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Title:
Hidden Vector Encryption Fully Secure Against Unrestricted Queries
Authors: Angelo De Caro, Vincenzo Iovino, Giuseppe Persiano
Abstract:Predicate encryption is an important cryptographic primitive (see \cite{BDOP04,BoWa07,Goyal06,KaSaWa08}) that enables fine-grained control on the decryption keys. Roughly speaking, in a predicate encryption scheme the owner of the master secret key \MSK can derive secret key \SK_P, for any predicate P from a specified class of predicates \mathbb{P}. In encrypting a message M, the sender can specify an {\em attribute} vector \x and the resulting ciphertext \tilde X can be decrypted only by using keys \SK_P such that P(\x)=1. Our main contribution is the {\em first} construction of a predicate encryption scheme that can be proved {\em fully} secure against {\em unrestricted} queries by probabilistic polynomial-time adversaries under non-interactive constant sized (that is, independent of the length \ell of the attribute vectors) hardness assumptions on bilinear groups of composite order. Specifically, we consider {\em hidden vector encryption} (HVE in short), a notable case of predicate encryption introduced by Boneh and Waters \cite{BoWa07} and further developed in \cite{ShWa08, IoPe08, SLNHJ10}. In a HVE scheme, the ciphertext attributes are vectors \x=\langle x_1,\ldots,x_\ell\rangle of length \ell over alphabet \Sigma, keys are associated with vectors \y=\langle y_1,\ldots,y_\ell\rangle of length \ell over alphabet \Sigma\cup\{\star\} and we consider the \Match(\x,\y) predicate which is true if and only if, for all i, y_i\ne\star implies x_i=y_i. Previous constructions restricted the proof of security to adversaries that could ask only {\em non-matching} queries; that is, for challenge attribute vectors \x_0 and \x_1, the adversary could ask only for keys of vectors \y for which$\Match(\x_0,\y)=\Match(\x_1,\y)=$ false. Our proof employs the dual system methodology of Waters \cite{Waters09}, that gave one of the first fully secure construction in this area, blended with a careful design of intermediate security games that keep into account the relationship between challenge ciphertexts and key queries.
ePrint: https://eprint.iacr.org/2011/546
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