Recently,Susilo et al.’s perfect concurrent signature scheme(PCS1) and Wang et al.’s improved perfect concurrent signature scheme(iPCS1) are proposed,which are considered as good improvements on concurrent signatures,and they adopt the same algorithms.In this paper,we develop generic perfect concurrent signature algorithms of which Susilo et al.and Wang et al.’s algorithms turn out to be a special instance.We also obtain numerous new,efficient variants from the generic algorithms which have not been proposed before.To display the advantage of these variants,a modified privacy-preserving PCS protocol is given.It shows that the new variants adapt to the protocol well and can form concrete privacy-preserving PCS schemes,while the original algorithms do not.Security proofs and efficiency analysis are also given. Recently, Susilo et al.’s perfect concurrent signature scheme (PCS1) and Wang et al.’s improved perfect concurrent signature scheme (iPCS1) are proposed, which are considered as good improvements on concurrent signatures, and they adopt the same algorithms. In this paper, we develop generic perfect concurrent signature algorithms of which Susilo et al. And Wang et al.’s algorithms turn out to be a special instance. We also obtain numerous new, efficient variants from the generic algorithms which have not been proposed BeforeTo display the advantage of these variants, a modified privacy-preserving PCS protocol is given. It shows that the new variants adapt to the protocol well and can form concrete privacy-preserving PCS schemes, while the original algorithms do not .Security proofs and efficiency analysis are also given.