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2018 | OriginalPaper | Buchkapitel

Making Public Key Functional Encryption Function Private, Distributively

verfasst von : Xiong Fan, Qiang Tang

Erschienen in: Public-Key Cryptography – PKC 2018

Verlag: Springer International Publishing

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Abstract

We put forth a new notion of distributed public key functional encryption. In such a functional encryption scheme, the secret key for a function f will be split into shares \(\mathsf {sk}_i^f\). Given a ciphertext \(\mathsf {ct} \) that encrypts a message x, a secret key share \(\mathsf {sk}_i^f\), one can evaluate and obtain a shared value \(y_i\). Adding all the shares up can recover the actual value of f(x), while partial shares reveal nothing about the plaintext. More importantly, this new model allows us to establish function privacy which was not possible in the setting of regular public key functional encryption. We formalize such notion and construct such a scheme from any public key functional encryption scheme together with learning with error assumption.

We then consider the problem of hosting services in the untrusted cloud. Boneh, Gupta, Mironov, and Sahai (Eurocrypt 2014) first studied such application and gave a construction based on indistinguishability obfuscation. Their construction had the restriction that the number of corrupted clients has to be bounded and known. They left an open problem how to remove such restriction. We resolve this problem by applying our function private (distributed) public key functional encryption to the setting of hosting service in multiple clouds. Furthermore, our construction provides a much simpler and more flexible paradigm which is of both conceptual and practical interests.

Along the way, we strengthen and simplify the security notions of the underlying primitives, including function secret sharing.

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Vorheriges Kapitel Simple and Generic Constructions of Succinct Functional Encryption

Nächstes Kapitel Full-Hiding (Unbounded) Multi-input Inner Product Functional Encryption from the k-Linear Assumption

Except the nice work of Agrawal et al. [AAB+13] which considered both above cases.

We remark that the construction was first sketched in [DHRW16]. Here we generalize it and provide a formal security proof for the stronger notions.

Looking ahead, we abuse the notation of \(S_2\) in the ideal distribution, by allowing it taking two kinds of inputs: 1. the description of function f, 2. the size of function f.

Looking ahead, we overload the notation of \(S_2\) in the ideal distribution, by allowing it to take two kinds of inputs: 1. the description of a function f; 2. the size of a function f.

We note that the distributed encoded program \(\tilde{P}_i\) does not require obfuscation.

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Titel: Making Public Key Functional Encryption Function Private, Distributively
verfasst von: Xiong Fan
Qiang Tang
Verlag: Springer International Publishing
Buch: Public-Key Cryptography – PKC 2018
Print ISBN: 978-3-319-76580-8

Electronic ISBN: 978-3-319-76581-5

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-76581-5_8

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