Construction And Security Proof Of Some Fundamental Public Key Cryptographic Schemes

In the framework of provable security, this dissertation mainly studies three kinds of cryptographic primitives, namely certificateless encryption/signatures,double-authentication-preventing signatures and tightly secure signatures. For these cryptographic primitives, this dissertation primarily works on some funda-mental issues, such as improving security models and formal definitions for cryp-tographic schemes, developing and formally modelling basic hard problems under-lying cryptographic schemes and generic constructions for cryptographic schemes.The main contributions of this dissertation are as follows.1. It provides the security proof in the standard model for the generic frame-work (Al-Riyami-Paterson transform) which transforms a certificateless encryp-tion/siganture scheme with KGC trust level 2 into that with KGC trust level 3. In fact, although this generic framework is very simple and efficient, but its security proof has been an open problem before our result.2. It proposes the new cryptographic notion of KGC trust level 3+, and presents a provably secure certificateless signature scheme reaching KGC trust level 3+. For KGC trust level 3+, once if the authority KGC abuses its power to impersonate one common user, not only the undeniable proof for this malicious behavior is unavoidable, but also this behavior automatically results in one crucial punishment on the KGC, such as the exposure of its master private key.3. It studies a new cryptographic primitive called double-authentication-preventing signatures (DAPS). Previous work provides a generic construction, but there is only one concrete instantiation based on IF. It proposes a new crypto-graphic primitive called invertible chameleon hash function with key exposure,improves the security model for DAPS signatures, and develops a provably secure generic framework which can transform an invertible chameleon hash function with key exposure into a double-authentication-preventing signature scheme.4. It researches the construction of tightly secure signature schemes. It pro-poses a new cryptographic primitive called strong chameleon hash function, and then presents the provably secure generic framework which can transform a strong chameleon hash function into a tightly secure signature scheme. There are many concrete tightly secure signature schemes following this framework, which includes Full-Domain-Hash-like (FDH-like) signatures and Fiat-Shamir-like (FS-like) signa-tures. These results roughly indicate that a few FDH-like tightly secure signature scheme can be viewed as the optimal variants of the corresponding FS-like ones.