Abstract: In order to increase the calculation speed of the n sharing's generation and the m partners to recover the secret in Shamir(m,n) threshold scheme, the discrete Fourier transform (DFT) over finite field is adopted other than the classical Lagrange interpolation. Because the DFT over finite field has some similar properties of the DFT over complex, such as the cycling convolution and the FFT algorithm, this method can improve the efficient of Shamir(m,n) threshold scheme. If m >n/2, it can increase the calculation speed of the trust center to divide the key to n sharing components. Moreover, if m=n and it is the power of 2, this scheme can increase the calculation speed of the partners to recover the secret key.