# Pastebin z90qGrvR
\begin{definition}\label{def:twcalw-nonsl}
If any PPT $\texttt{A}$ has at most a negligible advantage at the following game is said to satisfy TWCALW Non-Slanderability.
\begin{enumerate}
\item Challenger grants $\texttt{A}$ access to the oracles \texttt{KGO}, \texttt{CO}, and \texttt{SO} as in TWCALW Linkability.
\item $\texttt{A}$ outputs a target message $m^*$, ring $R^*$, and ring index $l^*$.
\item The challenger computes a target signature $\sigma^* \leftarrow \texttt{SO}(m^*, R^*, l^*)$ and sends $\sigma^*$ to $\texttt{A}$. 
\item $\texttt{A}$ outputs a message $m$, a ring $R$, and a signature $\sigma$, succeeding if all of the following hold.
\begin{enumerate}[(i)]
    \item   $\texttt{VERIFY}(m, R, S) = 1$, and
    \item  $\texttt{LINK}((m, R, S), (m^*, R^*, S^*)) = 1$, and
    \item all keys in $R$ or $R^*$ are from queries made to \texttt{KGO}, and
    \item  $\texttt{A}$ did not query \texttt{CO} with any $pk^*_{l^*} \in R^*$, and
    \item   for any message $m^\prime$, any ring $R^\prime$, any ring index $l^\prime$ such that $pk^\prime_{l^\prime} = pk^*_{l^*}$, $\texttt{A}$ did not query \texttt{SO} with $(m^\prime, R^\prime, l^\prime)$.
\end{enumerate}
\end{enumerate}
\end{definition}