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2016 | OriginalPaper | Buchkapitel

Attribute-Based Encryption for Range Attributes

verfasst von : Nuttapong Attrapadung, Goichiro Hanaoka, Kazuto Ogawa, Go Ohtake, Hajime Watanabe, Shota Yamada

Erschienen in: Security and Cryptography for Networks

Verlag: Springer International Publishing

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Abstract

Attribute-Based Encryption (ABE) is an advanced form of public-key encryption where access control mechanisms based on attributes and policies are possible. In conventional ABE, attributes are specified as strings. However, there are certain applications where it is useful to specify attributes as numerical values and consider a predicate that determines if a certain numerical range would include a certain value. Examples of these types of attributes include time, position coordinate, person’s age, rank, identity, and so on. In this paper, we introduce ABE for boolean formulae over Range Membership (ABE-RM). We show generic methods to convert conventional ABE to ABE-RM. Our generic conversions are efficient as they introduce only logarithmic overheads (in key and ciphertext sizes), as opposed to trivial methods, which would pose linear overheads. By applying our conversion to previous ABE schemes, we obtain new efficient and expressive ABE-RM schemes. Previous works that considered ABE with range attributes are specific and can only deal with either a single relation of range membership (Paterson and Quaglia at SCN 2010, and Kasamatsu et al. at SCN 2012), or limited classes of policies, namely, only AND-gates of range attributes (Shi et al. at IEEE S&P 2007, and some subsequent work). Our schemes are generic and can deal with expressive boolean formulae.

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Vorheriges Kapitel Non-zero Inner Product Encryption with Short Ciphertexts and Private Keys

Nächstes Kapitel Naor-Yung Paradigm with Shared Randomness and Applications

For example, an attribute set may look like: \((\text {`genre'}={{ music}}), (\text {`day'}=[20160501,20160525]), (\text {`hour'}=[0,6])\), while a policy may look like: \(\big ( (\text {`genre'}={{ sport}} \vee \text {`genre'}={{ music}}) \wedge 20160515 \in \text {`day'} \big ) \vee 22 \in \text {`hour'}\).

Although we explain our idea via ABE for Boolean formula here, for generality we will work on ABE for span programs in the main body, which is well-known to imply the former.

It is also called public-index predicate encryption, classified in the definition of Functional Encryption [18].

The latter implies the former via applying any collision-resistant hash \(H:\{0,1\}^* \rightarrow \mathcal {U}\), as done in [15, 22].

We remark that our segment tree method here should not be confused with another completely different tree-based method for the original ABE of Goyal et al. [22], which was used for expressing boolean formulae.

Intuitively, making a copy of \(A_i\) to all the rows with indexes from (i, 1) to \((i,k_i)\) corresponds to implementing the OR literal, namely, \(\bigvee _w H(\text {`day'},w)\) as in our example in Sect. 1.1. This is since any row from (i, 1) to \((i,k_i)\) will contribute the same vector \(A_i\) in the span when we evaluate the span program, as in Eq. (3). In other words, any of attributes in these rows acts the same when evaluating the policy: this exactly represents the OR functionality.

Recall that on the other hand, for simplicity and wlog, we let \(\mathrm {min}_a=1\).

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Titel: Attribute-Based Encryption for Range Attributes
verfasst von: Nuttapong Attrapadung
Goichiro Hanaoka
Kazuto Ogawa
Go Ohtake
Hajime Watanabe
Shota Yamada
Verlag: Springer International Publishing
Buch: Security and Cryptography for Networks
Print ISBN: 978-3-319-44617-2

Electronic ISBN: 978-3-319-44618-9

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-3-319-44618-9_3

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