A New (t, n)-Threshold Scheme Based on Difference Equations

In the paper, we propose three threshold secret sharing schemes that are based on difference equations. The first scheme is a (t, n)− threshold scheme which is an ideal perfect secure. The other two schemes add the restricted order structure to the set of shadows and the access structure of secret sharing policy. The basis of the access structure of one scheme allows that only subsets that contain consecutive shadows can compute the broken secret, but no other subset of shadows can do so. The basis of the access structure of the other scheme allows that shadow subsets contain an imperfect consecutive shadow subset that has one gap of size 1, and can compute the original secret.