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2015 | OriginalPaper | Buchkapitel

From Selective to Adaptive Security in Functional Encryption

verfasst von : Prabhanjan Ananth, Zvika Brakerski, Gil Segev, Vinod Vaikuntanathan

Erschienen in: Advances in Cryptology -- CRYPTO 2015

Verlag: Springer Berlin Heidelberg

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Abstract

In a functional encryption (FE) scheme, the owner of the secret key can generate restricted decryption keys that allow users to learn specific functions of the encrypted messages and nothing else. In many known constructions of FE schemes, security is guaranteed only for messages that are fixed ahead of time (i.e., before the adversary even interacts with the system). This so-called selective security is too restrictive for many realistic applications. Achieving adaptive security (also called full security), where security is guaranteed even for messages that are adaptively chosen at any point in time, seems significantly more challenging. The handful of known adaptively-secure schemes are based on specifically tailored techniques that rely on strong assumptions (such as obfuscation or multilinear maps assumptions).

We show that any sufficiently-expressive selectively-secure FE scheme can be transformed into an adaptively-secure one without introducing any additional assumptions. We present a black-box transformation, for both public-key and private-key schemes, making novel use of hybrid encryption, a classical technique that was originally introduced for improving the efficiency of encryption schemes. We adapt the hybrid encryption approach to the setting of functional encryption via a technique for embedding a “hidden execution thread” in the decryption keys of the underlying scheme, which will only be activated within the proof of security of the resulting scheme. As an additional application of this technique, we show how to construct functional encryption schemes for arbitrary circuits starting from ones for shallow circuits (NC1 or even TC0).

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Vorheriges Kapitel Multi-identity and Multi-key Leveled FHE from Learning with Errors

Nächstes Kapitel A Punctured Programming Approach to Adaptively Secure Functional Encryption

Waters [Wat14] also constructed an adaptively-secure scheme, but using specific ad-hoc techniques and in a significantly more complicated manner.

Our notions of security consider a single challenge, and in the public-key setting these are known to be equivalent to their multi-challenge variants via a standard hybrid argument.

Gorbunov et al. [GVW12] constructed a private-key functional encryption scheme that is adaptively secure for a single function query and many message queries based on any private-key encryption scheme (and thus based on any one-way function). Any such scheme can be turned into a function private one using the generic transformation of Brakerski and Segev [BS15], and then one can simply switch the roles of functions and messages [AAB+13, BS15]. This results in a private-key scheme that is adaptively secure for a single message query and many function queries.

That is, a private-key functional encryption scheme that is adaptively-secure for a single message query and many function queries (as discussed above).

Similarly to the class \(\mathsf {WEAK}\) defined in [App14].

[AAB+13]

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Titel: From Selective to Adaptive Security in Functional Encryption
verfasst von: Prabhanjan Ananth
Zvika Brakerski
Gil Segev
Vinod Vaikuntanathan
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_32

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