两个群签名方案的安全性分析

Security Analysis of Two Group Signature Schemes

群签名在电子现金、电子选举等领域有着广泛应用,因此基于不同的数学问题设计安全高效的群签名方案有着重要意义。对最近提出的一个基于中国剩余定理的群签名方案和一个基于RSA签名的群签名方案进行研究,发现这两个方案存在安全漏洞:第一个方案中,任何一个群成员均可以分解系统模数,从而可以计算出系统中所有人的私钥;第二个方案的群签名打开算法不正确,从而无法追踪到群签名的生成者。分析表明,这两个方案均是不安全的,需要进一步完善。

Group signature schemes have many applications, such as electronic cash and electronic vote. Thus, it is significant to devise efficient and secure group signature schemes based on all kinds of mathematic problems. In this paper, a group signature scheme based on Chinese remainder theorem and a group signature scheme based on RSA signature scheme are studied. Two security flaws in these schemes are found：in the former,the modulus of the system can be decomposed by every member of the group,so the private keys of everyone in the group can be computed; in the latter, the opening algorithm of the group signature scheme is incorrect, so the signer of the group signature can not be traced correctly. The analysis shows that the two schemes are not secure and need to be implemented.