in distributed system it is sometimes necessary for users to share the power to use a cryptosystem. The system secret is divided up into shares and securely stored by the entities forming the distributed cryptosystem. We propose a new Multi signature scheme without a trusted third party (TTP), based on a round optimal, publicly verifiable distributed key generation (DKG) protocol. In this propose system, we define a new propose ElGamal algorithm, in that ElGamal algorithm has two random numbers. The origina l ElGamal algorithm is that, it has only one random number. In order to improve its security, the proposed scheme adds one more random number. The security of the proposed signature scheme is the same with the ElGamal sig nature scheme which is based on the difficult computable nature of discrete logarithm over finite fields. In this paper, the algorithm is proposed to enhance the security and usage of more random number to make algorithm more complicate d, which can also make the link between the random number and the key more complicated. The scheme presented in this paper after analysis showed that the security level is kept high by using two random numbers and the time complex ity is reduced
