Tangent-Chebyshev rational maps and Redei functions
This work clarifies and extends cryptographic tools for finite field applications, but is incremental as it builds on existing Redei function theory.
The paper demonstrates that a recently introduced class of rational functions over odd-order finite fields is conjugate to classical Redei functions, deriving their properties from this connection, and extends this to characteristic 2 with new finite field trigonometry.
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.