Research On Verifiable Secret Sharing Based On Chinese Remainder Theorem

Secret sharing is an important branch of contemporary cryptography, has become an important method to protecting information security. The research on secret sharing has become a hot spot of information security. Secret sharing provides a new train of thought for key management, using secret sharing to saving and managing secret information can not only prevent excessive concentration of power being abused, but also ensure the robustness and security of data.Verifiable secret sharing permits participants to verify the authenticity of their secret shares, resolves the problem caused by dealer's cheating and deceive between participants satisfactorily. Verifiable secret sharing has important theoretical significance and application value in the field of Key management, Identity authentication, and E-Business. Presently, research on verifiable secret sharing is carried out from Lagrange Interpolation Polynomial; schemes based on Chinese Remainder Theorem are relatively scarce. Research on the anti-spoof problems of secret sharing based on Chinese Remainder Theorem is carried out in this dissertation, the main context is as follows:(1) Firstly, the backgrounds, status and related Mathematical tools of secret sharing are presented in the dissertation, several current research contents and achievements of threshold secret sharing are discussed. Then comprehensively studied the verifiable secret sharing base on Chinese Remainder Theorem.(2) In succession, Aiming at the existing problems of verifiable secret schemes based on Chinese Remainder Theorem, a new verifiable secret sharing scheme is proposed. Then the validity and security of the scheme are analyzed. In the process of computing shares, some additional data are generated as the verify information which are opened to all participants in the form of discrete logarithm. Participants can verify the correctness of shares by using public verifying information. Consequently, the scheme can not only detect fraud among the participants but also prevent dealer's cheating behavior.(3) A prototype system is implemented by using the big number lib Miracl under the compile environment VC++ 6.0. The experimental results show that the scheme is correct and feasible.