2-Step Multi-Client Quadratic Functional Encryption from Decentralized Function-Hiding Inner-Product

Michel Abdalla, David Pointcheval, and Azam Soleimanian

Abstract

In this paper, we present a multi-client quadratic functional encryption (MCQFE) scheme from function-hiding inner-product (FHIP). The main challenge in such construction is that all the clients require the access to the master secret key of the underlying FHIP scheme, which clearly breaches the security. To overcome this challenge, we present an efficient decentralized version of FHIP scheme of Lin (Crypto 16). This leads to a 2-step MCQFE (2-MCQFE) scheme. In a 2-step MCQFE scheme, the encryption phase is a (non-interactive) protocol among clients and a set of honest-but-curious authorities. More precisely, clients are the owner of messages and the master secret-key of the underlying FHIP is shared among authorities. In the first step, the client publishes a pre-ciphertext pct'' associated with its message. Then in the second step, each authority generates its share ct_i'' extracted from the pre-ciphertext. The public aggregation of these shares ct_i'' will generate the target ciphertext ct'' which then would be applied on the functional key sk_F'' to compute the quadratic functionality. The security model is strong enough to consider no trust among clients and authorities, and also the revelation of some secret keys (of clients or authorities) through corruptions. We instantiate our 2-MCQFE scheme and prove its security in the random-oracle model based on the SXDH assumption. Moreover, we show that its security holds as long as at least one of the authorities is not corrupted.

Available format(s)
Category
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Functional encryptionmulti-clientfunction-hiding.
Contact author(s)
michel abdalla @ ens fr
david pointcheval @ ens fr
azam soleimanian @ ens fr
History
Short URL
https://ia.cr/2021/001

CC BY

BibTeX

@misc{cryptoeprint:2021/001,
author = {Michel Abdalla and David Pointcheval and Azam Soleimanian},
title = {2-Step Multi-Client Quadratic Functional Encryption from Decentralized Function-Hiding Inner-Product},
howpublished = {Cryptology ePrint Archive, Paper 2021/001},
year = {2021},
note = {\url{https://eprint.iacr.org/2021/001}},
url = {https://eprint.iacr.org/2021/001}
}

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