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The Rijndael [2] S-box is based on the mapping x→ x− 1, where x− 1 denotes the multiplicative inverse in the field. There exist several efficient methods to calculate multiplicative inverses in a finite field GF (2m). In [1], an algorithm is presented, that is based on Euclid’s algorithm. It has an area complexity of O (m) and requires 2m time steps. Another possibility is to do calculations in GF (16). This method is discussed in the next section.