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papers/lux-validator-mpc/sections/02-problem-single-key-validator-architectur.tex
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\section{Problem: Single-Key Validator Architecture}
\label{sec:problem}
\subsection{Current Architecture}
In a standard PoS validator:
\begin{enumerate}[leftmargin=2em]
\item Key generation: $sk \leftarrow \mathbb{Z}_q$, $pk \leftarrow sk \cdot G$.
\item Block signing: $\sigma \leftarrow \textsf{Sign}(sk, \text{block})$.
\item The scalar $sk$ is stored in a single location (keystore file, HSM, or memory).
\end{enumerate}
\subsection{Attack Surface}
\begin{table}[ht]
\centering
\caption{Validator key compromise attack vectors.}
\label{tab:attack-vectors}
\begin{tabular}{lll}
\toprule
\textbf{Vector} & \textbf{Mechanism} & \textbf{Impact} \\
\midrule
Software exploit & RCE on validator node & Full key extraction \\
Insider threat & Operator with disk access & Full key extraction \\
Side channel & Timing/power analysis on signing & Key recovery over time \\
Cloud provider & VM snapshot, memory dump & Full key extraction \\
Supply chain & Malicious dependency in node software & Key exfiltration \\
HSM vulnerability & Firmware exploit (e.g., CVE-2019-15809) & Key extraction \\
\bottomrule
\end{tabular}
\end{table}
The common theme: every attack vector leads to \emph{complete} key compromise because
the key is a single scalar. There is no partial compromise, no graceful degradation.
\subsection{Threshold Architecture}
In a threshold architecture with parameters $(t, n)$:
\begin{enumerate}[leftmargin=2em]
\item Key generation: Each of $n$ parties receives a share $sk_i$. The master key
$sk$ is never materialized at any single location.
\item Signing: Any $t$ parties collaborate to produce a valid signature. The protocol
output is indistinguishable from a single-signer signature.
\item Compromise: An adversary who corrupts $< t$ parties learns nothing about $sk$.
\end{enumerate}
The validator's signing capability is distributed across multiple machines,
geographic locations, or organizational boundaries. Compromising any single
component yields zero useful information.
%% ========================================================================
%% 3. DISTRIBUTED KEY GENERATION
%% ========================================================================