Dickson Polynomials that are Involutions.

Abstract : Dickson polynomials which are permutations are interesting combinatorial objects and well studied. In this paper, we describe Dickson polynomials of the first kind in $\F_2[x]$ that are involutions over finite fields of characteristic $2$. Such description is obtained using modular arithmetic's tools. We give results related to the cardinality and the number of fixed points (in the context of cryptographic application) of this corpus. We also present infinite classes of Dickson involutions. We study Dickson involutions which have a minimal set of fixed points.
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Canteaut, Anne; Effinger, Gove; Huczynska, Sophie; Panario, Daniel; Storme, Leo. Contemporary Developments in Finite Fields and Their Applications., World Scientific Press, pp.22-45, 2016, 9789814719278. 〈10.1142/9789814719261_0003 〉
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https://hal.inria.fr/hal-01237332
Contributeur : Pascale Charpin <>
Soumis le : jeudi 3 décembre 2015 - 10:52:28
Dernière modification le : jeudi 11 janvier 2018 - 06:12:26

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Pascale Charpin, Sihem Mesnager, Sumanta Sarkar. Dickson Polynomials that are Involutions.. Canteaut, Anne; Effinger, Gove; Huczynska, Sophie; Panario, Daniel; Storme, Leo. Contemporary Developments in Finite Fields and Their Applications., World Scientific Press, pp.22-45, 2016, 9789814719278. 〈10.1142/9789814719261_0003 〉. 〈hal-01237332〉

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