A Novel ElGamal Type Threshold Signature Scheme without a Trusted Party

In ElGamal type signature scheme, a multiplication and a division as well as a linear combination should be computed, so it is difficult to design an efficient ElGamal type threshold signature scheme without a trusted party, and in the existing schemes at least 2t+1 members are required to produce a valid threshold signature while only t-security is accepted (that is to say t malicious members can conspire to recover group's secret key). In this paper, a more efficient ElGamal type threshold signature scheme was proposed, in which two extra polynomials Psiiand Psi'iwere imported so as to share kiand xikimore efficiently and to reduce the order of group secret polynomial. Analysis proves, this scheme is t-security while only t+1 members are needed in its signing procedure