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

2017 | OriginalPaper | Buchkapitel

Generic Transformations of Predicate Encodings: Constructions and Applications

verfasst von : Miguel Ambrona, Gilles Barthe, Benedikt Schmidt

Erschienen in: Advances in Cryptology – CRYPTO 2017

Verlag: Springer International Publishing

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Abstract

Predicate encodings (Wee, TCC 2014; Chen, Gay, Wee, EUROCRYPT 2015), are symmetric primitives that can be used for building predicate encryption schemes. We give an algebraic characterization of the notion of privacy from predicate encodings, and explore several of its consequences. Specifically, we propose more efficient predicate encodings for boolean formulae and arithmetic span programs, and generic optimizations of predicate encodings. We define new constructions to build boolean combination of predicate encodings. We formalize the relationship between predicate encodings and pair encodings (Attrapadung, EUROCRYPT 2014), another primitive that can be transformed generically into predicate encryption schemes, and compare our constructions for boolean combinations of pair encodings with existing similar constructions from pair encodings. Finally, we demonstrate that our results carry to tag-based encodings (Kim, Susilo, Guo, and Au, SCN 2016).

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Vorheriges Kapitel Stronger Security for Reusable Garbled Circuits, General Definitions and Attacks
Nächstes Kapitel Practical Functional Encryption for Quadratic Functions with Applications to Predicate Encryption
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Fußnoten
1
This transformation has side conditions, thus it is not universal, but all existing tag-based encodings (except one) satisfy these side conditions.
 
3
Decryption in the framework of predicate encodings needs 4 pairings under SXDH assumption or 6 under DLIN, in the framework of tag-based encodings decryption requires 8 pairings and the assumption is DLIN.
 
4
Note that if matrices \(\mathsf{A}_x\), \(\mathsf{B}_y\) or \(\mathsf{C}\) are invertible, they always satisfy their respective requirements.
 
5
Where every attribute appears at most once and the number of and-gates is lower than k (one could overcome the one-use restriction by considering duplicated attributes).
 
6
Being half when the bound on the number of and-gates is maximal.
 
7
In [21] there is a modification of their algorithm that produces matrices (Y, Z) such that the predicate associated is \(f(\varvec{x}) \ne 0\) (the double negation will cancel out).
 
8
Conjunction also preserves x-oblivious reconstruction, while disjunction does not.
 
9
This equivalence holds when \(|S| < p\), but in practice p is a large prime.
 
10
Note that \(\alpha \mathop {\leftarrow }\limits ^{\$}\mathbb {Z}_p\), \(r_1 \mathop {\leftarrow }\limits ^{\$}\mathbb {Z}_p^*\) and therefore, \(\alpha /r_1\) distributes uniformly over \(\mathbb {Z}_p\), so we can apply the \(\alpha \)-privacy property from the predicate encoding.
 
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Metadaten
Titel
Generic Transformations of Predicate Encodings: Constructions and Applications
verfasst von
Miguel Ambrona
Gilles Barthe
Benedikt Schmidt
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_2