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 Psi_i and Psi´_i were imported so as to share k _i and x_ik_i more 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