基于格的群签名方案

Group Signature Scheme Based on Lattice

提出了对亚洲密码学会2010给出的一个基于格的群签名方案的攻击,表明了已有的群签名不能防止陷害攻击,不诚实的群管理员可以得到所有群成员的签名秘钥进而伪造出所有群成员的合法签名.该方案也不能灵活有效地增删群成员,每新增一个群成员,系统需要更新系统公钥和所有群成员的签名密钥,计算量大,效率低,同时该方案也未给出有效删除群成员的方法,不适用于实际中的动态群.基于格上最近向量问题的困难性,利用统计零知识证明,同时引入时间参数,给出了一种改进方案,新方案可以有效抵御陷害攻击,能够实现动态增加或删除群成员,且效率更高,实用性更强.

An attack is mounted on a group signature scheme based on lattice posted in Asia Crypt 2010. It shows the group signature scheme is vulnerable to trap attacks and a dishonest group manager can get all group members＇ signing keys and then forge all group members＇ valid signatures. Meanwhile, the scheme can＇t increase or delete group members flexibly and efficiently which is not applicable to dynamic groups. Every time a new member joins, the system has to update the public key and all group members＇ signing keys which are of huge calculation and low efficiency. Also, the scheme doesn＇t provide an effective method to revoke group members. Using statistical zero-knowledge proofs and time parameters, an improved scheme based on the hardness of the closest vector problem is proposed. The improved scheme is anti-trap attacks and can dynamic increase or deletes group members more efficiently and applicably.