Certificateless cryptography not only solves the certificate management problem in the traditional public key cryptography, but also overcomes the key escrow problem in identity-based cryptography. On the basis of the certificateless cryptography, domestic and foreign researchers propose many signature schemes with special properties, such as group signature, multi-signatures, ring signature, blind signature and so on. A group signature scheme allows a group member to sign messages anonymously on behalf of the group, which meets the security requirements of anonymity, nonforgery, traceability, etc. On the basis of the certificateless public key cryptography and group signature, by introducing the concept of bilinear pairings and the DH,CDH and DDH difficult problems based on bilinear pairings, combining the advantages of the threshold signature and multi-signatures, this paper proposes a certificateless group signature scheme based on bilinear pairings. This scheme has the advantages of certificateless public key cryptography, meets the security requirements of group signature, and can easily achieve the accession and revocation of group members, which tracking group members is also more simple. Compared with the existing certificateless group signature schemes, this scheme need less bilinear pairings calculation number and the computational efficiency is higher.
