The cloud can be used to outsource data storage or data computation. Data computation outsourcing enables to move computationally expensive operations outside a mobile device. Many pairing-based cryptographic schemes are designed to enable documents' encryption while fulfilling some defined security requirements. In practice, client applications should be implemented for mobile devices. Their computational capabilities are significantly lower than standard computers. Thus, advanced cryptographic calculations, like bilinear pairing calculation, might take too much time for a good user experience. In this paper, we analyse the possibilities to securely outsource bilinear pairings computation from a mobile device to possibly dishonest servers. Several test scenarios were implemented. Also, we have modified one of the pairing-based schemes that allows to encrypt and decrypt documents and we have created its secure outsourced version. Next, we have tested execution times of encryption and decryption algorithms of the original scheme and its outsourced version. The tests were conducted using different outsourcing models. The execution times showing time spent on the mobile device and the server are presented and discussed. The tests have shown that in certain conditions outsourcing bilinear pairing calculation can speed up overall computation time. Also, it simplifies implementation on different mobile operating systems.