Über die minimale Fixpunktanzahl von Dickson-Permutationen auf Galoisfeldern. (On the minimum number of fixed points of Dickson permutations over Galois fields) (Q1073839)

As is is well known, the so-called Dickson permutations induce permutations on Galois fields GF(q) forming subgroups of GF(q). These Dickson permutations have applications in cryptography: They can be used for enciphering messages. In such applications it is important to restrict to Dickson permutations which have only a small number of fixed points. In this paper the minimum number of fixed points of Dickson permutations over a given Galois field GF(q) is determined. Further, formulas are derived for the number of Dickson permutations of GF(q) having only the minimum number of fixed points. Finally, algorithms allowing to choose such Dickson permutations are described.