From 2dabc0a1a47b364d6c02bc9f33d8cf23b5d4c88c Mon Sep 17 00:00:00 2001
From: Tobias Eidelpes <tobias@eidelpes.info>
Date: Tue, 28 Jun 2022 11:02:36 +0200
Subject: [PATCH] Add solution for 5k

---
 exam/ex.tex | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/exam/ex.tex b/exam/ex.tex
index 266bdf0..8e3d212 100644
--- a/exam/ex.tex
+++ b/exam/ex.tex
@@ -380,7 +380,13 @@
       Futhermore, the commitment is also not vulnerable to dictionary attacks,
       as is common with stored password hashes on the server's side.
 
-    \item \TODO
+    \item If the function generating the isomorphisms keeps the same $k=36$
+      first vertices, the security degrades considerably. Under normal
+      circumstances, the number of possible isomorphisms is $1107!$. If the
+      first $36$ vertices are always kept the same, the domain shrinks to
+      $(1107-36)!=1071!$. While the difference might not seem to be practically
+      relevant, the security degrades factorially with every further reduction
+      in graph size.
 
     \item The signer calculates a commitment with a predefined soundness error.
       Then the signer calculates the challenge by taking the hash of the message