Secret sharing schemes are multi-party protocols related to key establishment. They also facilitate distributed trust or shared control for critical activities (e.g., signing corporate cheques and opening bank vaults), by gating the critical action on cooperation from t(t ∈Z+) of n(n ∈Z+) users. A (t, n) threshold scheme (t < n) is a method by which a trusted party computes secret shares Γi(1 i n) from an initial secret Γ0 and securely distributes Γi to user. Any t or more users who pool their shares may easily recover Γ0, but any group knowing only t-1 or fewer shares may not. By the ElGamal public key cryptophytes and the Schnorr’s signature scheme, this paper proposes a new (t,n) threshold signature scheme with (k,m) (k,m ∈Z+) threshold verification based on the multivariate linear polynomial. Secret sharing schemes are multi-party protocols related to key establishment. They also facilitate distributed trust or shared control for critical activities (eg, signing corporate checks and opening bank vaults), by gating the critical action on cooperation from t (t ∈ Z +) A (t, n) threshold scheme (t