From ce0c4ca996af1a10473120f555d665902e0ef2cf Mon Sep 17 00:00:00 2001
From: Tobias Eidelpes <tobias@eidelpes.info>
Date: Tue, 21 Jun 2022 12:59:54 +0200
Subject: [PATCH] Add solution for 5f

---
 exam/ex.tex | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

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