Conclusion

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Fabrice Mouhartem 2018-06-19 17:45:22 +02:00
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@ -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. 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. 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}. 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} \begin{question}
Can we achieve better security proofs for cryptographic schemes? Can we achieve better security proofs for cryptographic schemes?

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publisher = {Springer}, 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;} @Comment{jabref-meta: databaseType:bibtex;}