First version of conclusion

chap-conclusion.tex

@@ -32,6 +32,8 @@ As is, this problem arises from the use of Regev's encryption scheme, which does
 However, finer analysis on GSW ciphertexts~\cite{GSW13} seems promising to achieve this at reasonable cost~\cite{BDPMW16}.
 Then, the main difficulty is to have compatible zero-knowledge proof with the access control and the encryption layers.
 
+\subsection*{Zero-Knowledge Proofs}
+
 \begin{question}
   Can we provide NIZK proofs in the standard model for all $\NP$ languages relying on standard $\LWE$ assumption only?
 \end{question}
@@ -56,6 +58,8 @@ If these proof systems can be used after applying a transformation from average-
 As we explained in the introduction, advanced cryptography from lattices often suffers from the use of lattice trapdoors.
 Thus, a natural question may be:
 
+\subsection*{Cryptographic Constructions}
+
 \begin{question}
   Does a trapdoor-free (H)IBE exists?
 \end{question}
@@ -66,4 +70,11 @@ Both these primitives are induced by identity-based encryption: the Canetti-Hale
 Actually, even the question of having a trapdoorless \textsf{IND-CCA2} public key encryption scheme still remains an open question.
 
 \begin{question}
+  Can we achieve better security proofs for cryptographic schemes?
 \end{question}
+
+Our work during this thesis also focus on the proof of cryptographic schemes.
+As explained in~\cref{ch:proofs}, it is important to rely on simple assumptions to prove strong security notions.
+Given the advances in cryptographic proofs~\cite{Hof16,KMP16,Hof17}, it is now possible to attain stronger security notions than what was claim before~\cite{DSYC18}.
+Another line of work looks at the quality of the reduction, aiming for \textit{tight security}~\cite{GHKW16,AHN+17}.
+This improves the understanding of the link between the cryptographic scheme and the security assumption, leading to more reliable schemes.