Geodesic
$\mathsf{XS}$-circuits' properties related to the guaranteed number of activations
Prikladnaya Diskretnaya Matematika. Supplement, no. 15 (2022), pp. 62-66.

Voir la notice de l'article provenant de la source Math-Net.Ru

The guaranteed number of activations (GNA) is an important characteristic that determines the efficiency of differential cryptanalysis of a given $\mathsf{XS}$-circuit. In the paper, we propose an approach to optimize the known GNA calculation algorithm based on the branch and bound method and the analysis of special matrices that define the $\mathsf{XS}$-circuit. Now, it is possible to compute GNA for more than 30 rounds, which would take significantly longer if the original algorithm were used. The optimized algorithm was used for exhaustive enumeration of low-dimensional $\mathsf{XS}$-schemes. We prove that the canonical forms of the $\mathsf{XS}$-circuit and its dual coincide, which provides a strict connection between the guaranteed number of linear and differential activations. Based on computational experiments, several hypotheses have been proposed. One of the hypotheses is that there are no $\mathsf{XS}$-circuits of dimension greater than two that achieve an optimal GNA in every round.
Keywords: guaranteed number of activations, $\mathsf{XS}$-circuit, differential cryptanalysis, linear cryptanalysis, branch and bound method. 
@article{PDMA_2022_15_a15,
     author = {D. R. Parfenov and A. O. Bakharev and A. V. Kutsenko and A. R. Belov and N. D. Atutova},
     title = {$\mathsf{XS}$-circuits' properties related to the guaranteed number of activations},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {62--66},
     publisher = {mathdoc},
     number = {15},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2022_15_a15/}
}
TY  - JOUR
AU  - D. R. Parfenov
AU  - A. O. Bakharev
AU  - A. V. Kutsenko
AU  - A. R. Belov
AU  - N. D. Atutova
TI  - $\mathsf{XS}$-circuits' properties related to the guaranteed number of activations
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2022
SP  - 62
EP  - 66
IS  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2022_15_a15/
LA  - ru
ID  - PDMA_2022_15_a15
ER  - 
%0 Journal Article
%A D. R. Parfenov
%A A. O. Bakharev
%A A. V. Kutsenko
%A A. R. Belov
%A N. D. Atutova
%T $\mathsf{XS}$-circuits' properties related to the guaranteed number of activations
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2022
%P 62-66
%N 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2022_15_a15/
%G ru
%F PDMA_2022_15_a15
D. R. Parfenov; A. O. Bakharev; A. V. Kutsenko; A. R. Belov; N. D. Atutova. $\mathsf{XS}$-circuits' properties related to the guaranteed number of activations. Prikladnaya Diskretnaya Matematika. Supplement, no. 15 (2022), pp. 62-66. http://geodesic.mathdoc.fr/item/PDMA_2022_15_a15/

[1] Agievich S. V., “$\mathsf{XS}$-circuits in block ciphers”, Matem. vopr. kriptogr., 10:2 (2019), 7–30 | MR | Zbl

[2] Agievich S. V., “On the guaranteed number of activations in $\mathsf{XS}$-circuits”, Matem. vopr. kriptogr., 12:2 (2021), 7–20 | MR | Zbl

[3] Realizatsiya algoritmov poiska garantirovannogo chisla aktivatsii, https://github.com/agievich/xs