On differential uniformity of permutations derived using a generalized construction

The work is dedicated to the theoretical substantiation of a directed search for 8-bit permutations with given cryptographic properties: differential uniformity and nonlinearity. The statements on the partition of the set of vectorial Boolean functions derived using generalized construction into equivalence classes are proved. The statements that allow one to reject functions from equivalence classes either by a high differential uniformity or by nonbijectivity are justified. The results of this work may be used to construct permutations with specified cryptographic properties, ensuring the resistance of encryption algorithms against the linear and differential methods of cryptographic analysis.