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2019 | OriginalPaper | Buchkapitel

Compact Adaptively Secure ABE for \(\mathsf {NC^1}\) from k-Lin

verfasst von : Lucas Kowalczyk, Hoeteck Wee

Erschienen in: Advances in Cryptology – EUROCRYPT 2019

Verlag: Springer International Publishing

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Abstract

We present compact attribute-based encryption (ABE) schemes for \(\mathsf {NC^1}\) that are adaptively secure under the k-Lin assumption with polynomial security loss. Our KP-ABE scheme achieves ciphertext size that is linear in the attribute length and independent of the policy size even in the many-use setting, and we achieve an analogous efficiency guarantee for CP-ABE. This resolves the central open problem posed by Lewko and Waters (CRYPTO 2011). Previous adaptively secure constructions either impose an attribute “one-use restriction” (or the ciphertext size grows with the policy size), or require q-type assumptions.

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Nächstes Kapitel Unbounded Dynamic Predicate Compositions in Attribute-Based Encryption

Note that there exist constructions of ABE for more general access policies like monotone span programs/Boolean formulas with threshold gates [17], and even polynomial-sized Boolean circuits [14, 16], but all such constructions sacrifice at least one of the properties (1)–(3).

Essentially, the dual system proof method provides guidance for transforming suitably-designed functional encryption schemes which are secure for one adversarial secret key request to the multi-key setting where multiple keys may be requested by the adversary. Our main technical contribution involves the analysis of the initial single-key-secure component, which we refer to later as our “Core 1-ABE” component.

Most directly by pushing all NOT gates to the input nodes of each circuit and using new attributes to represent the negation of each original attribute. It is likely that the efficiency hit introduced by this transformation can be removed through more advanced techniques à la [24, 29], but we leave this for future work.

Some works associate ciphertexts with a set \(S \subseteq [n]\) where [n] is referred to as the attribute universe, in which case \(\mathbf {x}\in \{0,1\}^n\) corresponds to the characteristic vector of S.

E.g.: \(k=1\) corresponds to security under the Symmetric External Diffie-Hellman Assumption (SXDH), and \(k=2\) corresponds to security under the Decisional Linear Assumption (DLIN).

Informally, \(\{\mathsf {H}^u\}\) describes the simulated games used in the security reduction, where the reduction guesses \(R'\) bits of information described by u about some choices z made by the adversary; these \(R'\) bits of information are described by \(h_\ell (z)\) in the \(\ell \)’th hybrid. In the \(\ell \)’th hybrid, the reduction guesses a \(u \in \{0,1\}^{R'}\) and simulates the game according to \(\mathsf {H}^u\) and hopes that the adversary will pick an z such that \(h_\ell (z) = u\); note that the adversary is not required to pick such an z. One way to think of \(\mathsf {H}^u\) is that the reduction is committed to u, but the adversary can do whatever it wants.

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Titel: Compact Adaptively Secure ABE for from k-Lin
verfasst von: Lucas Kowalczyk
Hoeteck Wee
Verlag: Springer International Publishing
Buch: Advances in Cryptology – EUROCRYPT 2019
Print ISBN: 978-3-030-17652-5

Electronic ISBN: 978-3-030-17653-2

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-17653-2_1

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