Efficient and Anonymous Certificateless Multi-Message and Multi-Receiver Signcryption Scheme Based on ECC

As the further extension of the multi-receiver signcryption, the multi-message and multi-receiver signcryption allows a sender to simultaneously signcrypt different messages for different receivers in only one logic operation, which makes it more flexible than the traditional multi-receiver signcryption in which only the same and unique message can be sent to all authorized receivers. The existing multi-message and multi-receiver signcryption schemes are constructed based on either the identity-based cryptography or the public key infrastructure-based cryptography, and thus, they have to suffer from the key escrow problem inherent in the identity-based cryptography or the public key certificate management burden related with the public key infrastructure-based cryptography. Certificateless public key cryptography provides an idea to solve the key escrow problem and eliminate the public key certificate management burden and has been applied to many cryptographic algorithms. In this paper, to avoid the above problems in the existing multi-message and multi-receiver signcryption schemes, the concept of the certificateless public key cryptography was introduced into the designing of the multi-message and multi-receiver signcryption, and a certificateless multi-message and multi-receiver signcryption scheme was proposed. The proposed scheme is free from the key escrow problem and the public key certificate management burden because it is constructed based on the certificateless public key cryptography. Moreover, compared with the existing schemes, it is improved in efficiency because it does not use the bilinear pairing operations but utilizes the limited number of scalar point multiplication on elliptic curve cryptography operations. At the same time, the proposed scheme achieves receiver anonymity.