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papers/mpc-custody/sections/08-formal-verification.tex
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\section{Formal Verification}
\label{sec:formal}
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The core properties are mechanized in Lean~4:
\begin{itemize}[nosep]
\item \texttt{Crypto.Threshold.CGGMP21}: keygen correctness,
identifiable abort, presignature one-time use, offline/online
separation, key never reconstructed.
\item \texttt{Crypto.FROST}: correctness, unforgeability, robustness,
majority threshold safety, share refresh.
\item \texttt{Crypto.Threshold.Reshare}: public key preservation,
old share invalidation, threshold maintenance, no key
reconstruction, Byzantine safety.
\item \texttt{Crypto.NonCustodial}: 2-of-3 non-custodial guarantee,
liveness (any 2 can sign), single-party impotence.
\end{itemize}
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