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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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Dates and versions

hal-01237332 , version 1 (25-01-2018)

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Cite

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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