中文摘要：

为了提高基于证书签名方案的效率和保证其不可伪造性,利用k双线Diffie-Hellman求逆问题的困难性和计算Diffie-Hellman问题的困难性构造了一个新的高效基于证书签名方案,并且在随机预言机模型下,形式化证明了其安全性.方案中,利用k双线Diffie-Hellman求逆问题的困难性来设计用户公钥和用户证书生成算法,保证用户公钥和用户证书的单向性质;利用k双线Diffie-Hell-man求逆问题的困难性和计算Diffie-Hellman问题的困难性来设计签名算法,保证签名的单向性质和不可伪造性.所构造方案的签名生成算法不需要任何双线性对计算,签名验证算法仅需要一个双线性对计算.与已有的基于证书签名方案进行了效率比较.结果表明：所提出的基于证书签名方案具有较大的效率优势.

英文摘要：

In order to improve the efficiency and guarantee the unforgery of certificate-based signature scheme,a new efficient certificate-based signature scheme was proposed based on the k-bilinear Diffie-Hellman Inverse（k-BDHI） problem and the Computational Diffie-Hellman（CDH） problem.The security of the proposed scheme was proved by random oracle model（ROM）.According to the difficulty of k-BDHI problem and the CDH problem,user public key and certificate generating algorithms were designed to guarantee the one-way of public key and certificate.User signature generating algorithm was also designed by the difficulty of k-BDHI problem and the CDH problem to ensure signature one-way and unforgery.In the proposed scheme,no bilinear pairing computation was needed in the signature generate algorithm,and only one was need in verification algorithm.The efficiency of the proposed scheme was compared with those of the available certificate-based signature schemes.The results show that the proposed scheme is more efficient than the available certificate-based signature schemes.