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IACR International Workshop on Public Key Cryptography

PKC 2019: Public-Key Cryptography – PKC 2019 pp 189–219Cite as

Function Private Predicate Encryption for Low Min-Entropy Predicates

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11443))

Abstract

In this work, we propose new constructions for zero inner-product encryption (ZIPE) and non-zero inner-product encryption (NIPE) from prime-order bilinear pairings, which are both attribute and function private in the public-key setting.

  • Our ZIPE scheme is adaptively attribute private under the standard Matrix DDH assumption for unbounded collusions. It is additionally computationally function private under a min-entropy variant of the Matrix DDH assumption for predicates sampled from distributions with super-logarithmic min-entropy. Existing (statistically) function private ZIPE schemes due to Boneh et al. [Crypto’13, Asiacrypt’13] necessarily require predicate distributions with significantly larger min-entropy in the public-key setting.

  • Our NIPE scheme is adaptively attribute private under the standard Matrix DDH assumption, albeit for bounded collusions. In addition, it achieves computational function privacy under a min-entropy variant of the Matrix DDH assumption for predicates sampled from distributions with super-logarithmic min-entropy. To the best of our knowledge, existing NIPE schemes from bilinear pairings were neither attribute private nor function private.

Our constructions are inspired by the linear FE constructions of Agrawal et al. [Crypto’16] and the simulation secure ZIPE of Wee [TCC’17]. In our ZIPE scheme, we show a novel way of embedding two different hard problem instances in a single secret key - one for unbounded collusion-resistance and the other for function privacy. For NIPE, we introduce new techniques for simultaneously achieving attribute and function privacy. We further show that the two constructions naturally generalize to a wider class of predicate encryption schemes such as subspace membership, subspace non-membership and hidden-vector encryption.

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Notes

  1. 1.

    The PE schemes in [12, 13] are not function private, even in the weaker computational setting, if the min-entropy requirements are relaxed any further.

  2. 2.

    The restriction on the size of the message space \(\mathcal {M}\) is necessary for correctness as explained subsequently. Note that this restriction does not prevent \(\mathcal {M}\) from being exponentially large.

  3. 3.

    The argument follows from the fact that both \(\mathbf {y}\) and \(\mathbf {r}\) are uniformly random vectors in \(\mathbb {Z}^m_q\) and \(\mathbb {Z}^k_q\), respectively, and \(|\mathcal {M}|<|\mathbb {G}_T|^{1/2}\).

  4. 4.

    Due to paucity of space, we only provide brief proof sketches in several cases. We refer the reader to the full version of the paper [35] for the detailed proofs.

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Acknowledgments

We thank the anonymous reviewers of PKC 2019 for useful comments. Patranabis and Mukhopadhyay are patially supported by Qualcomm India Innovation Fellowship grant. Mukhopadhyay is partially supported by a DST India Swarnajayanti Fellowship. Ramanna is partially supported by DST India Inspire Faculty award. We stress that the opinions, findings and conclusions expressed in this material are those of the authors and do not necessarily reflect the views of the funding organizations.

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  1. Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, Kharagpur, India

    Sikhar Patranabis, Debdeep Mukhopadhyay & Somindu C. Ramanna

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  1. Sikhar Patranabis
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Correspondence to Sikhar Patranabis .

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    Dongdai Lin

  2. NEC Corporation, Kawasaki, Japan

    Kazue Sako

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Patranabis, S., Mukhopadhyay, D., Ramanna, S.C. (2019). Function Private Predicate Encryption for Low Min-Entropy Predicates. In: Lin, D., Sako, K. (eds) Public-Key Cryptography – PKC 2019. PKC 2019. Lecture Notes in Computer Science(), vol 11443. Springer, Cham. https://doi.org/10.1007/978-3-030-17259-6_7

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