Tangent Function and Chebyshev-Like Rational Maps Over Finite Fields
| Autor: | Juliano B. Lima, Ricardo M. Campello de Souza |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Approximation theory
Pure mathematics Semigroup 020206 networking & telecommunications Field (mathematics) 0102 computer and information sciences 02 engineering and technology Characterization (mathematics) 01 natural sciences Chebyshev filter Finite element method Permutation Finite field 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Electrical and Electronic Engineering Mathematics |
| Zdroj: | IEEE Transactions on Circuits and Systems II: Express Briefs. 67:775-779 |
| ISSN: | 1558-3791 1549-7747 |
| DOI: | 10.1109/tcsii.2019.2923879 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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