Differentially low uniform permutations from known 4-uniform functions

Involutory Differentially 4-Uniform Permutations from Known Constructions

Substitution box (S-box) is an important component of block ciphers for providing confusion into the cryptosystems. The functions used as S-boxes should have low differential uniformity, high nonlinearity and high algebraic degree. Due to the lack of knowledge on the existence of APN permutations over F22k , which have the lowest differential uniformity, when k > 3, they are often constructed f...

Differentially 4-uniform functions

We give a geometric characterization of vectorial Boolean functions with differential uniformity ≤ 4. This enables us to give a necessary condition on the degree of the base field for a function of degree 2r − 1 to be differentially 4-uniform.

On Known and New Differentially Uniform Functions

Differentially 4-Uniform Permutations with the Best Known Nonlinearity from Butterflies

Recently, a new structure called butterfly introduced by Perrin et at. is attractive for that it has very good cryptographic properties: the differential uniformity is at most equal to 4 and algebraic degree is also very high when exponent e = 3. It is conjecture that the nonlinearity is also optimal for every odd k, which was proposed as a open problem. In this paper, we further study the butt...

More constructions of differentially 4-uniform permutations on 𝔽22k