A (t, n) Threshold Signature Scheme Against Conspiracy Attack

A (t, n) threshold signature allows t or more members of the group cooperate to generate a signature on behalf of the group while providing the anonymity of the signers. Unfortunately, most of (t, n) threshold signature schemes proposed so far can not against the conspiracy attack, thus the group secret key can be revealed. The design of an efficient scheme is remained open. In this paper, we propose a new (t, n) threshold signature scheme. The feature of the proposed scheme is that part of members cannot conspire to get any system secret parameters, and cannot forge a valid signature. That is, it can against conspiracy attacks. The security of the proposed scheme is based on the difficulty of computing the discrete logarithm modulo for a composite number. The size of the group signature and the verification time of the group signature are equivalent to that of an individual signature