The complexity of interpolation attacks on block ciphers depends on the degree of the polynomial approximation and/or on the number of terms in the polynomial approximation expression. In some situations, the round function or the S-boxes of the block cipher are expressed explicitly in terms of algebraic function, yet in many other occasions the S-boxes are expressed in terms of their Boolean function representation. In this case, the cryptanalyst has to evaluate the algebraic description of the S-boxes or the round function using the Lagrange interpolation formula. A natural question is what is the effect of the choice of the irreducible polynomial used to construct the finite field on the degree of the resulting polynomial. Another question is whether or not there exists a simple linear transformation on the input or output bits of the S-boxes (or the round function) such that the resulting polynomial has a less degree or smaller number of non-zero coefficients. In this paper we give an answer to these questions. We also present an explicit relation between the Lagrange interpolation formula and the Galois Field Fourier Transform.