Research On Chinese Remainder Theorem-Based Group Signature Schemes

As a kind of special digital signatures, Group signature allows any member of agroup to sign on behalf of the group without disclosing the signer’s information. Thisfeature of group signature makes it attractive in both electronic government affairs andelectronic business. In the fact, Issues such as how to protect the members’ private key,how to control the length of group signatures, and how to make member revocationefficiently become more and more important in research of group signature schemes.In order to solve these problems, recently some scholars put forward a new kind ofChinese Remainder Theorem-based group signature schemes. Using the theorem’smathematical properties, Group members can be increased or revoked without changingother legal members’ key. So the secret information of the group can be protected, andthe calculation can be simplified. However, the existing Chinese RemainderTheorem-based group signature schemes almost have some security shortcomings，which remain to be further discuss.The main results of this paper in research on Chinese Remainder Theorem-basedgroup signature schemes are listed as follows:(1)According to the shortcomings in member revocation of the scheme proposedby Wang et al, a new Chinese Remainder Theorem-based solution scheme is designed.Under the new scheme，the group members’ secret property key renew operators aredifferent from each other, in this way member revocation can be really achieved. Thenew scheme retains the merits of the original one, and it is more secure.(2)Analysis of the Chinese Remainder Theorem-based group signature schemeproposed by Li et al is provided, and some security drawbacks have been found: themember revocation having no effect, the signatures not being unlinkable or unforgeable,etc. Then an improved scheme is designed, which solves the security problems of theoriginal one through restricting some parameters of some processes and making thefinal signature finished by the group center.(3)A multiple Chinese Remainder Theorem-based group signature scheme isdesigned, which achieve that more than one members of a group sign a messagetogether, using a kind of Broadcasting Multi-signature. Member revocation withoutchanging other legal members’ key makes the new scheme secure and efficient. The security of the scheme based on difficulties for solving Discrete Logarithm Problem.Analysis shows that the new scheme resists forgerying attack and jointing attack.