Geodesic
Weight deficits of involutions and substitutions
Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 4, pp. 95-116 
V. N. Sachkov; I. A. Kruglov. Weight deficits of involutions and substitutions. Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 4, pp. 95-116. http://geodesic.mathdoc.fr/item/MVK_2016_7_4_a6/
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     title = {Weight deficits of involutions and substitutions},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $E_{2^m}$ be an ordered additive group of the finite field with $2^m$ elements. For the substitution $S: E_{2^m}\to E_{2^m}$ we introduce and investigate the index of the weight deficit of involution corresponding to the substitution $S$. By means of this index the security of $S$-boxes against the differential method of cryptoanalysis may be estimated. Some enumeration algorithms for involutions with given values of weight deficits are described.

[1] Sachkov V. N., “Kombinatornye svoistva differentsialno 2-ravnomernykh podstanovok”, Matematicheskie voprosy kriptografii, 6:1 (2015), 159–180

[2] Sachkov V. N., Kurs kombinatornogo analiza, NITs «Regulyarnaya i khaoticheskaya dinamika», M.–Izhevsk, 2013, 336 pp.

[3] Sachkov V. N., “Tsepi Markova iteratsionnykh sistem preobrazovanii”, Trudy po diskretnoi matematike, 6 (2002), 165–183

[4] Riordan Dzh., Vvedenie v kombinatornyi analiz, IL, M., 1963, 287 pp.

[5] Sachkov V. N., Kombinatornye metody diskretnoi matematiki, Nauka, M., 1977, 319 pp.