Model for undirected transitive signatures

The author modifies Bellare and Nevenʹs definition of undirected transitive signatures by explicitly introducing node signing and edge signing algorithms. In the proposed model, a signing algorithm defined over a transitive graph consists of a separate vertex signing algorithm and an edge signing algorithm. These two algorithms are allowed to share the state information of the transitive graph. The new model allows easier discussion about its security and extensions. The new model has been successfully applied to further study of directed graph authentication problems posed by Hohenberger and by Molnar. A concrete undirected transitive signature scheme is presented which can be proved to be secure in the standard complexity paradigm in this model.