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2017 | OriginalPaper | Chapter

Multi-input Inner-Product Functional Encryption from Pairings

Authors : Michel Abdalla, Romain Gay, Mariana Raykova, Hoeteck Wee

Published in: Advances in Cryptology – EUROCRYPT 2017

Publisher: Springer International Publishing

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Abstract

We present a multi-input functional encryption scheme (MIFE) for the inner product functionality based on the k-Lin assumption in prime-order bilinear groups. Our construction works for any polynomial number of encryption slots and achieves adaptive security against unbounded collusion, while relying on standard polynomial hardness assumptions. Prior to this work, we did not even have a candidate for 3-slot MIFE for inner products in the generic bilinear group model. Our work is also the first MIFE scheme for a non-trivial functionality based on standard cryptographic assumptions, as well as the first to achieve polynomial security loss for a super-constant number of slots under falsifiable assumptions. Prior works required stronger non-standard assumptions such as indistinguishability obfuscation or multi-linear maps.

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In this paper, we refer only to unbounded collusions (i.e. the adversary can request for any number of secret keys). See [12, 20, 21, 24] for results on bounded collusions.

This work is independent of both works.

Here, we use the implicit representation notation for group elements, using [s] to denote \(g^s\) and \([\mathbf {w}]\) to denote \(g^\mathbf {w}\), etc.

We note that in the private key setting of MIFE, we can make \(\mathsf {mpk}\) part of \({\mathsf {msk}}\), but we allow for a separate master public key for better clarity in our proofs. In constructions where we do not need \(\mathsf {mpk}\) we omit it.

That is, \(\mathsf {{\widetilde{Setup}}},\mathsf {{\widetilde{Encrypt}}},\mathsf {{\widetilde{KeyGen}}}\) correspond respectively to the simulated \(\mathsf {Setup},\mathsf {Enc},\mathsf {KeyGen}\).

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Title: Multi-input Inner-Product Functional Encryption from Pairings
Authors: Michel Abdalla
Romain Gay
Mariana Raykova
Hoeteck Wee
Publisher: Springer International Publishing
Book: Advances in Cryptology – EUROCRYPT 2017
Print ISBN: 978-3-319-56619-1

Electronic ISBN: 978-3-319-56620-7

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-319-56620-7_21

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