Certificateless public key cryptography （CL-PKC） avoids the inherent escrow of identity-based cryptography and does not require certificates to guarantee the authenticity of public keys. Based on CL-PKC, we present an efficient constant-round group key exchange protocol, which is provably secure under the intractability of computation Diffie-Hellman problem. Our protocol is a contributory key exchange with perfect forward secrecy and has only two communication rounds. So it is more efficient than other protocols. Moreover, our protocol provides a method to design efficient constant-round group key exchange protocols and most secret sharing schemes could be adopted to construct our protocol.
Ideal function is the fundamental component in the universally composable security model. However, the certification ideal function defined in the universally composable security model realizes the identity authentication by binding identity to messages and the signature, which fails to characterize the special security requirements of anonymous authentication with other kind of certificate. Therefore, inspired by the work of Marten, an anonymous hash certification ideal function and a more universal certificate CA model are proposed in this paper. We define the security requirements and security notions for this model in the framework of universal composable security and prove in the plain model （not in the random-oracle model） that these security notions can be achieved using combinations of a secure digital signature scheme, a symmetrical encryption mechanism, a family of pseudorandom functions, and a family of one-way collision-free hash functions. Considering the limitation of wireless environment and computation ability of wireless devices, this anonymous Hash certification ideal function is realized by using symmetry primitives.
