Design And Implementation Of The Threshold Signature Scheme Based On Chinese Remainder Theorem

With the rapid development of computer science and network technology, how toprotect the privacy of important and sensitive information gets more attention recently.Threshold signature is an important research branch of modern cryptography, whichplays a crucial role in protecting the integrity and privacy of data. Threshold signaturecan disperses the responsibility, which improves the security and robustness ofdifferent systems.Currently, research without a trusted center threshold signature schemes aremostly based on the Lagrange interpolation polynomial, meanwhile, schemes withouta trusted center threshold signature based on Chinese Remainder Theorem hasn’t beenproposed yet. The threshold signature without a trusted center is studied in thisthesis,which expands Asmuth-Bloom scheme. A threshold signature scheme without atrusted center is proposed on the basis of the Chinese Remainder Theorem.The main work of this thesis is as follows：(1) The research background, current status and related mathematical tools of thethreshold signature are introduced, some research interests of threshold secret sharingis explored, and several classical threshold secret sharing schemes are analyzed.(2) A threshold signature scheme without a trusted center that based on theChinese remainder theorem is proposed. In this scheme, we take every participant as asecret distributor that generates the group public key collaborative and the groupprivate key implicitly, which avoids the problem of “authority deceive” and “singlepoint failure” in the scheme with a trusted party. In signature process, any t membersout of the n participants produce their own partial signatures, and the t partialsignatures compose to one group signature. No one can get the group private key, sothat the reusability of the group private key is guaranteed.(3) Combined with PKI applications under the NetBeans environment, aprototype multiserver authentication system is designed. The results prove that ourscheme is correct and feasible with a certain practical value.Finally, the summary and outlook are given in this thesis.