mirror of
https://github.com/lux-apps/papers.git
synced 2026-10-30 18:15:21 +00:00
zeekay
9504b4c3ef
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/.
26 lines
2.0 KiB
TeX
26 lines
2.0 KiB
TeX
\section{Introduction}
|
|
|
|
%% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
Threshold signature schemes enable a group of $n$ parties to collectively produce signatures under a shared public key, such that any subset of $t$ or more parties can sign while any subset of $t - 1$ or fewer cannot. Two dominant protocols exist:
|
|
|
|
\begin{itemize}[nosep]
|
|
\item \textbf{CGGMP21}~\cite{cggmp21}: Threshold ECDSA with identifiable aborts, producing standard $(r, s, v)$ signatures compatible with Ethereum, Bitcoin, and all secp256k1 chains.
|
|
\item \textbf{FROST}~\cite{frost}: Two-round Schnorr threshold signatures for Ed25519 and BIP-340 Taproot, compatible with Solana, TON, Cosmos, Polkadot, and Bitcoin Taproot.
|
|
\end{itemize}
|
|
|
|
Both protocols assume a \emph{static} signer set: the participants are fixed at key generation time and cannot be changed without generating a new key pair. This is operationally infeasible for production systems requiring 24/7 uptime, where nodes must be rotated for maintenance, security incidents, or capacity changes.
|
|
|
|
\paragraph{Our Contribution.} LSS solves this by providing a \emph{live resharing} protocol that enables:
|
|
\begin{enumerate}[nosep]
|
|
\item Adding new signers to an existing group without downtime.
|
|
\item Removing signers (including compromised nodes) without key reconstruction.
|
|
\item Changing the threshold $t$ while maintaining the same public key.
|
|
\item Automatic rollback to previous shard generations on signing failure.
|
|
\item Unified multi-chain support through pluggable \texttt{SignerAdapter} interface.
|
|
\end{enumerate}
|
|
|
|
The key insight is that Shamir's Secret Sharing~\cite{shamir1979} is \emph{linear}: shares of a secret $s$ under polynomial $f(x)$ of degree $t - 1$ can be \emph{re-shared} into a new polynomial $g(x)$ of degree $t' - 1$ distributed to a potentially different set of $n'$ participants, without ever reconstructing $s$ in the clear. JVSS~\cite{pedersen1991} makes this verifiable.
|
|
|
|
%% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|