Public key encryption with equality test (PKEET) is useful in cloud computing to determine whether two ciphertexts encrypted using different public keys contain the same content part in order to filter or query the encrypted content. However, this is open to an attack by non-authorised clouds performing tests on candidate content parts to reveal it answers the query. To prevent this, PKEET with flexible authorisation (PKEET-FA) has been proposed. However, when PKEET-FA is deployed on low-resource devices in a more sustainable cloud context, such as Internet of Things (IoT) networks, its higher computational cost incurs a higher energy cost due to its complex Bilinear Pairings operations (BP) which are more time-consuming and energy-consuming than point multiplication operations. In this paper, we present a new energy-efficient PKEET-FA scheme called EPKEET-FA. Unlike PKEET-FA and other similar schemes, EPKEET-FA does not use BP operations but instead uses point multiplication operations on elliptic curves. Hence, it is better suited for sustainable cloud computing use. EPKEET-FA also supports flexible authorisation with a superior energy efficiency that other PKEET-related schemes cannot achieve. A series of experiments are conducted to validate the implementation of EPKEET-FA against similar schemes as baselines. The results show that the energy efficiency of EPKEET-FA is significantly better on the conventional client computer and the low-resource IoT device, as typical end devices of cloud computing.