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

In multi-client functional encryption (MC-FE) for predicate queries, clients generate ciphertexts of attributes $x_1, \ldots, x_n$ binding with a time period $T$ and store them on a cloud server, and the cloud server receives a token corresponding to a predicate $f$ from a trusted center and learns whether $f(x_1, \ldots, x_n) = 1$ or not by running the query 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 strong attribute hiding security with static corruptions. Our MC-HVE scheme is very efficient since a token is composed of four group elements, a ciphertext consists of $O(n)$ group elements, and the query algorithm only requires four pairing operations. Second, we propose an efficient multi-client range query encryption (MC-RQE) scheme and prove the weak attribute hiding security with static corruptions. Since our MC-RQE scheme uses a binary tree, it is efficient since a ciphertext consists of $O(n \log D)$ group elements and a token consists of $O(n \log D)$ group elements where $D$ is the maximum value of the range