基于同态加密体制的通用可传递签名方案

通过分析基于大整数分解、离散对数和双线性对等数学问题的特殊可传递签名方案，抽象出了可传递签名实现方法的共性。以此为基础，提出了一个基于同态加密体制的通用可传递签名方案，该方案利用同态加密体制能支持密文运算的特性实现了可传递签名及验证的一般模型，为基于同态密码体制构造安全可靠的可传递签名方案提供了一种通用框架。其次，通过适当定义安全目标和设计安全性实验，完成了该通用可传递签名方案的可证明安全性，指出若使用的同态加密方案是CPA安全而标准签名是CMA安全的，则所提出的方案就达到CMA安全。最后，给出了该通用可传递签名方案并进行了性能分析与比较。

General transitive signature scheme based on homomorphic encryption

After investigating the existing transitive signature schemes based on the mathematical assumptions of integer factorization problem, discrete logarithm and bilinear pairings, the common method of transitive signature schemes was extracted. Based on this, a general transitive signature scheme based on homomorphic encryption was proposed, which can achieve signature verification by using the properties of homomorphic encryption. The scheme provides a general construction for the transitive signature scheme based on the particular homomorphic signature schemes. Moreover, the security proofs were given by defining the appropriate security goals and designing security experiments. The proofs show the general transitive signature scheme is a CMA secure if and only if corresponding homomorphic encryption is CPA secure and the standard signature is CMA secure. Finally, analysis and comparison show that the proposed scheme is effective.