New certificateless public key encryption scheme without pairing

To satisfy the requirement of practical applications, many certificateless encryption schemes (CLE) without pairing have been proposed. Recently, Lai et al. proposed a CLE scheme without pairing and demonstrated that their scheme is provably secure in the random oracle model. The analysis shows that their scheme has better performance than the related schemes. However, Lai et al.´s scheme is not a standard CLE scheme since the user´s public key is used when generating his partial private key. In this study, the authors propose a new CLE scheme. Compared with Lai et al.´s scheme, the authors´ scheme is a standard CLE scheme at the cost of increasing the computational cost slightly. Besides, their scheme has better performance than the related schemes except Lai et al.´s scheme. They also show their scheme is provably secure in the random oracle model.