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IBE

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Fabrice Mouhartem 2018-06-19 17:49:54 +02:00
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chap-conclusion.tex
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@ -62,14 +62,14 @@ Thus, a natural question may be:
\subsection*{Cryptographic Constructions}
\begin{question}
Does an efficient trapdoor-free (H)IBE exists?
Does an efficient trapdoor-free \textsf{(H)IBE} exists?
\end{question}
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}.
Both these primitives are induced by identity-based encryption: the Canetti-Halevi-Katz transform generically turns an \textsf{IBE} into a \textsf{IND-CCA2} \PKE~\cite{CHK04}, and signatures are directly implied from \textsf{IND-CPA-}secure \textsf{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, 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.
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 \textsf{IBE}s 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.