Design And Analysis Of Certificateless Signature And Signcryption Schemes

The notion of "Certificateless Cryptography" was proposed by Al-Riyami and Paterson in ASIACRYPT 2003, to solve the inherent key escrow problem in identity-based cryptography. Unlike in the identity-based cryptography where user's private key is generated only by the Key Generating Center (KGC), in certificateless cryptography user's private key is generated by both the KGC and the user himself, in which way certificateless cryptography solves the escrow problem. Certificateless cryptography also overcomes the problem of the certificate management in the traditional certificate-based cryptography, as there's no need to authenticate the user's public key. Certificateless cryptography alleviates the key escrow problem in identity-based cryptography, at the same time, reduces the cost and simplifies the use of the technology when compared with the traditional certificate-based cryptography. This dissertation studies the pairing-free signature scheme, signcryption scheme, and signature scheme with message recovery in the certificateless setting.Firstly, we present a pairing-free certificateless signature scheme. This scheme is more computationally efficient than others built from pairings, as there's no heavily cost pairing operation in this scheme.Secondly, we present a security analysis of two certificateless signcryption schemes, and show that their schemes are insecure with concrete attacks. Then, we proposed a new pairing-free certificateless signcryption scheme, based on the pairing-free certificateless signature scheme.Finally, we propose two certificateless signature schemes with message recovery. The first scheme is restricted to deal with messages of fixed length, and the second one can deal with messages of arbitrary length. Compared with other known certificateless signature schemes with message recovery, our new schemes are more efficient in the communication cost and computation cost.