## 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

PRINCE
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### References:

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