Algorithms for computing cryptographic characteristics of vectorial Boolean functions | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2019. № 46. DOI: 10.17223/20710410/46/7

There are presented algorithms for calculating the cryptographic characteristics of vectorial Boolean functions, such as the order of correlation immunity, nonlinearity, component algebraic immunity, and differential uniformity order. In these algorithms, the components of a vectorial Boolean function are enumerated according to the Gray code. Experimental results are given for random vectorial Boolean functions, permutations, and two known classes Kn and Sn,k of invertible vectorial Boolean functions in n variables with coordinates essentially depending on all variables and on k variables, k < n, respectively. Some properties of differential uniformity are theoretically proved for functions in Kn and Sn,k, namely, the differential uniformity order δF equals 2ⁿ for any F ∈ S_n,_k, and the inequality 2ⁿ - 4(n - 1) ≤ δ_F ≤ 2ⁿ - 4 holds for any F ∈ Kn.