Research On Certificateless Digital Signatures

In Aisacrypt 2003, Al-Riyami and Paterson introduced the Certificateless Public Key Cryptography. Certificateless public key cryptosystem overcomes the problem of the certificate management in the certificate-based public key cryptosystem, for the reason that there is no need of certificate to authenticating the user's public key. In addition, the user's private key does not singly generate by the KGC(Key Generation Center) in the certificateless public key cryptosystem, but jointly generate by the user and the KGC which make the private key is only known to the user himself. Thus, it overcomes the inherent key escrow problem in the identity-based public key cryptosystem. In all the available certificateless signature schemes, there are so many bilinear pairing computations that the efficiency are low. Moreover, there are few certificateless signature schemes with additional properties by now.In this thesis, we construct a provably secure certificateless signature scheme with only one bilinear pairing computation, which achieves the highest efficiency among all the available provably secure certificateless signature schemes. Then, basing on the above certificateless signature scheme, we present a certificateless message recovery signature scheme and a certificateless partial message recovery signature scheme. In addition, we discuss the security flaws in a convertible limited verifier signature scheme. Furthermore, we give the definition of the certificateless convertible limited verifier signature and also a concrete certificateless convertible limited verifier signature scheme basing on our provably secure signature scheme.