Identity-based Linearly Homomorphic Signature And Its Applications

The rapid development of the Internet has made network infiltrated into various aspects of our life. Network not only provides us easy access of information, but also gives us efficient ways for communication, business, test and control. On the other hand, data security of network becomes increasingly severe. The data transmitted via network is subject to purposed falsification or forgery by malicious users. So how to guarantee the data security in the open network becomes a significant research issue. Digital signature can be used to provide data authenticity, integrity, and nonrepudiation, Various digital signatures with special properties have brought into existence due to the requirements of different application scenarios. Among them,the linearly homomorphic signature is one of the representatives that is attracting extensive attentions of the research community. It can be used to provide effective solution for data authenticity, integrity, and nonrepudiation in network coding and so on. This thesis mainly studies Identity-based linearly homomorphic signature and its applications.At first, we introduce the technique of linearly homomorphic signature into Identity-based cryptography to derive to the formal definition and security models of Identity-based linearly homomorphic signature schemes. Meanwhile the security notion of existential unforgeability under adaptive chosen subspace and adaptive chosen identity attack of Identity-based linearly homomorphic signature schemes is presented.Then two Identity-based linearly homomorphic signature schemes IB-LHS1 and IB-LHS2 with different characteristics are proposed. In the construction of the first scheme IB-LHS1,the tag for a data set(which is a subspace) is randomly chosen,a signature on a vector is generated by making use of the ideas from the linearly homomorphic signature scheme of Boneh et al. Its security is proved based on the co-CDH assumption in the random oracle.Whereas in the second scheme IB-LHS2, the tag for a data set is produced by using the Identity-based signature scheme of Hess, a signature on a vector is obtained from the technique used in the construction of BLS short signature scheme. The existential unforgeability of the scheme is based the hardness of the CDH problem in bilinear groups,and is also proved in the random oracle. The performance of the two schemes are analyzed and compared in detail.Finally, the practical applications of the two proposed Identity-based linearly homomorphic signature schemes are investigated. The scheme IB-LHSi is applied in network coding to effectively detect the polluted or injected fake message from malicious intermediate nodes so that the propagation of the polluted message to pollute some other nodes can be prevented as soon as possible. Furthermore the computation and communication cost of intermediate nodes can be reduced. The application of the scheme IB-LHS2 in wireless sensor networks is demonstrated. The use of Identity-based linearly homomorphic signature in wireless sensor networks can efficiently protect the integrity and authenticity of data in the process of transmission as well as cut down the cost of the sensor nodes for signing and communication.The properties of linearly homomorphic signatures make it applicable for supplying effective solutions for data integrity, authenticity and nonrepudiation in the area of network coding, sensor networks, and verifiable computation, etc. Thus the study of Identity-based linearly homomorphic signatures has both theoretic and practical significance in facilitating the development and applications of the technology of linearly homomorphic signatures.