Tangent Function and Chebyshev-Like Rational Maps Over Finite Fields
Juliano Bandeira Lima, Ricardo M. Campello de Souza · IEEE Transactions on Circuits & Systems II Express Briefs · 2019
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 Fq. This makes these maps suitable for practical use in both public- and secret-key cryptography.