LAUSR

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 δ , or equivalent, F ( x ) is differentially ( c , δ )-uniform, when the maximum number of solutions x ∈GF( p n ) of F ( x + a ) − c F ( x ) = 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 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.