{"body":"\n\\begin{definition}[Non-frameability]\nWe 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 $\\epsilon$.\n\\begin{enumerate}\n\\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 $\\texttt{A}$. \n\n\\item $\\texttt{A}$ is granted access to a corruption oracle $\\mathcal{CO}$ and a signing oracle $\\mathcal{SO}$.\n\n\\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 $\\mathcal{SO}(\\textbf{pk},m,\\underline{\\textbf{pk}}^*) \\to \\sigma$.\n\n\\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\n\\begin{enumerate}\n\\item $\\texttt{Verify}(m^\\prime, \\underline{\\textbf{pk}}^\\prime, \\sigma^\\prime) = 1$; and\n\\item $\\texttt{Link}(\\sigma,\\sigma^\\prime) = 1$.\n\\end{enumerate}\n\\end{enumerate}\n\\end{definition}","name":"","extension":"txt","url":"https://www.irccloud.com/pastebin/zL8X3cmW","modified":1580828849,"id":"zL8X3cmW","size":1558,"lines":17,"own_paste":false,"theme":"","date":1580828849}