## Cryptology ePrint Archive: Report 2018/061

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

Pratish Datta and 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.

Category / Keywords: public-key cryptography / multi-input functional encryption, inner products, full-hiding security, unbounded arity, bilinear maps

Original Publication (with major differences): IACR-PKC-2018

Date: received 15 Jan 2018, last revised 12 Feb 2018

Contact author: datta pratish at lab ntt co jp, okamoto tatsuaki@lab ntt co jp, tomida junichi@lab ntt co jp

Available format(s): PDF | BibTeX Citation

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

Short URL: ia.cr/2018/061

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