{"body":"\\begin{definition}\\label{def:twcalw-nonsl}\nIf any PPT $\\texttt{A}$ has at most a negligible advantage at the following game is said to satisfy TWCALW Non-Slanderability.\n\\begin{enumerate}\n\\item Challenger grants $\\texttt{A}$ access to the oracles \\texttt{KGO}, \\texttt{CO}, and \\texttt{SO} as in TWCALW Linkability.\n\\item $\\texttt{A}$ outputs a target message $m^*$, ring $R^*$, and ring index $l^*$.\n\\item The challenger computes a target signature $\\sigma^* \\leftarrow \\texttt{SO}(m^*, R^*, l^*)$ and sends $\\sigma^*$ to $\\texttt{A}$. \n\\item $\\texttt{A}$ outputs a message $m$, a ring $R$, and a signature $\\sigma$, succeeding if all of the following hold.\n\\begin{enumerate}[(i)]\n    \\item   $\\texttt{VERIFY}(m, R, S) = 1$, and\n    \\item  $\\texttt{LINK}((m, R, S), (m^*, R^*, S^*)) = 1$, and\n    \\item all keys in $R$ or $R^*$ are from queries made to \\texttt{KGO}, and\n    \\item  $\\texttt{A}$ did not query \\texttt{CO} with any $pk^*_{l^*} \\in R^*$, and\n    \\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 $(m^\\prime, R^\\prime, l^\\prime)$.\n\\end{enumerate}\n\\end{enumerate}\n\\end{definition}","name":"","extension":"txt","url":"https://www.irccloud.com/pastebin/z90qGrvR","modified":1580828758,"id":"z90qGrvR","size":1217,"lines":16,"own_paste":false,"theme":"","date":1580828758}