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(p(n)) to itself is said to have c-differential uniformity delta, or equivalent, F(x) is differentially (c,delta)-uniform, when the maximum number of solutions x is an element of GF(p(n)) of F(x + a) - cF(x) = b, a,b,c is an element of GF(p(n)), c not equal 1 if a = 0, is equal to delta. The objective of this paper is to study the (- 1)-differential uniformity of some 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.