A new construction for involutions over finite fields

Abstract

In 2020, Niu et al. [Cryptogr. Commun., 2020, 12(2): 165−185] studied the fixed points of involutions over the finite field with q-elements. This paper further discusses the relationship between the fixed points set and the non-fixed points set of two involutions f_1\left(x \right) and f_2\left(x \right) over the finite field {\mathbb{F}}_q, and then obtains a necessary and sufficient condition for that the composite function f_1\circ f_2\left(x \right) is also an involution over {\mathbb{F}}_q. In particular, a special class of involutions over some finite fields is determined completely.

Keywords

Permutation polynomial / involution / fixed point / non-fixed point

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Higher Education Press 2022