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On Removing Graded Encodings from Functional Encryption Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

Functional Encryption: Deterministic to Randomized Functions from Simple Assumptions

verfasst von : Shashank Agrawal, David J. Wu

Erschienen in: Advances in Cryptology – EUROCRYPT 2017

Verlag: Springer International Publishing

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Abstract

Functional encryption (FE) enables fine-grained control of sensitive data by allowing users to only compute certain functions for which they have a key. The vast majority of work in FE has focused on deterministic functions, but for several applications such as privacy-aware auditing, differentially-private data release, proxy re-encryption, and more, the functionality of interest is more naturally captured by a randomized function. Recently, Goyal et al. (TCC 2015) initiated a formal study of FE for randomized functionalities with security against malicious encrypters, and gave a selectively secure construction from indistinguishability obfuscation. To date, this is the only construction of FE for randomized functionalities in the public-key setting. This stands in stark contrast to FE for deterministic functions which has been realized from a variety of assumptions.
Our key contribution in this work is a generic transformation that converts any general-purpose, public-key FE scheme for deterministic functionalities into one that supports randomized functionalities. Our transformation uses the underlying FE scheme in a black-box way and can be instantiated using very standard number-theoretic assumptions (for instance, the DDH and RSA assumptions suffice). When applied to existing FE constructions, we obtain several adaptively-secure, public-key functional encryption schemes for randomized functionalities with security against malicious encrypters from many different assumptions such as concrete assumptions on multilinear maps, indistinguishability obfuscation, and in the bounded-collusion setting, the existence of public-key encryption, together with standard number-theoretic assumptions.
Additionally, we introduce a new, stronger definition for malicious security as the existing one falls short of capturing an important class of correlation attacks. In realizing this definition, our compiler combines ideas from disparate domains like related-key security for pseudorandom functions and deterministic encryption in a novel way. We believe that our techniques could be useful in expanding the scope of new variants of functional encryption (e.g., multi-input, hierarchical, and others) to support randomized functionalities.

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Vorheriges Kapitel On Removing Graded Encodings from Functional Encryption
Nächstes Kapitel Random Sampling Revisited: Lattice Enumeration with Discrete Pruning
Fußnoten
1
While there is a generic transformation from selectively-secure FE to adaptively-secure FE [10], it is described in the context of FE for deterministic functions. Though it is quite plausible that the transformation can be applied to FE schemes for randomized functions, a careful analysis is necessary to verify that it preserves security against malicious encrypters. In contrast, our generic transformation allows one to take advantage of the transformation in [10] “out-of-the-box” (i.e., apply it to existing selectively-secure FE schemes for deterministic functions) and directly transform adaptive-secure FE for deterministic functions to adaptively-secure FE for randomized functions.
 
2
Our transformation requires that the underlying FE scheme be perfectly correct. Using the transformations in [26, 51], approximately correct FE schemes can be converted to FE schemes that satisfy our requirement.
 
3
In the deterministic encryption setting of Fuller et al. [54], the hard-core function must additionally be robust. This is necessary because \(\mathsf {hc}(x)\) is not guaranteed to hide the bits of x, which in the case of deterministic encryption, is the message itself (and precisely what needs to be hidden in a normal encryption scheme!). Our randomized FE scheme does not require that the bits of k remain hidden from the adversary. Rather, we only need that \(\mathsf {hc}(k)\) does not reveal any information about h(k) (the share of the PRF key used for derandomization). This property follows immediately from the definition of an ordinary hard-core function.
 
4
In the specification of the experiments, the indices i always range over \([{q_c}]\) and the indices j always range over \([{q_1}]\).
 
5
The underlying FE scheme is for the derandomized class \(\mathcal {G}_\mathcal {F}\), so the only permissible functions \(\mathcal {S}^{(\textsc {fe})}_4\) can issue to \(\mathsf {FE}.\mathsf {KeyIdeal}\) are of the form \(g_{k'}^{f'}\) for some \(k'\) and \(f'\).
 
6
Recall that in the security definition (Definition 3.3), the decryption oracle accepts multiple ciphertexts, and invokes the simulator on each one individually. Thus, the simulator algorithm operates on a single ciphertext at a time.
 
7
We write \(\mathsf {poly}\) to denotes that the quantity does not have to be a-priori bounded, and can be any polynomial in \(\lambda \).
 
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Metadaten
Titel
Functional Encryption: Deterministic to Randomized Functions from Simple Assumptions
verfasst von
Shashank Agrawal
David J. Wu
Copyright-Jahr
2017
Buch
Advances in Cryptology – EUROCRYPT 2017

Print ISBN: 978-3-319-56613-9

Electronic ISBN: 978-3-319-56614-6

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-56614-6_2