Ambiguity and deficiency for differentially [formula omitted]-uniform monomial permutations on [formula omitted

Abstract

For a function f:Fq→Fq on a finite field Fq, new measures—ambiguity A(f) and deficiency D(f) of f were raised by Panario et al. (2010, 2011) to judge non-injectivity and non-surjectivity of the difference functions Δaf:Fq→Fq(a∈Fq∗). In this paper, we determine the values of A(f) and D(f) for three differentially 4-uniform monomial permutations, i.e., inverse function, Gold function and Dobbertin function on F2n (2∣n).