papers/zoo-identity-chain/sections/06-integration-with-t-chain.tex

\section{Integration with T-Chain}


\subsection{Threshold Credential Signing}

\IChain{} delegates cryptographic signing to \TChain{} (Zoo's threshold signature chain) \cite{zoo-threshold-signatures}. This separation ensures that \IdentityVM{} handles identity semantics while \TChain{} handles key material.

The integration follows a request-response pattern:

\begin{enumerate}
\item \IdentityVM{} constructs the credential body and submits a signing request to \TChain{}.
\item \TChain{} coordinates $t$-of-$n$ partial signature generation across the validator committee.
\item \TChain{} returns the aggregated signature to \IdentityVM{}.
\item \IdentityVM{} attaches the signature and finalizes the credential.
\end{enumerate}

\subsection{Key Rotation via K-Chain}

When validator keys are rotated (managed by \KChain{} \cite{zoo-key-management}), \IChain{} must update its committee configuration. This is handled through cross-chain events:

\begin{enumerate}
\item \KChain{} emits a \texttt{KeyRotated} event with the new public key share.
\item \IdentityVM{} updates the committee member's verification key.
\item Outstanding signing requests using the old key are voided and resubmitted.
\end{enumerate}

The formal relationship between chains is:

\begin{equation}
\text{I-Chain} \xrightarrow{\text{signing requests}} \text{T-Chain} \xrightarrow{\text{key material}} \text{K-Chain}
\end{equation}