### Full-Hiding (Unbounded) Multi-Input Inner Product Functional Encryption from the $k$-Linear Assumption

Pratish Datta, Tatsuaki Okamoto, and Junichi Tomida

##### Abstract

This paper presents two non-generic and practically efficient private key multi-input functional encryption (MIFE) schemes for the multi-input version of the inner product functionality that are the first to achieve simultaneous message and function privacy, namely, the full-hiding security for a non-trivial multi-input functionality under well-studied cryptographic assumptions. Our MIFE schemes are built in bilinear groups of prime order, and their security is based on the standard $k$-Linear ($k$-LIN) assumption (along with the existence of semantically secure symmetric key encryption and pseudorandom functions). Our constructions support polynomial number of encryption slots (inputs) without incurring any super-polynomial loss in the security reduction. While the number of encryption slots in our first scheme is apriori bounded, our second scheme can withstand an arbitrary number of encryption slots. Prior to our work, there was no known MIFE scheme for a non-trivial functionality, even without function privacy, that can support an unbounded number of encryption slots without relying on any heavy-duty building block or little-understood cryptographic assumption.

Note: The current version fixes some issues with the references in the earlier version.

Available format(s)
Category
Public-key cryptography
Publication info
A major revision of an IACR publication in PKC 2018
Keywords
multi-input functional encryptioninner productsfull-hiding securityunbounded aritybilinear maps
Contact author(s)
datta pratish @ lab ntt co jp
okamoto tatsuaki @ lab ntt co jp
tomida junichi @ lab ntt co jp
History
2018-02-13: last of 2 revisions
See all versions
Short URL
https://ia.cr/2018/061

CC BY

BibTeX

@misc{cryptoeprint:2018/061,
author = {Pratish Datta and Tatsuaki Okamoto and Junichi Tomida},
title = {Full-Hiding (Unbounded) Multi-Input Inner Product Functional Encryption from the $k$-Linear Assumption},
howpublished = {Cryptology ePrint Archive, Paper 2018/061},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/061}},
url = {https://eprint.iacr.org/2018/061}
}

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