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Reversed Dickson polynomials over finite fields. (English) Zbl 1228.11174
Summary: Reversed Dickson polynomials over finite fields are obtained from Dickson polynomials \(D_n(x,a)\) over finite fields by reversing the roles of the indeterminate \(x\) and the parameter \(a\). We study reversed Dickson polynomials with emphasis on their permutational properties over finite fields. We show that reversed Dickson permutation polynomials (RDPPs) are closely related to almost perfect nonlinear (APN) functions. We find several families of nontrivial RDPPs over finite fields; some of them arise from known APN functions and others are new. Among RDPPs on \(\mathbb F_q\) with \(q<200\), with only one exception, all belong to the RDPP families established in this paper.

MSC:
11T06 Polynomials over finite fields
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