New ElGamal type threshold digital signature scheme

In a (k, n) threshold digital signature scheme, k out of n signers must cooperate to issue a signature. In this paper, we show an efficient (k, n) threshold ElGamal type digital signature scheme with no trusted center. We first present a variant of ElGamal type digital signature scheme which requires only a linear combination of two shared secrets when applied to the (k, n)-threshold scenario. More precisely, it is a variant of Digital Signature Standard (DSS) which was recommended by the U.S. National Institute of Standard and Technology (NISIT). We consider that it is meaningful to develop an efficient (k, n)-threshold digital signature scheme for DSS. The proposed (k, n)-threshold digital signature scheme is proved to be as secure as the proposed variant of DSS against chosen message attack.