papers/zoo-bridge/sections/07-security-analysis.tex

\section{Security Analysis}

\label{sec:security}

\subsection{Bridge Safety}

\begin{theorem}[Bridge Safety Reduction]
Zoo Bridge safety reduces to Warp protocol safety: if the Warp protocol is safe (no invalid messages verified), then the bridge cannot process invalid transfers.
\end{theorem}

\begin{proof}
Every bridge action (mint, unlock, create) is triggered exclusively by a verified Warp message. The bridge contract checks:
\begin{enumerate}
    \item Warp signature verification passes
    \item Nonce is strictly monotonic (no replay)
    \item Asset type matches expected format
    \item Amount/metadata matches source chain state
\end{enumerate}
If Warp verification is sound, conditions 1--4 are guaranteed by the source chain's consensus. An adversary cannot forge a bridge transfer without forging a Warp message, which requires corrupting $\geq 67\%$ of validator stake.
\end{proof}

\subsection{Liveness}

\begin{theorem}[Bridge Liveness]
If both source and destination chains are live and the Warp quorum threshold is met, bridge transfers complete within bounded time.
\end{theorem}

The timeout is set to 5 minutes. If a Warp message is not verified within 5 minutes, the source chain automatically unlocks the escrowed assets.

\subsection{Double-Spend Prevention}

Each bridge transfer is assigned a unique nonce per (source, destination, asset) triple. The destination bridge contract maintains a nonce counter and rejects any message with a nonce $\leq$ the last processed nonce. Combined with Quasar's finality guarantee, this prevents double-spend attacks.

\subsection{Model NFT Integrity}

\begin{theorem}[NFT Metadata Integrity]
If a Model NFT is bridged from Zoo to Beluga, the License NFT on Beluga faithfully represents the original model's metadata.
\end{theorem}

\begin{proof}
The Warp message payload includes the model hash, architecture, accuracy, and custody key---all verified by Zoo validators before signing. The Beluga bridge contract creates the License NFT deterministically from this payload. Metadata tampering requires forging the Warp signature.
\end{proof}