Research On Some Topics Of Threshold Cryptography With Non-trusted Dealer

With the rapid development of computer science and network communication, the security of distributed environment has become more and more important, which is closely related to every member’s profits in the network. Threshold cryptography can solve this problem very well. Thus, the research on the threshold cryptography’s theory, technology and its application has been a hot area in the field of information security, and ranks in a higher position in modern cryptology. Most of the current cryptosystems rely on a trusted dealer which is responsible for the generation and distribution of the threshold key. While in the network environment which uses threshold cryptography, each member in the group should be regarded not fully trusted. This means a contradiction in some degree.On this account, we investigate threshold cryptography with non-trusted dealer. Our achievements are as follows:1. We propose the formal definition and security model of identity-based threshold signature with non-trusted dealer. Then, we point out that Gao etc’s threshold scheme does not meet robustness and give a modified scheme. The correctness, robustness, and existential unforgeability of the modified scheme is proved.2. We propose a threshold signature scheme with non-trusted dealer in standard model via combining Gennaro’s distributed secret key generation solution and Gu’s basic signature scheme. The correctness and security of this scheme is proved. The comparison with two similar threshold signature schemes shows that our proposed scheme needs less computation, especially the number of times of bilinear pairing computation in the verification of signature share falls to1.3. We investigate the application of threshold cryptography in Ad-Hoc network. We propose a verifiable secret key redistribution scheme with non-trusted dealer which can be used in Ad-Hoc network. The correctness and security of this scheme is proved. The comparison with similar schemes shows that, in our proposed scheme, the number of parameter needed to be refreshed significantly reduces.