A complete characterization of the APN property of a class of quadrinomials

07/08/2020

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by   Kangquan Li, et al.

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In this paper, by the Hasse-Weil bound, we determine the necessary and sufficient condition on coefficients a_1,a_2,a_3∈𝔽_2^n with n=2m such that f(x) = x^3·2^m + a_1x^2^m+1+1 + a_2 x^2^m+2 + a_3x^3 is an APN function over 𝔽_2^n. Our result resolves the first half of an open problem by Carlet in International Workshop on the Arithmetic of Finite Fields, 83-107, 2014.