Abstract: The partially blind signature scheme without trusted Private Key Generator (PKG) proposed by Feng Tao et al. was analyzed, and it was found that this scheme did not satisfy unforgeability. A dishonest PKG could forge a valid partially blind signature. By using gap Diffie-Hellman group and bilinear pairings, a new partially blind signature scheme without trusted PKG was proposed. The analysis shows that the proposed scheme can overcome the defect of the original scheme and it possesses unforgeability, correctness, partially and tracility. Compared with the original scheme, the proposed scheme performs more efficiently in computation because it reduces two pairing operations.

Key words: partially blind signature, Private Key Generator (PKG), gap Diffie-Hellman group, bilinear pairings, unforgeability, tracility

摘要： 通过对冯涛等人提出的无可信私钥生成中心(PKG)部分盲签名方案进行分析，发现该方案不具有不可伪造性。不诚实的PKG可以伪造一个有效的部分盲签名。利用gap Diffie-Hellman群和双线性对，提出一个新的无可信PKG的部分盲签名方案。分析表明提出的方案能够克服原方案的缺陷，具有不可伪造性、正确性、部分盲性和可追踪性。与原方案相比，提出方案更高效，它减少了两个对运算。

关键词: 部分盲签名, 私钥生成中心, gap Diffie-Hellman群, 双线性对, 不可伪造性, 可追踪性