On a Class of Permutation Trinomials Over Finite Fields

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ON A CLASS OF PERMUTATION TRINOMIALS OVER FINITE.pdf (393.68 KB)

Date

2024

Authors

Temür, Burcu Gülmez
Özkaya, Buket

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Tubitak Scientific & Technological Research Council Turkey

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

In this paper, we study the permutation properties of the class of trinomials of the form f (x) = x4q+1 + λ1xq+4 + λ2x2q+3 ∈ Fq2 [x] , where λ1, λ2 ∈ Fq and they are not simultaneously zero. We find all necessary and sufficient conditions on λ1 and λ2 such that f (x) permutes Fq2 , where q is odd and q = 22k+1, k ∈

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Özkaya, Buket/0000-0003-2658-5441
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Keywords

Permutation polynomials, finite fields, Hasse -Weil bound, cryptography

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Turkish Journal of Mathematics

Volume

48

Issue

4

Start Page

778

End Page

792

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https://doi.org/10.55730/1300-0098.3540
 https://search.trdizin.gov.tr/en/yayin/detay/1252453/on-a-class-of-permutation-trinomials-over-finite-fields

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