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

For a function f : F q → F q on a finite field F q , 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 Δ a f : F q → F q ( a ∈ F q ∗ ) . 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 F 2 n ( 2 ∣ n ). [ABSTRACT FROM AUTHOR]