papers/lux-threshold-mpc/sections/99-conclusion.tex

\section{Conclusion}

\label{sec:conclusion}
% ============================================================

We have presented a unified threshold cryptographic framework that covers 17 blockchain
families through two complementary protocols: FROST for Schnorr/EdDSA chains and
CGGMP21 for ECDSA chains. The framework provides:

\begin{enumerate}[nosep]
  \item \textbf{Universal coverage}: Every major blockchain is supported with native
    signature verification---no custom verifier contracts.
  \item \textbf{Constant on-chain cost}: One signature verification regardless of
    threshold size, yielding up to 90\% gas savings over multisig.
  \item \textbf{Strong security}: Unforgeability under $t{-}1$ corruption (Theorems
    \ref{thm:frost-uf-full},~\ref{thm:cggmp-uf}), identifiable abort
    (Theorem~\ref{thm:cggmp-ia}), forward security under proactive refresh
    (Theorem~\ref{thm:forward}), and safe protocol composition
    (Theorem~\ref{thm:composition}).
  \item \textbf{Bitcoin Taproot}: FROST KeygenTaproot produces x-only public keys
    (BIP-340) for key-path spends indistinguishable from single-signer outputs.
  \item \textbf{MPC group address}: On-chain verification uses a single aggregate
    key ($\texttt{ecrecover} == \texttt{mpcGroupAddress}$), not individual signers.
  \item \textbf{Operational safety}: Configurable rotation delay (default 24h, 0 for
    instant, max 7d) with on-chain visibility; proactive key refresh without public
    key change; LSS dynamic resharing for threshold changes.
  \item \textbf{Production performance}: 98ms end-to-end FROST signing, 47ms CGGMP21
    online signing with presignatures, 0.14ms LSS reshare ($3 \to 5$), in
    geographically distributed deployment.
\end{enumerate}

The framework is deployed in Lux Teleport, securing cross-chain asset transfers across
270+ blockchains. Implementation is open-source at \texttt{github.com/luxfi/threshold}
and \texttt{github.com/luxfi/mpc}.

% ============================================================
% References
% ============================================================
\bibliographystyle{plain}
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