Geodesic
On a heuristic approach to constructing bijective vector Boolean functions with given cryptographic properties
Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 181-184

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Bijective vector Boolean functions (permutations) 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 permutations 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 permutations. 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: Boolean function, nonlinearity, differential uniformity.
Mots-clés : permutation 
@article{PDMA_2021_14_a42,
     author = {M. A. Kovrizhnykh and D. B. Fomin},
     title = {On a heuristic approach to constructing bijective vector {Boolean} functions with given cryptographic properties},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {181--184},
     publisher = {mathdoc},
     number = {14},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2021_14_a42/}
}
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M. A. Kovrizhnykh; D. B. Fomin. On a heuristic approach to constructing bijective vector Boolean functions with given cryptographic properties. Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 181-184. http://geodesic.mathdoc.fr/item/PDMA_2021_14_a42/