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Erschienen in:
Nonlinear Invariant Attack Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Dual System Encryption Framework in Prime-Order Groups via Computational Pair Encodings

verfasst von : Nuttapong Attrapadung

Erschienen in: Advances in Cryptology – ASIACRYPT 2016

Verlag: Springer Berlin Heidelberg

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Abstract

We propose a new generic framework for achieving fully secure attribute based encryption (ABE) in prime-order bilinear groups. Previous generic frameworks by Wee (TCC’14) and Attrapadung (Eurocrypt’14) were given in composite-order bilinear groups. Both provide abstractions of dual-system encryption techniques introduced by Waters (Crypto’09). Our framework can be considered as a prime-order version of Attrapadung’s framework and works in a similar manner: it relies on a main component called pair encodings, and it generically compiles any secure pair encoding scheme for a predicate in consideration to a fully secure ABE scheme for that predicate. One feature of our new compiler is that although the resulting ABE schemes will be newly defined in prime-order groups, we require essentially the same security notions of pair encodings as before. Beside the security of pair encodings, our framework assumes only the Matrix Diffie-Hellman assumption (Escala et al., Crypto’13), which includes the Decisional Linear assumption as a special case.
Recently and independently, prime-order frameworks are proposed also by Chen et al. (Eurocrypt’15), and Agrawal and Chase (TCC’16-A). The main difference is that their frameworks can deal only with information-theoretic encodings, while ours can also deal with computational ones, which admit wider applications. We demonstrate our applications by obtaining the first fully secure prime-order realizations of ABE for regular languages, ABE for monotone span programs with short-ciphertext, short-key, or completely unbounded property, and ABE for branching programs with short-ciphertext, short-key, or unbounded property.

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Vorheriges Kapitel Verifiable Functional Encryption
Nächstes Kapitel Efficient IBE with Tight Reduction to Standard Assumption in the Multi-challenge Setting
Fußnoten
1
Traditionally, ABE refers to only ABE for Boolean formulae predicate [21]. In this paper, however, we use the term ABE for arbitrary predicate R. Indeed, it corresponds to the “public-index predicate encryption" class of functional encryption, as per [12].
 
2
Or more precisely, ABE for monotone span programs, which implies ABE for Boolean formulae [21]. We will use both terms interchangeably.
 
3
Note that we consider only Boolean branching programs here as in [19], in contrast with [14, 25], where arithmetic branching programs are also considered.
 
4
A preliminary version of our full version [4] has been made available before that of [2].
 
5
Nevertheless, since we use the same notion of pair encoding as in the composite-order framework of [3], it can be said that our framework together with [3] provide a unified framework albeit with two generic constructions.
 
6
For a polynomial u, we say that \(u \in {\varvec{v}}=(v_1,\ldots ,v_q)\), if \(u = v_i\) for some \(i\in [q]\).
 
7
The only difference is that now it is defined in prime-order groups, instead of prime-order subgroups of composite-order groups.
 
8
Looking ahead, it corresponds to the hybrid game between type 1 and 2 keys (cf. Eqs. (), ()).
 
9
Details can be found in the proof for the hybrid between the games \(\mathsf {G}_{i,1}\) and \(\mathsf {G}_{i,2}\), deferred to [4].
 
10
For formality and ease of viewing, we depict these game definitions in Fig. 1 in [4].
 
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Metadaten
Titel
Dual System Encryption Framework in Prime-Order Groups via Computational Pair Encodings
verfasst von
Nuttapong Attrapadung
Copyright-Jahr
2016
Verlag
Springer Berlin Heidelberg
Buch
Advances in Cryptology – ASIACRYPT 2016

Print ISBN: 978-3-662-53889-0

Electronic ISBN: 978-3-662-53890-6

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-662-53890-6_20

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