Research On Group Signature Based On The Chinese Remainder Theorem

The concept of group signature was first proposed by Chaum and Heyst in 1991.It allows group members to sign messages on behalf of the group without revealing the signer's identity information,that is to say,the group signature can provide anonymity.When there is a dispute,the group administrator can open the signature to confirm the identity of the signer.Because of the above traceability of conditional anonymity,group signatures have broad application prospects in political,military,economic and other fields.Such as in the application of electronic elections,electronic voting,electronic cash system and other practical issues.Thus it has attracted the attention of many researchers.In practical applications,group members are always dynamic,that is to say,someone should be able to join or revoke the group safely and efficiently.In order to solve the problem of dynamic updating of members in group signatures,the group signature scheme based on the Chinese Remainder Theorem was proposed in recent years.Using the good mathematical characteristics of the Chinese Remainder Theorem,the key information of group members is integrated and hidden,so that the group signature scheme based on the Chinese Remainder Theorem can quickly join and revoke group members without changing other valid group members' keys.Considering the practical application requirements of group signature,designing a group signature scheme based on Chinese Remainder Theorem,which can satisfy various security characteristics,is the focus of current and future for a long time.In addition,as an important security risk in the field of information security,key leakage has not been taken into account in many group signature schemes based on the Chinese Remainder Theorem.In this paper,the group signature scheme based on the Chinese Remainder Theorem is studied and analyzed,and the main results are as follows:(1)After analyzing the security of group signature scheme based on Chinese Remainder Theorem proposed by Chen Zewen and others,it is found that there are security vulnerabilities of common mode attack in the scheme,which results in that the scheme does not satisfy the security characteristics of anti-counterfeiting attack and anti-joint attack.Therefore,on the basis of retaining the advantages of the Chinese Remainder Theorem and combining with Schnorr algorithm,this paper designs an improved group signature scheme.The new scheme not only solves the above security threats,but also makes the new scheme meet the characteristics of anti-replay attack due to the introduction of the concept of timestamp.(2)In order to solve the problem of key leakage,with reference to ElGamal algorithm,this paper proposes a forward secure group signature scheme based on the Chinese Remainder Theorem.Forward security means that even if an attacker obtains the key of a certain period,he can not threaten the key before that period.At the same time,the security of the scheme is analyzed.The results show that the scheme has the characteristics of forgery,anonymity,revocation,traceability and forward security.