In the above case, we could calculate a polynomial p(x) from I(x). When we use an extension_factor of 8, we will calculate another 32(8-1)* points on p(x). Since two different polynomials with D degree will share at most D points, an example polynomial pair with a valid polynomial (which satisfies the above constraints) and a fake polynomial with D degree (which does not satisfy the above constraints) will share at most D points.