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 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.