Tangent Function and Chebyshev-Like Rational Maps Over Finite Fields

摘要

The main contribution of this brief is the introduction and the characterization of a novel Chebyshev-like rational map over finite fields. The referred map is identified as $t$ -Chebyshev map and depends on the definition of a finite field tangent function, which is also proposed. Among other new and interesting results, we demonstrate that the semigroup property holds for $t$ -Chebyshev maps and give a necessary and sufficient condition under which one of such maps induces a permutation on the set of elements of a field $mathbb {F}_{q}$ . This makes these maps suitable for practical use in both public- and secret-key cryptography.