中文摘要：

有序多重签名是多个用户按一定顺序对同一消息文件进行的签名和认证。许艳等提出一个在随机预言机模型下可证明安全的无证书有序多重签名方案,该方案生成的多重签名有固定长度,且验证签名的双线性对运算是固定的。指出许艳等的方案在签名验证算法的双线性对计算部分存在不足,并纠正了该缺陷,但纠正后的方案实施效率大大降低。接着提出一个高效的无证书有序多重签名方案,生成的多重签名仅为1个群元素,签名的验证仅需2个双线性对。

英文摘要：

A sequential multi-signature enabled multiple users to jointly sign a document in order. Xu, et al proposed a provably-secure certificateless sequential multi-signature scheme with constant signature length and pairing computations. However, it was shown that the scheme had a drawback in the verifying algorithm, and then it overcame the drawback. But, the efficiency of the corrected scheme was greatly reduced. An efficient certificateless sequential multi-signature scheme is constructed, and the multi-signature generated by proposed scheme consists of one group element and the verification algorithm requires only 2 bilinear pairings.