Add solution for 5i

exam/ex.tex

@@ -292,7 +292,19 @@
 
     \item \TODO
 
-    \item \TODO
+    \item For completeness see 5e.
+
+    Special soundness: given two accepting transcripts for the same commitment
+    $\mathsf{trans} = (G',\mathsf{ch},\phi_{ch}^{-1}\psi)$ and $\mathsf{trans}'
+    = (G',\mathsf{ch'},\phi_{ch'}^{-1}\psi)$ we have \[ \psi =
+    \frac{\mathsf{resp}-\mathsf{resp}'}{\phi_{ch}^{-1}-\phi_{ch'}^{-1}} \] which
+    means that the witness can be extracted with probability 1.
+
+    For special HVZK: given $\mathsf{ch}\in\{0,\dots,2^{130}-1\}$ choose
+    $\mathsf{resp}\xleftarrow{\$}\mathcal{I}_{1107}$ and calculate
+    $G'\leftarrow\mathsf{resp}(G_{ch})$. The distributions of real transcripts
+    and simulated transcripts are the same. A given valid transcript occurs with
+    probability $1/2^{130}$.
 
     \item \TODO