Geodesic
Weight deficits of involutions and substitutions
Matematičeskie voprosy kriptografii, Tome 7 (2016), pp. 95-116

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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. 
@article{MVK_2016_7_a6,
     author = {V. N. Sachkov and I. A. Kruglov},
     title = {Weight deficits of involutions and substitutions},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {95--116},
     publisher = {mathdoc},
     volume = {7},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2016_7_a6/}
}
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V. N. Sachkov; I. A. Kruglov. Weight deficits of involutions and substitutions. Matematičeskie voprosy kriptografii, Tome 7 (2016), pp. 95-116. http://geodesic.mathdoc.fr/item/MVK_2016_7_a6/