From 1ef78ca08811792fa790faae84844a47c2dfa795 Mon Sep 17 00:00:00 2001 From: Fabrice Mouhartem Date: Tue, 19 Jun 2018 17:49:54 +0200 Subject: [PATCH] IBE --- chap-conclusion.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/chap-conclusion.tex b/chap-conclusion.tex index 6ff9e63..78e6e53 100644 --- a/chap-conclusion.tex +++ b/chap-conclusion.tex @@ -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.