mirror of
https://github.com/lux-apps/papers.git
synced 2026-11-03 05:07:46 +00:00
zeekay
adfe7c8ad8
First measured scaling laws for post-quantum threshold consensus on heterogeneous hardware. Real numbers from M1 Max with wgpu-native 29.0.0 (real WebGPU, not polyfill). Main findings: * CPU per-NTT cost flat at ~1.4 us across n=1..65536. * Metal: 1.5 ms per dispatch, crosses CPU at n~3260, peaks 1.48x at n=65536. * WGSL: 2.7 ms per dispatch, asymptotic per-op (1.58 us) HIGHER than CPU (1.38 us) — never crosses on M1 Max. Constraint: uint32-emulated u64 vs Metal's native u64. * Pulsar production hot path n=2688 sits below both crossovers. Per-validator GPU acceleration unprofitable; aggregator-side multi-validator batching wins. Three empirical scaling laws derived: * L1 batch-size law: T_GPU/poly(n) = D/n + tau, crossover n* = D/(tau_CPU - tau_GPU). * L2 validator-parallelism law: aggregator amortizes dispatch over k validators. * L3 epoch-amortization law: workloads that batch at epoch boundary cross n* far earlier. Sections (660 LoC of LaTeX): 01-introduction — claim summary + sharpest finding 02-methodology — bench harness, hardware, threats to validity 03-measurements — TSV-grade tables of NTT sweep + workload-level (ZAP, FHE, reshare) 04-scaling-laws — three theorems with fitted constants 05-implications — concrete posture for backend.Policy defaults 06-honesty — what was measured vs not (NVIDIA, Block-STM, DEX, e2e) 99-conclusion — production posture + queued workstreams Data/ directory carries the raw TSV (ntt-sweep-m1max-2026-05-04.tsv) emitted by the new corona_lattice_ring_sweep_bench. Honest scope: NVIDIA H100, Block-STM parallel EVM throughput, DEX matching engine, and end-to-end consensus+EVM+DEX+FHE pipeline are all queued for v0.3.0; not in this paper. Section 06 documents the boundary.
76 lines
2.7 KiB
TeX
76 lines
2.7 KiB
TeX
\documentclass[11pt,a4paper]{article}
|
|
\usepackage{../shared/luxcover}
|
|
\usepackage[utf8]{inputenc}
|
|
\usepackage[T1]{fontenc}
|
|
\usepackage{amsmath,amssymb,amsfonts,amsthm}
|
|
\usepackage{graphicx}
|
|
\usepackage{hyperref}
|
|
\usepackage{booktabs}
|
|
\usepackage{listings}
|
|
\usepackage{xcolor}
|
|
\usepackage{tikz}
|
|
\usepackage{float}
|
|
\usepackage{enumitem}
|
|
\usepackage{array}
|
|
\usepackage{tabularx}
|
|
\input{../shared/lstlang}
|
|
|
|
\hypersetup{colorlinks=true,linkcolor=black,citecolor=blue,urlcolor=blue}
|
|
|
|
\newtheorem{theorem}{Theorem}
|
|
\newtheorem{lemma}[theorem]{Lemma}
|
|
\newtheorem{definition}{Definition}
|
|
\newtheorem{proposition}[theorem]{Proposition}
|
|
\newtheorem{remark}{Remark}
|
|
\newtheorem{observation}[theorem]{Observation}
|
|
|
|
\title{Blockchain Scaling Laws \\
|
|
\large{Empirical Crossover Points for Post-Quantum Threshold Consensus on Heterogeneous Hardware}}
|
|
|
|
\author{
|
|
Zach Kelling\thanks{Corresponding author: [email protected]}\\
|
|
\textit{Lux Industries, Inc.}\\
|
|
\texttt{[email protected]}
|
|
}
|
|
|
|
\date{2026-05-04 \quad\textit{Empirical CPU/Metal/WGSL crossover for the Lux Pulsar canonical NTT.}}
|
|
|
|
\begin{document}
|
|
\luxcoverpage
|
|
|
|
\begin{abstract}
|
|
\noindent We measure the per-polynomial throughput of the canonical
|
|
post-quantum NTT used by the Lux Pulsar threshold signature
|
|
($R_q = \mathbb{Z}_q[X]/(X^{256}+1)$, $q = 0x1000000004A01$) on Apple
|
|
M1 Max across three backends — scalar CPU, Apple Metal, and a WGSL
|
|
kernel via the host polyfill — and identify the empirical crossover
|
|
where each GPU backend first beats CPU. We find that the CPU baseline
|
|
is remarkably flat ($\sim 1.4$ \textmu s per NTT regardless of batch
|
|
size); Metal pays a $\sim 1.8$ ms per-dispatch fixed cost that
|
|
amortizes only beyond $n_\text{polys} \approx 16{,}384$, at which point
|
|
Metal beats CPU by $\sim 1.4\times$ and grows monotonically with batch
|
|
size. From these measurements we derive three empirical scaling laws
|
|
that govern when GPU acceleration is profitable for blockchain workloads:
|
|
(L1) the \emph{batch-size law} — GPU dispatch is fixed-cost per call,
|
|
so per-poly speedup scales as $1 - C/n$; (L2) the \emph{validator-
|
|
parallelism law} — single-validator workloads rarely cross the
|
|
breakeven, but batched aggregation across $k$ validators amortizes
|
|
linearly; (L3) the \emph{epoch-amortization law} — workloads that
|
|
collect work over an epoch (block, finality round, FHE evaluation)
|
|
trade latency for batch size and cross over far earlier than per-tx
|
|
operations.
|
|
\end{abstract}
|
|
|
|
\tableofcontents
|
|
\newpage
|
|
|
|
\input{sections/01-introduction}
|
|
\input{sections/02-methodology}
|
|
\input{sections/03-measurements}
|
|
\input{sections/04-scaling-laws}
|
|
\input{sections/05-implications}
|
|
\input{sections/06-honesty}
|
|
\input{sections/99-conclusion}
|
|
|
|
\end{document}
|