Geodesic
Algorithm of construction of optimal according to criterion of zero correlation non-binary $S$-boxes
Problemy fiziki, matematiki i tehniki, no. 3 (2015), pp. 94-97.

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

This paper considers the construction of cryptographic $S$-boxes of the length $N=3^k$, which are optimal from the point of view of the absence of correlation between the output and input vectors. Constructed sets of $S$-boxes can be recommended for upgrading of the existing block symmetric ciphers, as well as for the synthesis of new high-speed encryption algorithms based on the principles of multi-valued logic.
Keywords: $S$-box, Kim scheme.
Mots-clés : matrix of correlation coefficients 
@article{PFMT_2015_3_a16,
     author = {O. N. Zhdanov and A. V. Sokolov},
     title = {Algorithm of construction of optimal according to criterion of zero correlation non-binary $S$-boxes},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {94--97},
     publisher = {mathdoc},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2015_3_a16/}
}
TY  - JOUR
AU  - O. N. Zhdanov
AU  - A. V. Sokolov
TI  - Algorithm of construction of optimal according to criterion of zero correlation non-binary $S$-boxes
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2015
SP  - 94
EP  - 97
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2015_3_a16/
LA  - ru
ID  - PFMT_2015_3_a16
ER  - 
%0 Journal Article
%A O. N. Zhdanov
%A A. V. Sokolov
%T Algorithm of construction of optimal according to criterion of zero correlation non-binary $S$-boxes
%J Problemy fiziki, matematiki i tehniki
%D 2015
%P 94-97
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2015_3_a16/
%G ru
%F PFMT_2015_3_a16
O. N. Zhdanov; A. V. Sokolov. Algorithm of construction of optimal according to criterion of zero correlation non-binary $S$-boxes. Problemy fiziki, matematiki i tehniki, no. 3 (2015), pp. 94-97. http://geodesic.mathdoc.fr/item/PFMT_2015_3_a16/

[1] FIPS 197, Advanced encryption standard, , 2001 (Date of access: 03.03.2015) http://csrc.nist.gov/publications/

[2] Sistemy obrabotki informatsii. Zaschita kriptograficheskaya. Algoritm kriptograficheskogo preobrazovaniya, GOST 28147-89, IPK Izdatelstvo standartov, M., 1996, 28 pp.

[3] M. I. Mazurkov, “Metod sinteza optimalnykh podstanovochnykh konstruktsii po kriteriyu nulevoi korrelyatsii mezhdu vykhodnymi i vkhodnymi vektorami dannykh”, Izvestiya vysshikh uchebnykh zavedenii. Radioelektronika, 55:12 (2012), 12–22 | MR | Zbl

[4] M. I. Mazurkov, A. V. Sokolov, “Metod sinteza $S$-blokov po kriteriyu nulevoi korrelyatsii mezhdu vykhodnymi i vkhodnymi vektorami dannykh i strogomu lavinnomu kriteriyu”, Izvestiya vysshikh uchebnykh zavedenii. Radioelektronika, 57:8 (2014), 54–60

[5] K. Kim, “Construction of DES-like $S$-boxes Based on Boolean Functions Satisfying the SAC”, Advances in Cryptology — ASIACRYPT'91, International Conference on the Theory and Application of Cryptology (Fujiyosida, Japan, November 1991), Lecture Notes in Computer Science, 739, Springer-Verlag, 1991, 59–72 | DOI

[6] N. Sh. Kremer, Teoriya veroyatnostei i matematicheskaya statistika, Yuniti, M., 2004, 573 pp.

[7] O. N. Zhdanov, Metodika vybora klyuchevoi informatsii dlya algoritma blochnogo shifrovaniya, INFRA-M, M., 2013, 90 pp.

[8] M. I. Mazurkov, A. V. Sokolov, “Nelineinye $S$-bloki podstanovki na osnove kompozitsionnykh kodov stepennykh vychetov”, Izvestiya vysshikh uchebnykh zavedenii. Radioelektronika, 56:9 (2013), 34–43