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Characterizations and constructions of triple-cycle permutations of the form \(x^rh(x^s)\). (English) Zbl 1465.11231

Summary: Let \(\mathbb{F}_q\) be the finite field with \(q\) elements and let \(f\) be a permutation polynomial over \(\mathbb{F}_q\). Let \(S_q\) denote the symmetric group on \(\mathbb{F}_q\). In this paper, we mainly investigate some characterizations on the elements \(f\in S_q\) of order 3, i.e., \(f\circ f\circ f=I\), where \(f\) is also called a triple-cycle permutation in the literature. Some explicit triple-cycle permutations are constructed.

MSC:

11T06 Polynomials over finite fields
94A60 Cryptography

Software:

PRINCE
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References:

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