Researcli On The Fully Distributed Threshold Short Signature Schemes

With the booming development of the information technology and the web applica-tions, digital signature plays a more and more important role in real life. Ordinary digital signature has been unable to meet the demand for some new applications. Meanwhile, how to resolve the single point failure problem in the network system and enhance the anti-attack ability of system, the security problem in the distributed surroundings has become more and more concerned by public. Threshold signature is an important research branch of modern cryptography, which plays a crucial role in protecting the integrity, privacy and non-repudiation of the data. Threshold sig-nature can disperse the responsibility, which can improve the security and robustness of the systems.In recent years, threshold signature has been researching by the domestic and foreign scholars, and it has become a research hotspot in cryptography. However, as far as we know, the research on the threshold signature scheme is not ideal enough under the different cryptosystems. At first, the research on the common threshold signature has more. But the study of the threshold short signature is less. For the common threshold signature, its length is too long, which may affect the efficiency of transmission and storage of the signature, especially in bandwidth constrained environment. Secondly, the vast majority of the previous threshold schemes were not fully distributed. Among from them, it existed an individual party who alone mastered the important secret information. These information once was leaked, which would bring a very bad impact to the system. Therefore, research on the threshold short signature scheme not only has the important theory significance, but also has the widespread practical values.Based on a detailed summarization and analysis of related literatures, we focus on the fully distributed threshold short signature aiming at the above drawbacks in this thesis. The main achievements of this thesis are given as follows:1. According to the concepts of the identity-based and certificateless thresh-old signature, learning from the security model of signature or threshold (short) signature schemes under the different cryptosystem. Adequately considering the ca-pabilities and targets of the different types of the adversary, analyzing the security model of the existing threshold signature schemes, we establish the security model of our schemes.2. Based on the simple and efficient identity-based signature (Based on C-L-W’s scheme [1]), using the verifiable secret sharing and distributed key generation technology, we construct a fully distributed identity-based threshold short signature (FD-IBTHSS) scheme. Similarly, we construct a fully distributed certificateless threshold short signature (FD-CLTHSS) scheme by the similar techniques (Based on Chen et.al’s scheme [2]). The features of the scheme (Take the cetificateless cryptosystem) as follows:Firstly, many KGCs jointly generate the master secret key using the verifiable secret sharing and distributed technology.Secondly, all the signers jointly generate the random number which was used in the phase of the the secret value generation and the signature generation using distributed key generation technology. This ensures that our distributed secret value generation and signature algorithm is robustness and confidentiality, and the security of our schemes is also greatly improved.Thirdly, any secret information of the system is mastered by the several partic-ipants, and there is no separate party who can alone master or recover the secret information.3. We prove the security of our schemes according to the security model. The se-curity proof of the identity-based threshold signature and the certificateless threshold signature can be attributed to the simulatability of the threshold signature (assum-ing the corresponding basic signature scheme is secure). According to the concept of the simulatability in the existing literature, and referring to the proof of the sim-ulatability of the threshold DSS signature scheme, we can finish the proof for the schemes.4. Programming for signature algorithm is studied. We implement the signature algorithm using C language and PBC (Pairing-Bilinear cryptography) library in Linux system. We firstly give the computational cost of the basic operation in the cryptography, and analyse the computational cost and communication cost in theory. We can constantly optimize the signature algorithm by comparison and analyses, and reduce the computational cost and communication cost of the schemes.