A Threshold Signature Scheme Withstanding the Conspiracy Attack

[[abstract]]A threshold signature, first proposed by Desmedt and Frankel, allows or more members of the group cooperate to generate a signature on behalf of the group while providing the anonymity of the signers. Unfortunately, all threshold signature schemes proposed so far can not withstand the conspiracy attack, thus the group secret key can be revealed. In this paper, we propose a new threshold signature scheme to avoid the conspiracy attack. The security of the proposed threshold signature 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