On (− 1)-differential uniformity of ternary APN power functions

Very recently, a new concept called multiplicative differential and the corresponding c-differential uniformity were introduced by Ellingsen et al. (IEEE Trans. Inform. Theory 66(9), 5781–5789 2020). A function F(x) over finite field GF(pn) to itself is said have δ, or equivalent, differentially (c,δ)-uniform, when maximum number of solutions x ∈GF(pn) F(x + a) − cF(x) = b, a,b,c ∈GF(pn), c≠ 1 if 0, equal δ. The objective this paper study (− 1)-differential some ternary APN power functions xd GF(3n). We obtain with low uniformity, them are almost perfect 1)-nonlinear.