Abstract: The certificateless public key cryptography (CLPKC) has attracted wide attention since it could solve the certificate management problem in the traditional public cryptography and the key escrow problem in the ID-based cryptography．Many certificateless signcryption (CLSC) schemes using pairing have been proposed．The pairing operation is a very complicated operation．So the performance of these schemes is not very good．In this paper,we study the CLSC schemes without pairing ,and find that Selvi et al．Is scheme is not a standard CLSC scheme since the user must verify the public key before using it．This not only inverses the thought of the CLPKS but also increases the user’s computational cost．To solve the problem,three new CLSC schemes without pairing have been proposed．In this paper,we will show the three CLSC schemes provide neither unforgeability property nor confidentiality property．To improve security,we also propose a new CLSC scheme without pairing and demonstrate it is provably secure in the random oracle model.

Key words: CLPKC signcryption scheme,Bilinear pairings,Elliptic curve,Random oracle model