Conclusion

chap-conclusion.tex

@@ -68,7 +68,10 @@ Thus, a natural question may be:
 For instance, in the group encryption scheme of~\cref{ch:ge-lwe}, trapdoors are used in two places.
 To have a secure public key encryption scheme under adaptive chosen-ciphertext attacks and for the signature scheme.
 Both these primitives are induced by identity-based encryption: the Canetti-Halevi-Katz transform generically turns an IBE into a \textsf{IND-CCA2} \PKE~\cite{CHK04}, and signatures are directly implied from \textsf{IND-CPA-}secure IBE~\cite{BF01,BLS01}.
-Actually, even the question of having a trapdoorless \textsf{IND-CCA2} public key encryption scheme still remains an open question.
+%Actually, even the question of having a trapdoorless \textsf{IND-CCA2} public key encryption scheme still remains an open question.
+Actually, a recent construction from Brakerski, Lombardi, Segev and Vaikuntanathan~\cite{BLSV18} gives a candidate which relies on garble circuits, and is fairly inefficient compared to IBEs with trapdoors.
+Even the question of an \textsf{IND-CCA2} public key encryption still does not have a satisfactory response. 
+The construction of Peikert and Waters~\cite{PW08} is indeed trapdoor-free, but is still less efficient than trapdoor-based ones.
 
 \begin{question}
   Can we achieve better security proofs for cryptographic schemes?

these.bib

@@ -3108,4 +3108,25 @@
   publisher = {Springer},
 }
 
+@InProceedings{BLSV18,
+  author    = {Brakerski, Zvika and Lombardi, Alex and Segev, Gil and Vaikuntanathan, Vinod},
+  title     = {{Anonymous IBE, Leakage Resilience and Circular Security from New Assumptions}},
+  booktitle = {{Eurocrypt}},
+  year      = {2018},
+  series    = {LNCS},
+  pages     = {535--564},
+  publisher = {Springer},
+  abstract  = {In anonymous identity-based encryption (IBE), ciphertexts not only hide their corresponding messages, but also their target identity. We construct an anonymous IBE scheme based on the Computational Diffie-Hellman (CDH) assumption in general groups (and thus, as a special case, based on the hardness of factoring Blum integers).},
+  isbn      = {978-3-319-78381-9},
+}
+
+@InProceedings{PW08,
+  author    = {Peikert, Chris and Waters, Brent},
+  title     = {{Lossy Trapdoor Functions and Their Applications}},
+  booktitle = {STOC},
+  year      = {2008},
+  pages     = {187--196},
+  publisher = {ACM},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}