Abstract: In 2002, Micali and Rivest firstly introduced the concept of transitive signature, constructed first undirected transfer signature scheme, and left construction of directed transitive signature scheme as open problems to be solved. In order to solve above problem, this paper presents the concept of direction state function which is used for pointing out the direction relationship between the nodes of the graph that makes transitive signature scheme for complex directed graph. Combined with the node certification paradigm, the paper proposes a directed transitive signature scheme based on discrete logarithm problem by using the secret of the node values. The proposed scheme is proved secure under adaptive chosen message attack in the random oracle model.

Key words: undirected transitive signature, directed transitive signature, random oracle model, discrete logarithm difficulty problem

摘要： 2002年，Micali和Rivest首次提出了传递签名的概念，构造了第一个无向传递签名方案，并把构造有向传递签名方案作为公开问题。为了解决上述问题，提出了一个方向状态函数的概念，用于表示有向图节点之间的方向关系，使传递签名的明文空间扩展到任意的复杂有向图。结合节点签名范例，利用节点秘密值，构造了一个基于离散对数困难问题的有向传递签名方案，并在随机预言模型下证明了该方案在自适应选择消息攻击下是安全的。

关键词: 无向传递签名, 有向传递签名, 随机预言模型, 离散对数困难问题