A trigonometric approach for Dickson polynomials over fields of characteristic two

In this paper, we first introduce a trigonometric approach for Dickson polynomials of the first and the second kinds over fields of characteristic two. Employing the proposed concepts, we revisit known properties of such polynomials. Additionally, we derive new results regarding the fixed points and the involutive behavior of Dickson polynomials of the second kind over $${\mathbb {F}}_{2^n}$$.