,amsfonts,amsthm}
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\usepackage{graphicx}
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\usepackage{hyperref}
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\usepackage{booktabs}
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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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\usepackage{tikz}
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\usepackage{float}
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\usepackage{enumitem}
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\usepackage{array}
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\usepackage{multirow}
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\usepackage{tabularx}
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\input{../shared/lstlang}
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\usetikzlibrary{arrows.meta,positioning,shapes.geometric,fit,calc}
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\hypersetup{colorlinks=true,linkcolor=black,citecolor=blue,urlcolor=blue}
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\lstset{
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basicstyle=\ttfamily\scriptsize,
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breaklines=true,
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frame=single,
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numbers=left,
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numberstyle=\tiny\color{gray},
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keywordstyle=\color{blue!70!black}\bfseries,
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commentstyle=\color{green!50!black}\itshape,
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stringstyle=\color{red!60!black},
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showstringspaces=false,
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}
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\newtheorem{theorem}{Theorem}
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{definition}{Definition}
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\newtheorem{proposition}[theorem]{Proposition}
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\newtheorem{remark}{Remark}
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\title{GPU-Optimized Blockchain Cryptography:\\Methodology for CPU/GPU Determinism Testing,\\Crossover Thresholds, and Safety}
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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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\textit{A subsidiary of Hanzo Industries Inc}\\
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\texttt{[email protected]}
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}
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\date{2026}
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\begin{document}
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\luxcoverpage
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\begin{abstract}
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We describe a methodology for shipping production-grade cryptographic primitives held to a byte-equality contract across CPU and three GPU backends (Metal, CUDA, WGSL). The methodology has three components: (i) a byte-equality contract enforced between a first-party CPU canonical and every shipping GPU kernel on $N{=}1000$ randomized inputs per release; (ii) a per-algorithm crossover-threshold sweep that determines, empirically, the batch size $N^{*}$ at which the GPU kernel becomes faster than the single-thread CPU baseline; and (iii) a safety analysis that combines test-oracle isolation (the audited upstream is never linked into shipped libraries), GPU-memory hygiene (secret state never leaves attested GPU memory on the hot path), and brand-neutral C-ABI symbol layout.
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We apply the methodology to a 29-primitive corpus covering hashes, AEAD, elliptic curves (including pairing-friendly), polynomial commitments, lattice primitives, post-quantum signatures and KEMs, threshold schemes, FHE building blocks, and EVM precompile wrappers. Per-algorithm formal specs live in their own Lux Improvement Proposals (LP-026, LP-029, LP-066, LP-069, LP-070--077, LP-110--126, LP-131, LP-146--159); this paper covers the GPU mode that all of them share.
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Empirical results from the same methodology: $144.22\times$ on fused BLS aggregation \cite{lp137benchmarks}, $16.92\times$ on FHE Metal NTT (10-iter median, kernel-only) \cite{lp137benchmarks}, $26.7\times$ on batched Ed25519 RFC 8032 verify at $N{=}4096$ \cite{lp137benchmarks}, and CPU NTT throughput of 6--9 Mops/s at $N=2^{20}$ on Apple M2 Ultra (LP-164 six-step) \cite{lp164}. Crossover thresholds range from $N^{*}{=}1$ (FHE NTT) to $N^{*}{=}1024$ (SHA-256), validated on a single Apple Silicon M2 Ultra device. Byte-equality is enforced on every release: 36 of 36 BN254 KAT vectors match \texttt{gnark-crypto v0.19.2} \cite{gnarkcrypto,lp146}, with cross-oracle KAT verification against \texttt{arkworks-rs} \cite{arkworks} for adversarial distance.
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This paper provides the substrate-level methodology for LP-137 of the Lux Improvement Proposals \cite{lp137}. Per-algorithm formal content (parameters, KAT sources, security analysis) lives in the per-algorithm LPs cited above; this paper carries no per-algorithm specification beyond a pointer index. Acceleration-kernel-level specs that augment the substrate (batched Montgomery inversion, Pippenger MSM, combined-pair Miller, Karatsuba modexp, six-step NTT, Pedersen tree-reduce, threshold pre-sign) live in LP-160 through LP-166 \cite{lp160,lp161,lp162,lp163,lp164,lp165,lp166}.
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\end{abstract}
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\tableofcontents
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\newpage
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\input{sections/01-introduction}
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\input{sections/02-architecture}
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\input{sections/03-per-algorithm-spec}
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\input{sections/04-determinism-harness}
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\input{sections/05-performance}
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\input{sections/06-security-analysis}
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\input{sections/07-related-work}
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\input{sections/99-conclusion}
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\bibliographystyle{plain}
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\bibliography{references}
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\end{document}
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