### Function Private Predicate Encryption for Low Min-Entropy Predicates

Sikhar Patranabis, Debdeep Mukhopadhyay, and Somindu C. Ramanna

##### Abstract

In this work, we propose new predicate encryption schemes for zero inner-product encryption (ZIPE) and non-zero inner-product encryption (NIPE) predicates 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 superlogarithmic 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. It is also computationally function private 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. With respect to NIPE, we introduce new techniques for simultaneously achieving attribute and function privacy. We also show natural generalizations of our ZIPE and NIPE constructions to a wider class of subspace membership, subspace non-membership and hidden-vector encryption predicates.

Available format(s)
Category
Public-key cryptography
Publication info
A minor revision of an IACR publication in PKC 2019
Contact author(s)
sikharpatranabis @ gmail com
History
Short URL
https://ia.cr/2018/1250

CC BY

BibTeX

@misc{cryptoeprint:2018/1250,
author = {Sikhar Patranabis and Debdeep Mukhopadhyay and Somindu C.  Ramanna},
title = {Function Private Predicate Encryption for Low Min-Entropy Predicates},
howpublished = {Cryptology ePrint Archive, Paper 2018/1250},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/1250}},
url = {https://eprint.iacr.org/2018/1250}
}

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