  Recently Lima and Campello de Souza introduced a new class of rational
functions over odd-order finite fields, and explained their potential
usefulness in cryptography. We show that these new functions are conjugate to
the classical family of Redei rational functions, so that the properties of the
new functions follow from properties of Redei functions. We also prove new
properties of these functions, and introduce analogous functions in
characteristic 2, while also introducing a new version of trigonometry over
finite fields of even order, which is of independent interest.
