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中文摘要：
无证书有序多重签名可用于解决信任链推荐信息的认证问题。秦艳琳等提出一个高效的无证书有序多重签名方案,并在随机语言机模型下证明方案的安全性可归约为CDH（computational Diffie-Hellman）困难问题。对该方案的安全性证明过程进行分析,指出方案难以抵抗伪造攻击：攻击者已知某个多重签名,则可以伪造其他消息的多重签名。随后构造一个更加高效的无证书有序多重签名方案,方案使用更少的双线性对,且只有一个签名消息,占用更小的计算代价和通信代价。最后证明方案在随机预言机模型下具有不可伪造性。
英文摘要：
Certificate less sequential multi-signature scheme could resolve the problem of authentication of recommendation information transmitted through trust train. Qin yan-lin, et al proposed an efficient certificateless sequential multi-signature scheme, and proved the security is based on the fact that computational Diffie-Hellman problem is hard in the random oracle. It is found that Qin＇s scheme is insecure against the forgery attack after analysing the security proof. If an adversary has obtained the signers＇ multi-signature, it can forgery the multi-signature for any other message. Then, a more efficient certificateless sequential multi-signature scheme is construced which has lower computation cost and communication cost for using less bilinear pairings and only generating one signature message. Finally, the security proof shows that the proposed scheme can resist the forgery attack under the model of random oracle.
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