An algorithm for constructing S-boxes for block symmetric encryption

Year 2018, Volume: 1 Issue: 1, 29 - 32, 11.03.2018

Alijon Bozorbayevicha Sattarov , Bakhtiyor Fayzievich Abdurahimov

https://doi.org/10.32323/ujma.393155

Abstract

This article presents an algorithm for the generation of S-boxes with the maximum algebraic immunity and high nonlinearity. The algorithm is founded method of the permutation of output element of S-box. On basis of the proposed method, $S(8\times 8)$-box created, with the algebraic immunity 3 (441) and nonlinearity 104. The algorithm given in this article can be used for oscillation of $S(8\times 8)$)-boxes with the increased resistance to algebraic, linear, differential and linear and differential methods of a cryptanalysis, for block symmetric algorithms of encryption.

Keywords

S-box, algebraic cryptanalysis, algebraic immunity, nonlinearity

References

• [1] A. Eilertsen, K. Kazymyrov, V. Kazymyrova, M. Storetvedt, A Sage Library For Analysis Of Nonlinear Binary Mappings, Selmer Center, Department of Informatics, University of Bergen, Norway. CECC’14, May 21, 2014.
• [2] A. Sokolov, New methods of synthesis of non-linear transformations of the modern encryptions, LAP LAMBERT Academic Publishing house (Saarbrucken, Germany), 2015. ISBN: 978-3-659-67440-2.
• [3] J. Daemen, The design of Rijndael: AES-the advanced encryption standard, Berlin; Heidelberg: Springer, 2002.
• [4] N. Courtois, J. Pieprzyk, Cryptanalysis of block ciphers with overdefined systems of equations, ASIACRYPT, 2002. – P. 267-287.
• [5] O. A. Logachev, A. A. Salnikov, V. V. Yashchenko, S. Smyshlyaev, Boolean functions in the theory of coding and cryptology, Institute of problems of an inform.security of MSU. – 2nd prod., additional – M.: MTsNMO, 2012. – 583 pages.
• [6] S. Fischer and W. Meier, Algebraic Immunity of S-boxes and Augmented Functions, FHNW, CH-5210 Windisch, Switzerland.
• [7] Y. Yu, Constructing Differentially 4 Uniform Permutations from Known Ones, Chinese Journal of Electronics. – 2013. – Vol. 22, No. 3. – River 495–499.