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.

翻译：最近,利马和德索萨坎佩罗引入了针对奇序有限字段的新型理性功能,并解释了其在加密中的潜在作用。 我们表明这些新功能与Redei理性功能的经典体系相提并论,因此新功能的属性源自Redei功能的属性。 我们还证明了这些功能的新属性,并引入了特征2中的类似功能,同时还引入了新版本的对偶序有限字段的三角测量,这是独立感兴趣的。