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2015 | OriginalPaper | Buchkapitel

Predicate Encryption for Circuits from LWE

verfasst von : Sergey Gorbunov, Vinod Vaikuntanathan, Hoeteck Wee

Erschienen in: Advances in Cryptology -- CRYPTO 2015

Verlag: Springer Berlin Heidelberg

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Abstract

In predicate encryption, a ciphertext is associated with descriptive attribute values x in addition to a plaintext \(\mu \), and a secret key is associated with a predicate f. Decryption returns plaintext \(\mu \) if and only if \(f(x) = 1\). Moreover, security of predicate encryption guarantees that an adversary learns nothing about the attribute x or the plaintext \(\mu \) from a ciphertext, given arbitrary many secret keys that are not authorized to decrypt the ciphertext individually.

We construct a leveled predicate encryption scheme for all circuits, assuming the hardness of the subexponential learning with errors (LWE) problem. That is, for any polynomial function \(d = d(\lambda )\), we construct a predicate encryption scheme for the class of all circuits with depth bounded by \(d(\lambda )\), where \(\lambda \) is the security parameter.

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Vorheriges Kapitel Communication Complexity of Conditional Disclosure of Secrets and Attribute-Based Encryption

Nächstes Kapitel Bilinear Entropy Expansion from the Decisional Linear Assumption

In fact, there is a syntactic mismatch since \(\hat{f}(\cdot )\) is not a predicate, as it outputs an FHE ciphertext.

A reader familiar with [GKP+13] might wonder whether replacing single-use garbled circuits in their construction with reusable garbled circuits (also from [GKP+13].) might remove this limitation. We remark that this does not seem possible, essentially because the construction in [GKP+13] relies crucially on the simplicity of computing garbled inputs from the “garbling key”. In particular, in Yao’s garbled circuit scheme, the garbling key is (many) pairs of “strings” \(L_0\) and \(L_1\), and a garbling of an input bit b is simply \(L_b\). This fits perfectly with the semantics of ABE (rather, a variant termed two-input ABE in [GKP+13]) that releases one of two possible “messages” \(L_0\) or \(L_1\) depending on the outcome of a computation. In contrast, computing a garbled input in the reusable garbling scheme is a more complex and randomized function of the garbling key, and does not seem to align well with the semantics of ABE.

Recall that no circular security assumption needs to be made for leveled bootstrapping.

Sometimes also referred as weak attribute-hiding.

Sometimes also referred as full attribute-hiding.

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Titel: Predicate Encryption for Circuits from LWE
verfasst von: Sergey Gorbunov
Vinod Vaikuntanathan
Hoeteck Wee
Verlag: Springer Berlin Heidelberg
Buch: Advances in Cryptology -- CRYPTO 2015
Print ISBN: 978-3-662-47999-5

Electronic ISBN: 978-3-662-48000-7

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-662-48000-7_25

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