mirror of
https://github.com/lux-apps/papers.git
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zooqueen
12912be1b5
- canonical lux-corona-pq paper: rank-7 Module-LWE (A in R_q^{8x7}, q=48-bit), Module-SIS
- scrub residual Corona Ring-LWE/R-LWE labels across ethos-of-lux, pqsafe-il5,
lux-whitepaper, lux-quasar-composition, lp-020; Corona<->Pulsar = parameter regime,
both Module-LWE (not rank-1-vs-rank-k)
- LLM.md: drop stale 'Corona as rank-1' wobble note; align to code/Ringtail params
- rebuild affected PDFs
87 lines
3.6 KiB
TeX
87 lines
3.6 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{amsmath,amssymb,amsfonts,amsthm}
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\usepackage{graphicx}
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\usepackage{hyperref}
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\usepackage{algorithm}
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\usepackage{algpseudocode}
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\usepackage{xcolor}
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\usepackage{booktabs}
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\usepackage{enumitem}
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\usepackage{tikz}
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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{\textbf{Corona: Two-Round Module-LWE Threshold\\Signatures for Public Permissionless Chains}}
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\author{
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Zach Kelling\thanks{Corresponding author: [email protected]}
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\quad
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Vishnu Seesahai\\
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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 Corona, a two-round Module-LWE threshold signature scheme designed for
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public, permissionless blockchain consensus. Corona enables any $t$-of-$n$ subset of
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a validator set to collaboratively sign blocks without any single party ever holding
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the full secret key, while providing security against quantum adversaries. The scheme
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operates in two rounds: a message-independent precomputation and commitment round,
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followed by a signing round, with a non-interactive combine producing the final
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aggregate signature.
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Corona is Lux's first-party fork of Ringtail~(Boschini et al., IACR ePrint 2024/1113).
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It builds on the Module-LWE assumption over the cyclotomic ring
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$R_q = \mathbb{Z}_q[X]/(X^N + 1)$ with $N = 256$ and a 48-bit prime modulus
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$q = \texttt{0x1000000004A01}$, instantiated as a module of dimension $M = 8 \times N' = 7$:
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the public key is a matrix relation $\mathbf{b} = \mathbf{A}\mathbf{s} + \mathbf{e}$ with
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$\mathbf{A} \in R_q^{M \times N'}$, $\mathbf{s} \in R_q^{N'}$, and $\mathbf{e} \in R_q^{M}$,
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with Module-SIS commitments. We prove that the scheme achieves existential unforgeability
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under chosen-message attacks (EUF-CMA) in the random oracle model, reducing security to
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the hardness of Module-LWE together with Module-SIS, at NIST security Category~1
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($\sim$128-bit classical, $\sim$130-bit quantum). A Corona threshold signature is
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approximately 33--35\,KB and verifies in approximately 1.6\,ms; it is \emph{not}
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byte-equal to any FIPS standard (that byte-equality is a property of the sibling scheme
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Pulsar, LP-4450, not of Corona).
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Corona's distinguishing contribution is making the academic two-round lattice threshold
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construction work for public, permissionless validator sets that change over time:
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leaderless distributed key generation with no trusted dealer (Feldman/Pedersen
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commitments), dynamic resharing across a changing validator set, and on-chain ceremony
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binding anchored to the Lux Q-Chain. It is the intra-lattice diversity leg of the
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Aurora certificate profile (Pulsar $\|$ Corona) under Quasar, verified by the raw EVM
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precompile at \texttt{0x012206}. Corona is a distinct production artifact derived from
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Ringtail.
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\end{abstract}
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\tableofcontents
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\newpage
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%% -----------------------------------------------------------------------
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%% 1. INTRODUCTION
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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-the-corona-scheme}
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\input{sections/04-security-analysis}
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\input{sections/05-integration-with-lux-quasar}
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\input{sections/06-empirical-evaluation}
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\input{sections/07-related-work}
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\input{sections/99-conclusion}
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\end{document}
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