Group-oriented undeniable signature schemes with a trusted center

At Auscrypt '92, Harn and Yang firstly proposed the concept of group-oriented undeniable signature. Two threshold undeniable signature schemes were devised in their article, where t can be either 1 or n. However, Langford in 1996 showed that the Harn-Yang (n, n) threshold undeniable signature scheme is not secure enough. In 1996, Lin et al. also proposed a new (t, n) threshold undeniable signature scheme without a trusted center. Unfortunately, the Langford attack can be applied to Lin et al.'s scheme as well. Thus, the problem of designing a general group-oriented (t, n) threshold undeniable signature scheme is remained open. The purpose of this article is to propose a (t, n) threshold undeniable signature scheme, where 1≤t≤n. Moreover, the signing policy will be extended to the generalized case, where any authorized subset can sign messages.