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/.
87 lines
2.7 KiB
TeX
87 lines
2.7 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{listings}
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\input{../shared/lstlang}
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\usepackage{xcolor}
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\usepackage{enumitem}
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\usepackage{float}
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\usepackage{tikz}
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\usetikzlibrary{arrows.meta,positioning}
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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{definition}{Definition}
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\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{remark}{Remark}
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\newtheorem{example}{Example}
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\lstset{
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basicstyle=\small\ttfamily,
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keywordstyle=\color{blue}\bfseries,
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commentstyle=\color{gray},
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stringstyle=\color{red},
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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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}
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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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\title{Lattice Cryptography from First Principles:\\A Builder's Guide}
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\author{
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Zach Kelling \\
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Lux Industries, Inc.\thanks{Corresponding author: [email protected]}\\
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\texttt{[email protected]}
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}
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\date{2025}
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\begin{document}
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\luxcoverpage
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\begin{abstract}
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Lattice-based cryptography is the foundation of post-quantum security: ML-DSA
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for signatures, ML-KEM for key encapsulation, and Pulsar for threshold schemes
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all build on the hardness of lattice problems. This paper teaches lattice cryptography
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from the ground up---not as a survey of results, but as a builder's guide for engineers
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implementing these schemes. We cover: lattices and their geometry, the Learning With Errors
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(LWE) problem and why it is hard, Ring-LWE and Module-LWE for practical efficiency, the
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Number Theoretic Transform (NTT) for polynomial arithmetic, how ML-DSA and ML-KEM work
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step by step, and how Pulsar extends these to threshold operations. We include Go code
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for every non-trivial algorithm and explain every design decision in terms of the
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security/performance tradeoff it represents. This is the paper we wish existed when we
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started implementing post-quantum cryptography for Lux Network.
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\end{abstract}
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\tableofcontents
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\newpage
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%% ============================================================
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\input{sections/01-what-is-a-lattice}
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\input{sections/02-learning-with-errors-lwe}
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\input{sections/03-ring-lwe-and-module-lwe}
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\input{sections/04-the-number-theoretic-transform}
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\input{sections/05-how-ml-kem-kyber-works}
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\input{sections/06-how-ml-dsa-dilithium-works}
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\input{sections/07-corona-threshold-lattice-signatures}
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\input{sections/08-our-go-implementation}
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\input{sections/09-security-parameters-and-concrete-hardnes}
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\input{sections/10-common-implementation-pitfalls}
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\input{sections/99-conclusion}
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\end{document}
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