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Erschienen in:
Stronger Security for Reusable Garbled Circuits, General Definitions and Attacks Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

Practical Functional Encryption for Quadratic Functions with Applications to Predicate Encryption

verfasst von : Carmen Elisabetta Zaira Baltico, Dario Catalano, Dario Fiore, Romain Gay

Erschienen in: Advances in Cryptology – CRYPTO 2017

Verlag: Springer International Publishing

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Abstract

We present two practically efficient functional encryption schemes for a large class of quadratic functionalities. Specifically, our constructions enable the computation of so-called bilinear maps on encrypted vectors. This represents a practically relevant class of functions that includes, for instance, multivariate quadratic polynomials (over the integers). Our realizations work over asymmetric bilinear groups and are surprisingly efficient and easy to implement. For instance, in our most efficient scheme the public key and each ciphertext consist of \(2n+1\) and \(4n+2\) group elements respectively, where n is the dimension of the encrypted vectors, while secret keys are only two group elements. Our two schemes build on similar ideas, but develop them in a different way in order to achieve distinct goals. Our first scheme is proved (selectively) secure under standard assumptions, while our second construction is concretely more efficient and is proved (adaptively) secure in the generic group model.
As a byproduct of our functional encryption schemes, we show new predicate encryption schemes for degree-two polynomial evaluation, where ciphertexts consist of only O(n) group elements. This significantly improves the \(O(n^2)\) bound one would get from inner product encryption-based constructions.

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Vorheriges Kapitel Generic Transformations of Predicate Encodings: Constructions and Applications
Nächstes Kapitel Memory-Tight Reductions
Fußnoten
1
Here by complex we intend, for instance, functions that are supposed to have some computational hiding properties. In particular, Boneh et al. [13] argue that, in applications where security relies on such properties, indistinguishability might become problematic.
 
2
Indeed, we note that a functional encryption for linear polynomials can be used to support, say, quadratic polynomials, by simply encrypting all the degree-two monomials in advance. This however leads to an inefficient solution where the size of the ciphertexts is quadratic in the number of variables.
 
3
Here we adopt the, by now standard, implicit representation \([x]_s = g^x \in \mathbb G_s\). This notion can be easily extended to vectors and matrices (see [18]).
 
4
This means that in our scheme messages and functions coefficients are assumed to be sufficiently small integers.
 
5
Furthermore, with a close look one can see that the last \(n-m\) components of the vectors \([\varvec{b}]_2\), \(\varvec{d}\) and \(\varvec{\widehat{d}}\) would become useless and thus can be discarded.
 
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Metadaten
Titel
Practical Functional Encryption for Quadratic Functions with Applications to Predicate Encryption
verfasst von
Carmen Elisabetta Zaira Baltico
Dario Catalano
Dario Fiore
Romain Gay
Copyright-Jahr
2017
Buch
Advances in Cryptology – CRYPTO 2017

Print ISBN: 978-3-319-63687-0

Electronic ISBN: 978-3-319-63688-7

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-63688-7_3