From 2a8fc8fc0d013d0a41510fa2459a5636a33827e1 Mon Sep 17 00:00:00 2001
From: Aaron Kaiser <a_kaiser@posteo.de>
Date: Wed, 21 Jun 2023 19:21:21 +0200
Subject: [PATCH] Add abstract

---
 docker/Dockerfile              |  2 +-
 thesis/Abschlussarbeit.tex     | 13 ++++++++-----
 thesis/sections/conclusion.tex |  2 +-
 3 files changed, 10 insertions(+), 7 deletions(-)

diff --git a/docker/Dockerfile b/docker/Dockerfile
index b296019..59f450d 100644
--- a/docker/Dockerfile
+++ b/docker/Dockerfile
@@ -1,6 +1,6 @@
 FROM pandoc/latex
 
 RUN apk update && apk add texlive ghostscript
-RUN tlmgr install koma-script xpatch enumitem preprint braket algorithm2e ifoddpage relsize cancel cite algpseudocodex algorithmicx fifo-stack varwidth tabto-ltx totcount tikzmark datetime fmtcount
+RUN tlmgr install koma-script xpatch enumitem preprint braket algorithm2e ifoddpage relsize cancel cite algpseudocodex algorithmicx fifo-stack varwidth tabto-ltx totcount tikzmark datetime fmtcount mathtools
 
 CMD /bin/bash
diff --git a/thesis/Abschlussarbeit.tex b/thesis/Abschlussarbeit.tex
index d6fc2ea..d5eb3e1 100644
--- a/thesis/Abschlussarbeit.tex
+++ b/thesis/Abschlussarbeit.tex
@@ -64,9 +64,7 @@ Masterarbeit
 {\textbf{von}}\\    
 \vspace{1em}
 {\large\textbf{
-Aaron Kaiser\\
-% TODO: remove compiletime notice
-Compiled on \today\ at \currenttime
+Aaron Kaiser
 }}\\
 \end{center}
 \newpage
@@ -77,8 +75,13 @@ Compiled on \today\ at \currenttime
 
 
 \begin{abstract}
- 
-abstract
+EdDSA is a signature scheme which is widely used in practice due to its high performance. Despite the wide adoption of EdDSA, no tight security proof exists for the signature scheme. The only existing security proof analyzes the signature scheme as a canonical identification scheme onto which the Fiat-Schamir transformation is being applied, yielding a non-tight security proof.
+
+In this thesis the security of EdDSA is analyzed, utilizing the random oracel model and the algebraic group model. Using this two methods yields a tight security proof using special variants of the discrete logarithm problem. This variant is the result of the key generation algorithm used in EdDSA. The hardness of this variant of the discrete logarithm problem is then analyzed in the generic group model.
+
+In addition a proof in the single-user setting, a proof in the multi-user setting is also performed. This proof uses a variant of the one-more discrete logarithm, also because of the key generation algorithm.
+
+Finally, it is shown that Ed25519 - one widely used instantiation of EdDSA - provides 125 bit security in the single-user setting and 124 bit of security in the multi-user setting. Ed448 - also a widely used instantiation of EdDSA - provides 221 bits of security in the single-user setting and 220 bits of security in the multi-user setting.
 
 \end{abstract}
 
diff --git a/thesis/sections/conclusion.tex b/thesis/sections/conclusion.tex
index b3035bf..9c76aa8 100644
--- a/thesis/sections/conclusion.tex
+++ b/thesis/sections/conclusion.tex
@@ -10,4 +10,4 @@ According to the results of this thesis, EdDSA has been proven to be a secure si
 
 \paragraph{Acknowledgments}
 
-Many thanks to Dominik Hartmann and Eike Kiltz for the many discussions that helped me during this thesis.
\ No newline at end of file
+Many thanks to Dominik Hartmann and Eike Kiltz for the many discussions that helped me during the creation of this thesis.
\ No newline at end of file