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/.
79 lines
3.0 KiB
TeX
79 lines
3.0 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{hyperref}
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\usepackage{booktabs}
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\usepackage{enumitem}
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\usepackage{algorithm}
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\usepackage{algpseudocode}
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\usepackage{xcolor}
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\usepackage{tikz}
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\usetikzlibrary{arrows.meta,positioning,shapes.geometric,fit}
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\hypersetup{colorlinks=true,linkcolor=black,citecolor=blue,urlcolor=blue}
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\newtheorem{theorem}{Theorem}[section]
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{proposition}[theorem]{Proposition}
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\newtheorem{definition}{Definition}[section]
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\newtheorem{remark}{Remark}[section]
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\title{Threshold FHE for Regulatory Compliance:\\Operator-Blind Computation with Forced Decryption}
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\author{
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Zach Kelling\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{2024}
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\begin{document}
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\luxcoverpage
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\begin{abstract}
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We present a threshold Fully Homomorphic Encryption scheme for regulated
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financial infrastructure in which an operator evaluates arbitrary boolean
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circuits on encrypted data without observing plaintext, while a regulator
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holding $t$ of $n$ key shares retains the ability to force decryption for
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lawful inspection. The construction combines TFHE gate evaluation (AND, OR,
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NOT, NAND, MUX over LWE ciphertexts on the torus $\mathbb{T}$) with
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Shamir-based threshold decryption: the FHE secret key $\mathbf{s}$ is split
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into $n$ shares such that any $t$ shares reconstruct the partial decryption
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vector, while any $t-1$ shares are information-theoretically independent
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of $\mathbf{s}$. We prove three properties: (1)~\emph{operator blindness}---the
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compute node that evaluates homomorphic circuits learns nothing about the
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plaintext inputs or outputs; (2)~\emph{threshold decryptability}---any
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coalition of $t$ share-holders can decrypt any ciphertext produced by
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the system; (3)~\emph{privacy below threshold}---any coalition of fewer
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than $t$ share-holders gains no information beyond the public parameters.
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We instantiate the scheme on the Lux F-Chain using seven concrete
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applications (private balance, encrypted transfer, sealed-bid auction,
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private voting, encrypted ML inference, dark pool matching, compliance
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screening) and report benchmarks from the \texttt{luxfi/fhe} library:
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12ms per bootstrapped gate, 47ms per encrypted order match, and 230ms
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per encrypted compliance check at NIST Level~1 (128-bit) security.
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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-introduction}
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\input{sections/02-preliminaries}
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\input{sections/03-formal-construction}
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\input{sections/04-security-proofs}
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\input{sections/05-compliance-architecture}
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\input{sections/06-concrete-instantiations}
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\input{sections/07-performance}
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\input{sections/08-formal-verification}
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\input{sections/09-related-work}
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\input{sections/99-conclusion}
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\end{document}
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