高效的无证书有序多重签名方案

针对分布式环境下信任建模中信任链上推荐信息的认证问题，研究了无证书有序多重签名方案的安全模型，进而基于椭圆曲线密码和双线性映射提出一个无证书有序多重签名方案，并在随机预言机模型下，证明方案的安全性建立在计算 Diffie-Hellman 问题的困难性上。该方案无需证书管理中心，多重签名的长度与单用户的签名长度相当，与签名人数无关，在部分签名阶段不需双线性对运算，在部分签名及整体签名的验证阶段都只需一个双线性对运算，与同类方案相比，具有运行效率上的优势，可方便地应用于大规模分布式环境下信任传播的过程中。

Efficient certificateless sequential multi-signature scheme

The authentication of recommendation information transmitted through trust train is important for trust model in distributed environment. To solve this problem, the security model for the certificateless sequential multi-signature scheme was studied and then a certificateless sequential multi-signature scheme using elliptic curve cryptography and bilinear pairings was proposed. It is proven in the random oracle that the security of the scheme is based on the fact that the computational Diffie-Hellman problem is hard. Meanwhile, the scheme needs no certificate management center and the length of signature is independent of the number of signers. It needs no bilinear pairing operation in the phase of partial signing, and just needs one each in verification phases of partial signing and integral signing. So it is computationally efficient compared to the existing signature schemes and can be applied conveniently to trust transitivity in large scale distributed environment.