On -1-differential uniformity of ternary APN power functions

01/26/2021

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by   Haode Yan, et al.

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Very recently, a new concept called multiplicative differential and the corresponding c-differential uniformity were introduced by Ellingsen et al. A function F(x) over finite field GF(p^n) to itself is called c-differential uniformity δ, or equivalent, F(x) is differentially (c,δ) uniform, when the maximum number of solutions x∈GF(p^n) of F(x+a)-F(cx)=b, a,b,c∈GF(p^n), c≠1 if a=0, is equal to δ. The objective of this paper is to study the -1-differential uniformity of ternary APN power functions F(x)=x^d over GF(3^n). We obtain ternary power functions with low -1-differential uniformity, and some of them are almost perfect -1-nonlinear.