Paper 2018/1021

Multi-Client Functional Encryption with Repetition for Inner Product

Jérémy Chotard, Edouard Dufour-Sans, Romain Gay, Duong Hieu Phan, and David Pointcheval

Abstract

Recently, Chotard et al. proposed a variant of functional encryption for Inner Product, where several parties can independently encrypt inputs, for a specific time-period or label, such that functional decryption keys exactly reveal the aggregations for the specific functions they are associated with. This was introduced as Multi-Client Functional Encryption (MCFE). In addition, they formalized a Decentralized version (DMCFE), where all the clients must agree and contribute to generate the functional decryption keys: there is no need of central authority anymore, and the key generation process is non-interactive between the clients. Eventually, they designed concrete constructions, for both the centralized and decentralized settings, for the inner-product function family. Unfortunately, there were a few limitations for practical use, in the security model: (1) the clients were assumed not to encrypt two messages under the same label. Then, nothing was known about the security when this restriction was not satisfied; (2) more dramatically, the adversary was assumed to ask for the ciphertexts coming from all the clients or none, for a given label. In case of partial ciphertexts, nothing was known about the security either. In this paper, our contributions are three-fold: we describe two conversions that enhance any MCFE or DMCFE for Inner Product secure in their security model to (1) handle repetitions under the same label and (2) deal with partial ciphertexts. In addition, these conversions can be applied sequentially in any order. The latter conversion exploits a new tool, which we call Secret Sharing Layer (SSL). Eventually, we propose a new efficient technique to generate the functional decryption keys in a decentralized way, in the case of Inner Product, solely relying on plain DDH, as opposed to prior work of Chotard et al. which relies on pairings. As a consequence, from the weak MCFE for Inner Product proposed by Chotard et al., one can obtain an efficient Decentralized MCFE for Inner Product that handles repetitions and partial ciphertexts. Keywords. Functional Encryption, Inner Product, Multi-Client, Decentralized.