Research On Several Problems Of Signcryption And Generalized Signcryption

Identity-based cryptosystem, in which an entity's public key is derived directly from certain aspects of its identity, simplifies the key management process in the traditional certificate-based cryptosystems, has been one of the most active area of research and currently is of great interest to the cryptographic society. Users'private keys are generated by a trusted third party called PKG, which introduces the key escrow problem. One of the efficient ways of solving the key escrow problem in IBC is using multiple PKGs, another is using certificateless cryptosystem. With the development of the internet and e-business, there are many requirements that users in a domain would like to securely communicate with users in other domains. CLPKC has undergone quite rapid development because it alleviates the key escrow problem in IBC and simplifies the use of certificate management in conventional PKI. In the open Internet environments, the co-trust between each other and securely work of system is provided by confidentiality, authentication, intergrety and delegation etc, which is related to the combinations of key establishment, encryption, digital signature, identification systems and so on. The security is provided with high communication and computation efficiency.This dissertation investigates the design and analysis of signcryption and generalized signcryption schemes in identity based and certificateless cryptosystem, including identity based signcryption, identity based signcryption in multiple PKGs, identity based generalized signcryption, identity based generalized signcryption in multiple PKGs and certificateless generalized signcryption. The main contributions of this thesis are summarized as follows:1. Research on the security proof of identity based signcryption schemes in the standard model which are based on Waters'S-E algorithms, by which we prove the security of improved Yu-IBSC scheme. This method can be extended to other identity based cryptosystem and certificateless cryptosystem which have the same setup algorithm and extract algorithm as those in Waters IBE.2. Research on the design and analysis of identity based signcryption in multiple PKGs. Firstly we propose two IBSCMP schemes which are based on Waters'S-E algorithms, and then we show their security under DBDH assumption and CDH assumption. Its security is achieved in the standard model, that is, its confidentiality is IND-CCA2 secure and unforgeability is EUF-CMA secure.3. Research on the design and analysis of identity based generalized signcryption in single and multiple PKG environments. For identity based generalized signcryption in single PKG, we give the first IBGSC scheme that is secure in the standard model. For identity based generalized signcryption in multiple PKGs, we present the formal definition and security notion of identity based generalized signcryption in multiple PKG environments for the first time. Then a new identity based generalized signcryption scheme in multiple PKG environments is obtained in this thesis with security proof in the standard model. Our schemes can securely work in encryption, signature and signcryption model. 4. Research on the design and analysis of certificateless generalized signcryption. We propose the notion of certificateless generalized signcryption for the first time. We give the formal definition and two security notions of certificateless generalized signcryption, and then propose two certificateless generalized signcryption schemes with security proof. For the two security notion, in the first one, we consider the Type II attacker is"honest but curious"KGC, while in the second security notion, we consider the Type II attacker is"malicious but passive"KGC. For the two schemes, the first one is secure in the first security notion, with security proof in random oracle model, while the second scheme is secure in the second security notion, with security proof in the standard model. Our two schemes improve the weakness of some existing certificateless signcryption schemes, can work as an encryption, signature and signcryption scheme securely.