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The conspiracy attack on (t,n) threshold signature is still an open problem. For solving the problem, this paper proposes a new signature scheme, which is based on the idea of opening the sets of ID authentication information. Using two sets of secret key algorithm, the scheme attaches a secret random ID authentication information to the shareholder's secret key and provide a verify equation for the ID authentication information. Then, the new scheme opens the sets of the enciphered ID authentication information and makes that an important parameter to against conspiracy attack. The security discussion shows that more than t collusive members cooperate can neither forge the threshold signature nor impersonate other members to forge partial signatures, and the forged threshold signature which implies traceability of adversarial members can be discovered by the signature verifier in time.