一种格上的群签名

A Group Signature Scheme Based on Lattice

通过对2010年亚洲密码会上格基群签名方案进行安全性分析,发现已有的格基群签名方案不能抵抗陷害攻击.由于群管理员拥有所有群成员的签名密钥,因而能够伪造出所有群成员的合法签名.并且在群成员加入时,系统必须更新所有群成员的公私钥及追踪密钥,计算量大且效率低.并且该方案没有给出撤销群成员的方法,不能适应实际应用需求.本文基于格上最近向量的困难性,利用GPV签名,构造出一种能够抵抗陷害攻击并且能够有效进行群成员加入和撤销的格上群签名方案,并在随机预言机模型下证明了方案的安全性.分析了方案的性能,在相同安全条件下,新方案效率更高,实用性更强.

Through the security analysis of a group signature scheme from lattice assumptions posted in Asia Crypto 2010,it shows that the existing scheme is vulnerable to trap attacks. The signing keys are generated by the group manger in the original scheme,thus the group manger can forge all group members＇ valid signatures. Besides, the group manger needs to update the public keys and all the group members＇ signing keys when group members join in, which is of high calculation and low efficiency. Meanwhile, the scheme dosen＇t provide a method to revoke group member, which is not applicable. Using GPV signature, an improved scheme based on the hardness of the closest vector problem is proposed, which is anti-trap attacks and proven to be secure in random model and can icrease and revoke group members dynamically more efficiently and applicably.