diff --git a/exam/ex.tex b/exam/ex.tex index bf71734..c1c3dc4 100644 --- a/exam/ex.tex +++ b/exam/ex.tex @@ -276,7 +276,14 @@ $G=\phi_{ch}^{-1}(G_{ch})$ and therefore $G'=\psi(\phi_{ch}^{-1}(G_{ch}))$ so the verifier will always accept. - \item \TODO + \item Suppose $G_{ch}$ is not isomorphic to $G$. $\mathcal{P}$ prepares in + advance for a challenge $ch^*$ and so + $G'=\psi(\phi_{ch^*}^{-1}(G_{ch^*}))$. $\mathcal{P}$ commits to $G'$. If + the challenge by $V$ is $ch^*$ (so $ch=ch^*$), $\mathcal{V}$ accepts, + otherwise it rejects. Because $ch\in\{0,\dots,2^{130}-1\}$, the + probability that $\mathcal{P}$ convinces $\mathcal{V}$ is + $\frac{1}{2^{130}}$ (soundness error). + \item \TODO