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

2020/07/08 by Kangquan Li, Li, Kangquan, Chunlei Li +5 · 1 citation
Computer Science · Engineering · #Coding theory and cryptography #Cryptography and Residue Arithmetic #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2007.03996

Abstract

In this paper, by the Hasse-Weil bound, we determine the necessary and sufficient condition on coefficients a₁,a₂,a₃∈\mathbbF_2ⁿ with n=2m such that f(x) = x^3⋅2m + a₁x^2^m+1+1 + a₂ x^2m+2 + a₃x³ is an APN function over \mathbbF_2ⁿ. Our result resolves the first half of an open problem by Carlet in International Workshop on the Arithmetic of Finite Fields, 83-107, 2014.

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