papers/lp-checkpoint-anchor/sections/06-adversary-model.tex

\section{Adversary Model}

\label{sec:adversary}

\begin{theorem}[Anchor Integrity]
Let $\mathcal{A}$ be an adversary controlling the Base server but not
$\geq 1/3$ of chain validators. $\mathcal{A}$ cannot produce an anchor
$(appID, h, r')$ for $r' \neq r$ at height $h$ if an honest anchor
$(appID, h, r)$ was already finalized.
\end{theorem}

\begin{proof}
The height monotonicity invariant prevents overwriting: once height $h$ is
anchored, no transaction with height $\leq h$ for the same appID is
accepted. Reverting the anchor requires a chain reorganization past the
Quasar finality depth, which requires compromising $\geq 1/3$ of
validators across all three signature schemes (BLS, ML-DSA, Pulsar).
\end{proof}

\paragraph{Withholding attack.}
The server can refuse to anchor, or anchor selectively. This is detectable:
if the user expects an anchor at height $h$ and \texttt{getLatest(appID)}
returns $h' < h$, the server is withholding. Mitigation: let clients
submit anchors directly (the precompile accepts any \texttt{msg.sender}).

\paragraph{Equivocation.}
The server anchors root $r_1$ at height $h$ on-chain but presents root
$r_2$ to a client. The client detects this on verification (step 4 above).
The on-chain record is authoritative.

\paragraph{Reorg protection.}
On Q-Chain, a QuasarCert-finalized anchor is irreversible under the Quasar
security model. On C-Chain, wait for 2 block confirmations ($\approx 4$s)
for probabilistic finality equivalent to $10^{-9}$ reorg probability.

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