Method of S-boxes synthesis based on the criterion of zero correlation between the output and input data vectors and the strict avalanche criterion

Authors

  • Michael I. Mazurkov Odessa National Polytechnic University, Ukraine
  • Artem V. Sokolov Odessa National Polytechnic University, Ukraine

DOI:

https://doi.org/10.3103/S0735272714080068

Keywords:

S-box, correlation immunity, matrix of correlation coefficients, strict avalanche criterion

Abstract

A constructive method of synthesis of correlation-immune S-boxes of length N = 256 satisfying the strict avalanche criterion has been proposed. Its properties and estimates of the number of optimal S-boxes that can be obtained by using the proposed method were determined. In addition a regular method of multiplication of the obtained optimal S-boxes was proposed.

References

MAZURKOV, M.I. Synthesis method of optimal substitution constructions based on the criterion of zero correlation between the output and input data vectors. Izv. Vyssh. Uchebn. Zaved., Radioelektron., v.55, n.12, p.12-22, 2012, http://radio.kpi.ua/article/view/S0021347012120023 [in Russian]; Radioelectron. Commun. Syst., v.55, n.12, p.533-543, 2012, DOI: http://dx.doi.org/10.3103/S0735272712120023.

KIM, KWANGJO; MATSUMOTO, TSUTOMU; IMAI, HIDEKI. A recursive construction method of S-boxes satisfying strict avalanche criterion. Lect. Notes Comput. Sci., v.537, p.565-574, 1991, DOI: http://dx.doi.org/10.1007/3-540-38424-3_39.

MAZURKOV, M.I.; SOKOLOV, A.V. Synthesis methods of pseudo-random binary sequences with the property of the k-gram distribution for encryption tasks. Odes’kyi Politechnichnyi Universystet. Pratsi, n.1, p.188-198, 2012, http://pratsi.opu.ua/articles/show/804.

YAKOVLEV, S.V. Balanced quality criteria of the long-term key elements of the algorithm in accordance with standard GOST 28147-89. Informatsiini Tekhnologii ta Kompiuterna Inzheneriia, p.5-12, 2009.

KIM, KWANGJO. Construction of DES-like S-boxes based on Boolean functions satisfying the SAC. Lect. Notes Comput. Sci., v.739, p.59-72, 1993, DOI: http://dx.doi.org/10.1007/3-540-57332-1_5.

MAZURKOV, M.I.; SOKOLOV, A.V. Cryptographic properties of nonlinear transform of Rijndael cipher based on complete classes of irreducible polynomials. Odes’kyi Politechnichnyi Universystet. Pratsi, n.2, p.183-189, 2012, http://pratsi.opu.ua/articles/show/864.

FIPS 197. Advanced encryption standard, 2001, http://csrc.nist.gov/publications/.

Published

2014-08-12

Issue

Section

Research Articles