Об эвристическом подходе к построению биективных векторных булевых функций с заданными криптографическими характеристиками

Прикладная дискретная математика. Приложение. 2021. № 14. С. 181–184.

Коврижных М. А., Fomin D.

Bijective vector Boolean functions (permuta- tions) are used as nonlinear primitives of many symmetric ciphers. In this paper, we study a generalized construction of (2m, 2m)-functions using monomial and arbitrary m-bit per- mutations as constituent elements. A heuristic algorithm for obtaining bijective Boolean functions with given nonlinearity and differential uniformity, based on this construction, is proposed. For this, a search is carried out for auxiliary permutations of a lower dimension using the ideas of spectral-linear and spectral-difference methods. The proposed algorithm consists of iterative multiplication of the initial randomly generated 4-bit permutations by transposition, selecting the best ones in nonlinearity, the differential uniformity, and the corresponding values in the linear and differential spectra among the obtained 8-bit permu- tations. The possibility of optimizing the calculation of cryptographic properties at each iteration of the algorithm is investigated; 8-bit 6-uniform permutations with nonlinearity 108 are experimentally obtained.

Keywords: булева функция, нелинейность, nonlinearity, Boolean function, permutation, подстановка, differential uniformity, дифференциальная равномерность