From a75260a8391db68eb7a972e612246d7212e0d0b3 Mon Sep 17 00:00:00 2001
From: Fabrice Mouhartem <fabrice.mouhartem@ens-lyon.org>
Date: Fri, 15 Jun 2018 19:17:55 +0200
Subject: [PATCH] Conclusion

---
 chap-conclusion.tex | 34 ++++++++++++++++++++++++++++++++++
 main.tex            |  1 +
 2 files changed, 35 insertions(+)

diff --git a/chap-conclusion.tex b/chap-conclusion.tex
index e69de29..10e76d1 100644
--- a/chap-conclusion.tex
+++ b/chap-conclusion.tex
@@ -0,0 +1,34 @@
+\begin{comment}
+\section %hack for vim-latexsuite
+\end{comment}
+
+In this thesis, we presented new cryptographic schemes that relies on lattice or pairing assumptions.
+These contributions focus on the design and analysis of new cryptographic schemes that target privacy-preserving applications.
+
+In pairing-related cryptography, we propose a practical dynamic group signature scheme, for which security is well understood.
+It relies on broadly used assumptions with simple statements that exists for more than ten years.
+This work is also supported by a practical implementation in C.
+
+Our work in the lattice work give rise of three fundamental schemes that were missing in the landscape of lattice-based privacy-preserving primitives.
+Even if these schemes suffer from some efficiency issues due to their novelty, we do believe that it's one step toward a quantum-secure privacy-friendly world.
+
+In the way of doing it, improvements have been made in the state of zero-knowledge proofs in the lattice setting as well as providing building blocks that, we believe, are of independent interest.
+As of our signature with efficient protocols, which have been used to provide a lattice-based e-cash system~\cite{LLNW17}.
+
+All these works are proven under strong security model within simple assumptions.
+This made a breeding ground for new theoretical constructions, as well as going toward practicality.
+
+\section*{Open Problems}
+
+The path of providing new cryptographic primitives and proving them is sometimes uneven.
+The most obvious questions that stem from this work are about how to tackle the compromises we made in the design of those primitives.
+
+\begin{question}
+  Is it possible to build an adaptive oblivious transfer with access control with polynomially-large approximation factor?
+\end{question}
+
+In other words, is it possible to avoid smudging to keep message-privacy in the oblivious transfer scheme of~\cref{ch:ot-lwe}.
+
+\begin{question}
+
+\end{question}
diff --git a/main.tex b/main.tex
index b809d16..d95b02e 100644
--- a/main.tex
+++ b/main.tex
@@ -56,6 +56,7 @@
 \declaretheorem[numberwithin=chapter]{theorem}
 \declaretheorem[sibling=theorem]{lemma}
 \declaretheorem[numberwithin=chapter,style=definition]{definition}
+\declaretheorem[style=remark]{question}
 
 % References
 \usepackage[capitalise]{cleveref}