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Add binding solution for 5d

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Tobias Eidelpes 2022-06-21 19:59:27 +02:00
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exam/ex.tex
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@ -300,7 +300,11 @@
$\mathcal{G}_{\mathsf{ch}}$ isomorphic to $\mathcal{G}$ as input and $\mathcal{G}_{\mathsf{ch}}$ isomorphic to $\mathcal{G}$ as input and
outputs $\top$ if the result matches $\mathcal{G}'$ and $\bot$ otherwise. outputs $\top$ if the result matches $\mathcal{G}'$ and $\bot$ otherwise.
\item \TODO \item Computational binding: Suppose $\mathsf{Comm}(\psi,\mathcal{G}_0) =
\mathsf{Comm}(\psi,\mathcal{G}_1)$. This means that $\psi(\mathcal{G}_0) =
\psi(\mathcal{G}_1)$ and the adversary has found an isomorphism which maps
two different graphs to the same output which corresponds to solving the
CGI problem.
\item If $G_{ch}=\phi_{ch}(G)$ and $G'=\psi(G)$, it follows that \item If $G_{ch}=\phi_{ch}(G)$ and $G'=\psi(G)$, it follows that
$G=\phi_{ch}^{-1}(G_{ch})$ and therefore $G'=\psi(\phi_{ch}^{-1}(G_{ch}))$ $G=\phi_{ch}^{-1}(G_{ch})$ and therefore $G'=\psi(\phi_{ch}^{-1}(G_{ch}))$