Geodesic
On the properties of substitution blocks on the base of a~modified additive generator and on the base of the block cipher NASH
Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 57-61.

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Here, we present two algorithms for computing substitution blocks (S-boxes) of the size $16\times16$ bits. The first one is based on a modified additive generator, the second – on the lightweight block cipher NASH. For both algorithms, we give the numerical values for some cryptographic properties of S-boxes produced by them, namely for differential probability, for linear probability, for nonlinearity order of coordinate functions and their linear combinations and compare them with the similar values related to S-boxes of some known block ciphers (AES, Kuznechik and others). Also, we show that the running time of these algorithms is 3.5–5 times more than the running time needed to compute the same S-boxes in the table form.
Keywords: modified additive generator, NASH block cipher, S-box, $16$-bit S-box, algorithmic implementation of S-boxes, maximum differential probability, maximum linear probability, nonlinear order. 
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     title = {On the properties of substitution blocks on the base of a~modified additive generator and on the base of the block cipher {NASH}},
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V. M. Bobrov; S. M. Komissarov. On the properties of substitution blocks on the base of a~modified additive generator and on the base of the block cipher NASH. Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 57-61. http://geodesic.mathdoc.fr/item/PDMA_2018_11_a17/

[1] Fomichev V. M., Lolich D. M., Yuzbashev A. V., “Algoritmicheskaya realizatsiya s-boksov na osnove modifitsirovannykh additivnykh generatorov”, Prikladnaya diskretnaya matematika. Prilozhenie, 2017, no. 10, 102–104

[2] Metodicheskie rekomendatsii TK26. Zadanie uzlov zameny bloka podstanovki algoritma shifrovaniya GOST 28147-89, , M., 2013 https://tc26.ru/standarts/metodicheskie-rekomendatsii/zadanie-uzlov-zameny-bloka-podstanovki-algoritma-shifrovaniya-gost-28147-89.html

[3] Fomichev V. M., Kyazhin S. N., “Lokalnaya primitivnost matrits i grafov”, Diskretnyi analiz i issledovanie operatsii, 24:1 (2017), 97–119 | DOI | MR | Zbl

[4] Lebedev A., Karondeev A., Kozlov A., New Block Cipher, [Elektronnyi resurs], https://ist.ac.at/eurocrypt2016/slides/121.pdf

[5] Fomichev V. M., Metody diskretnoi matematiki v kriptologii, Ucheb. posobie, Dialog-MIFI, M., 2010

[6] Menyachikhin A., “Spectral-linear and spectral-difference methods for generating cryptographically strong S-boxes”, CTCrypt Preproc., Yaroslavl, 2016, 232–252 https://mjos.fi/doc/rus/CTCrypt2016Preproceedings.pdf

[7] Wood C. A., Large Substitution Boxes with Efficient Combinational Implementations, Thesis, Rochester Institute of Technology, 2013