摘要： 分析洪东招等人提出的无证书签名方案(计算机应用，2010年第7期)，指出该方案不能抵抗公钥替换攻击和恶意的私钥产生器(PKG)攻击，同时采用由PKG生成用户公钥并公开的方法对方案进行改进。安全性分析结果表明改进方案可抵抗公钥替换攻击和恶意PKG攻击，并基于q-SDH问题和扩展逆计算Diffie-Hellman问题是困难的假设，在随机预言模型中证明该方案的安全性。

关键词: 无证书签名, 双线性对, q-SDH问题, 公钥替换攻击, 扩展逆计算Diffie-Hellman问题, 恶意私钥产生器攻击

Abstract: This paper shows that Hong’s efficient certificateless signature scheme is insecure against public key replacement attacks and malicious Private Key Generator(PKG) attacks. Aiming at these problems, the scheme is improved by the means that PKG generates the user’s public key and makes it public. The analysis of security shows that the improved scheme is able to resist public key replacement attacks and malicious PKG attacks. Its security relies on the hardness of the q-Strong Diffie- Hellman(q-SDH) problem and Extended-Inverse-Computational Diffie-Hellman(E-Inv-CDH) problem. Under the random oracle model, the improved scheme is proved to be secure against existential forgery on adaptively chosen message attacks.

Key words: certificateless signature, bilinear pairing, q-SDH problem, public key replacement attack, Extended-Inverse- Computational Diffie-Hellman(E-Inv-CDH) problem, malicious Private Key Generator(PKG) attack

中图分类号: 

• TP309.2