中文摘要：

已有的无双线性对的无证书签密方案，大都存在着机密性漏洞和签名选择性伪造问题。针对此问题，基于有限乘法交换群上的离散对数难题，提出一种无双线性对的无证书签密方案，并进行了安全分析和证明。指出采用随机预言模型的证明方法可能忽略不解决DL难题时对签密方案的攻击，不能证明破解签密方案的难度与解决DL难题相等价。通过对参数的数学分析，证明了破解本签密方案的必要条件是解决DL难题，不存在不解决DL难题攻击本签密方案的多项式时间算法。与已知所有方案相比，所提方案安全性更高。

英文摘要：

Message confidential vulnerability and signature selective forgery vulnerability exist in most of the existing no pal- ring certificateless signcryption schemes. To solve these vulnerabilities, based on discrete logarithm problem in limited multi- plication Abel group, this paper proposed a certificateless signcryption scheme without bilinear pairing, and analysed the secu- rity of the proposed scheme. This paper pointed out that the proof methods of the random oracle model might ignore the attacks which did not solve the discrete logarithm problem, the model could not prove that the difficulty of cracking the signcryption scheme was equal to solving the discrete logarithm problem. By mathematical analysis of the parameters, the necessary condi- tion of cracking the proposed signcryption scheme is solving the discrete logarithm problem, there is no existed not solving the discrete logarithm problem polynomial time attacking algorithm aimed at the proposed signcryption scheme. Compared to all known schemes, the security of the proposed scheme is higher.