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 $x_{1}, \ldots, x_{n}$ binding with a time period $T$ and store them on a cloud server, and the cloud server receives a function key corresponding to a predicate $f$ from a trusted center and learns whether $f(x_{1}, \ldots, x_{n}) = 1$ 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 $O(\ell)$ group elements where $\ell $ 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 $O(\log D)$ group elements and a function key consists of $O(n \log D)$ group elements where $D$ is the maximum value of a range.

Keywords

• Functional encryption
• predicate encryption
• multi-client setting
• hidden vector encryption
• bilinear maps