A t out of n threshold scheme is such that shares are distributed to n participants so that any set of t participants can compute the secret, whereas any set of less than t participants gain no information about the secret. In [4], Desmedt and Frankel introduced a threshold scheme that can be used with any finite Abelian group. Hence it can be used to provide threshold RSA. In this scheme, the size of the share is on the order n times the size of the secret. Further, due to a complicated algebraic setting, and the large shares, this schemes requires a “large” amount of computations. Recent work have addressed how to reduce the resource requirements. Within this paper we provide improved methods and demonstrate the computational requirements of the Desmedt- Frankel scheme using our method is, in many cases, better than other existing threshold RSA signature schemes.