Efficient Multi-Client Functional Encryption for Conjunctive Equality and Range Queries

Abstract

In multi-client functional encryption (MC-FE) for predicate queries, clients generate ciphertexts of plaintexts <i>x</i>₁,...,<i>x_n</i> binding with a time period <i>T</i> and store them on a cloud server, and the cloud server receives a function key corresponding to a predicate <i>f</i> from a trusted center and learns whether <i>f</i> (<i>x</i>₁,...,<i>x_n</i>) = 1 or not by running the decryption algorithm on the multiple ciphertexts of the same time period. MC-FE for predicates can be used for a network event or medical data monitoring system based on time series data gathered by multiple clients. In this paper, we propose efficient MC-FE schemes that support conjunctive equality or range queries on encrypted data in the multi-client settings. First, we propose an efficient multi-client hidden vector encryption (MC-HVE) scheme in bilinear groups and prove the selective security with static corruptions. Our MC-HVE scheme is very efficient since a function key is composed of four group elements, a ciphertext consists of <i>O</i>(&#x2113;) group elements where &#x2113; is the size of a plaintext, and the decryption algorithm only requires four pairing operations. Second, we propose an efficient multi-client range query encryption (MC-RQE) scheme and prove the selective weak security with static corruptions. Our MC-RQE scheme which uses a binary tree is efficient since a ciphertext consists of <i>O</i>(log<i>D</i>) group elements and a function key consists of <i>O</i>(<i>n</i>log<i>D</i>) group elements where <i>D</i> is the maximum value of a range.