Research On Aggregate Signature And Aggregate Signcryption

In this dissertation, we firstly make a description about aggretage signature, aggregate signcryption and its security. Then, we reviewed the related mathematical knowledge. At last, we mainly research on ID-based aggregate signature, certificateless aggregante signature and certicateless aggregate signcryption. The main contributions are as follows:1. We show that an ID-based aggregate signature scheme can't resist the forgery attack, because an attacker can generate a valid signature for any message if he has ever obtained a signature. Then, an improved scheme to overcome their weakness is proposed, and it is provably secure in random oracle model.2. Aggregate signature allows n different users to sign n different messages; the major challenge of designing this signature is how to achieve both security and efficiency. Certificateless cryptosystem can solve the key escrow of ID-based cryptosystem and the public key authentication of certification-based cryptosystem. A formal model of certificateless aggregate signature is proposed. Then propose a concrete certificateless aggregate signature, which the length of the signature is independent of the signers. Based on the hardness of computational Diffie-Hellman problem, the proposed scheme is secure against existential forgery under adaptive chosen identities and messages in random oracle model.3. A formal model of certificateless aggregate signcryption is proposed, which allows n different users to signcrypt n different messages. Then we propose a concrete certificateless aggregate signcryption scheme. Based on the Bilinear Diffie-Hellman Problem and Computational Diffie-Hellam Problem, the proposed scheme captures existential unforgeability against chosen message attacks (EUF-CMA) and indistinguishability of encryptions under adaptively chosen ciphertext attacks (IND-CCA2) in the random oracle model.