papers/zoo-fhe-ai/sections/08-security-analysis.tex

\section{Security Analysis}


\subsection{Encryption Security}

\begin{theorem}[Semantic Security]
Zoo FHE achieves IND-CPA security under the Ring-LWE assumption with parameters providing 128-bit post-quantum security.
\end{theorem}

The parameters ($N = 2^{14}$, $\log Q = 438$) are chosen according to the Homomorphic Encryption Standard~\cite{albrecht2018hes} and provide security against both classical and quantum adversaries.

\subsection{Threshold Security}

\begin{theorem}[Threshold Robustness]
Under the $(5, 9)$-threshold scheme, an adversary controlling up to 4 committee members cannot decrypt any ciphertext.
\end{theorem}

\begin{proof}
Shamir secret sharing over the key space ensures that fewer than $t = 5$ shares reveal no information about the secret key. Each partial decryption is verified by a zero-knowledge proof, preventing malicious shares from corrupting the reconstruction.
\end{proof}

\subsection{Data Privacy Guarantees}

\begin{enumerate}
    \item \textbf{Input privacy}: Data providers encrypt locally; the Zoo network never sees plaintext inputs.
    \item \textbf{Model privacy}: Model weights are encrypted; neither validators nor users learn the model parameters.
    \item \textbf{Output privacy}: Inference results remain encrypted until threshold decryption is authorized.
    \item \textbf{Gradient privacy}: Individual training contributions are encrypted; only the aggregate is revealed.
\end{enumerate}