Research On Some Problems Of The Theory Of Security Protocols

The modular design of security protocols is a hot point in the protocol design field. The universally composable security, pointed by Canetti, supplied a viable approach to the modular design of cryptographic protocols. However, several unsolved problems still existed in the theory of universally compsable security. For example, the different ideal functionalities for the same cryptographic task should represent different grades of security, but the relationship between them are not definitioned at all, and most of the cryptographic tasks haven't owned corresponding Ideal Functionalities to support.After deeply analyzing the universally composable security, we defined the level of different ideal functionalities for the same cryptographic task, and pointed out the rationality in defining the levels of ideal functionalities. According to this definition, we compared the levels of the two ideal functionalities of digital signatiure given by Canetti, and proved the different levels of the above ideal functionalities.Later, we mainly discussed the definition of ideal functionality of identity-based schemes. For the identity-based signature, we presented two different ideal functionalities. Then according to our definition we proved that one is not weaker than the other, and proved that the weaker one is equivalent to the security notion of secure against existential forgery on adaptively chosen message and identity attacks. For the identity-based encryption, we proposed an ideal functionality and proved that any identity-based encryption scheme which is secure against adaptive chosen-ciphertext and identity attacks, can securely realize it.