Almost Perfect Nonlinear Power Functions on GF(2 n ): A New Case for n Divisible by 5

Hans Dobbertin ()
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Hans Dobbertin: University of Klagenfurt, Department of Mathematics

A chapter in Finite Fields and Applications, 2001, pp 113-121 from Springer

Abstract: Abstract We prove that for d = 24s + 23s + 22s + 2 s − 1 the power function x d is almost perfect nonlinear (APN) on L = GF(25s ), i.e. for each a ∈ L the equation (x + 1) d + x d = a has either no or precisely two solutions in L. The proof of this result is based on a new “multi-variate” technique which was recently introduced by the author in order to confirm the conjectured APN property of Welch and Niho power functions.

Keywords: Cyclic Code; Minimal Polynomial; Bend Function; Hyperplane Section; Weight Enumerator (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-56755-1_11

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DOI: 10.1007/978-3-642-56755-1_11

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