# Pastebin zL8X3cmW

\begin{definition}[Non-frameability]
We say that a given PPT algorithm $\texttt{A}$ is a $(t, \epsilon, q_c, q_s, \kappa(-))$-solver of the frameability game if, within time at most $t$, with at most $q_c$ oracle queries to $\mathcal{CO}$, and with at most $q_s$ oracle queries to $\mathcal{SO}$, $\texttt{A}$ can succeed at the following game with probability at least $\epsilon$.
\begin{enumerate}
\item Challenge keys $\left\{(\textbf{sk}_i, \textbf{pk}_i)\right\}_{i=1}^{\kappa(\lambda)} \leftarrow \texttt{KeyGen}(1^\lambda)$ are selected and the public keys $\underline{\textbf{pk}} = \left\{\textbf{pk}_i\right\}_{i=1}^{n(\lambda)}$ are sent to $\texttt{A}$. 

\item $\texttt{A}$ is granted access to a corruption oracle $\mathcal{CO}$ and a signing oracle $\mathcal{SO}$.

\item $\texttt{A}$ chooses a challenger key $\textbf{pk}$ that was not queried to $\mathcal{CO}$, a message $m$, a ring of public keys $\underline{\textbf{pk}}^* \subset \underline{\textbf{pk}}$ containing $\textbf{pk}$, and queries $\mathcal{SO}(\textbf{pk},m,\underline{\textbf{pk}}^*) \to \sigma$.

\item $\texttt{A}$ outputs a tuple $(m^\prime, \underline{\textbf{pk}}^\prime, \sigma^\prime)$ such that $\underline{\textbf{pk}}^\prime \subset \underline{\textbf{pk}}$ and $\sigma^\prime$ was not the output of any query to $\mathcal{SO}$. We say $\texttt{A}$ wins if
\begin{enumerate}
\item $\texttt{Verify}(m^\prime, \underline{\textbf{pk}}^\prime, \sigma^\prime) = 1$; and
\item $\texttt{Link}(\sigma,\sigma^\prime) = 1$.
\end{enumerate}
\end{enumerate}
\end{definition}