Methods and systems for implementing a switch box (S-box) in a cryptographic application are described. An input to the S-box is converted from a Galois field representation GF(N.sup.2) to a Galois subfield representation GF(N).sup.2. The input is converted using a generating polynomial of the form x.sup.2+Ax+B, where A and B are elements in GF(N) and where A has a value other than unity. The multiplicative inverse of the Galois subfield representation GF(N).sup.2 is determined. The multiplicative inverse is converted back to the Galois field representation GF(N.sup.2). An affine transformation of the multiplicative inverse is then performed.