The Formal Study Of Secure Threshold Cryptographic Schemes

With the rapid development of computer network and information technology, how tosolve the single-point failure in network system and the security problem in distributed sur-roundings has become more and more concerned. The threshold cryptography is one of themost efficient and potential techniques. Meanwhile, the distributed system is far more com-plex than the centralized one, which brings great difficulty and challenge to researchers. Inrecently years, many specialists both at home and abroad have made deep research on thresh-old cryptography. However, as far as we know, the research on threshold cryptography'sformal security is not ideal enough. While, the most important principle in evaluating a cryp-tosystem is whether it can be proved to be secure formally. Therefore, from the viewpointof theory and applications, to research the threshold cryptosystem with formal method is ofgreat importance and plays an important role in network security and academic value.Thereby, our point in this thesis is to study and design threshold cryptography schemessystematically via formalization means,to complete the study on threshold system in publickey setting. Our main achievements are as follows:1. From the point of view of reducing the cost of pubic key management in cryptosys-tem, the study on identity based threshold cryptosystem is significant. However, theresearch on identity based threshold cryptography is insufficient. Thus we design aseries of identity based threshold decryption schemes, including two provable secureidentity based threshold decryption schemes, and a scheme focusing on the dynamicproblem of threshold cryptosystem. Our scheme is provably secure in the full model.Especially, we take the ?exibility of distributed system into consideration. We im-proved the related works and accomplished the modeling and formal study of identitybased distributed cryptosystem.2. Certificateless cryptography is one of the most important topics in modern cryptog-raphy. However, as far as we know, the certificateless threshold cryptography is notyet been studied specifically. Moreover, the bandwidth and the cost of communication need to be minimized in distributed surrounding. Thus, we define the formal model ofcertificateless threshold cryptosystem, and construct a certificateless threshold cryp-tosystem and an efficient certificateless key encapsulation mechanism. We provideprovable security proof in the random oracle model for each of them. We formalizethe study on certificateless cryptosystem in the distributed system for the first time,which lays foundation of the future work.3. Key escrow problem acts as the bottleneck in the application of identity based cryp-tosystem. However, to balance the user's privacy and the government's monitoringpower, we need to use the concept of the threshold key escrow. Since the relative studyis established at present, we proposed a generic construction to solve the key escrowproblem in identity based cryptosystem. Then we gave the formal definition of thresh-old key escrow and proposed a fully secure scheme. At last, we designed a dynamicthreshold key escrow system based on conic curve. The general construction solvesthe bottleneck in identity based cryptosystem from some point of view. We abstractedthe security model for threshold key escrow system, and lays foundation for analysingthe threshold key escrow cryptosystem with formalized methods.