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Year 2018, , 29 - 32, 11.03.2018
https://doi.org/10.32323/ujma.393155

Abstract

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.

An algorithm for constructing S-boxes for block symmetric encryption

Year 2018, , 29 - 32, 11.03.2018
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.

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.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Alijon Bozorbayevicha Sattarov

Bakhtiyor Fayzievich Abdurahimov This is me

Publication Date March 11, 2018
Submission Date February 10, 2018
Acceptance Date March 6, 2018
Published in Issue Year 2018

Cite

APA Sattarov, A. B., & Abdurahimov, B. F. (2018). An algorithm for constructing S-boxes for block symmetric encryption. Universal Journal of Mathematics and Applications, 1(1), 29-32. https://doi.org/10.32323/ujma.393155
AMA Sattarov AB, Abdurahimov BF. An algorithm for constructing S-boxes for block symmetric encryption. Univ. J. Math. Appl. March 2018;1(1):29-32. doi:10.32323/ujma.393155
Chicago Sattarov, Alijon Bozorbayevicha, and Bakhtiyor Fayzievich Abdurahimov. “An Algorithm for Constructing S-Boxes for Block Symmetric Encryption”. Universal Journal of Mathematics and Applications 1, no. 1 (March 2018): 29-32. https://doi.org/10.32323/ujma.393155.
EndNote Sattarov AB, Abdurahimov BF (March 1, 2018) An algorithm for constructing S-boxes for block symmetric encryption. Universal Journal of Mathematics and Applications 1 1 29–32.
IEEE A. B. Sattarov and B. F. Abdurahimov, “An algorithm for constructing S-boxes for block symmetric encryption”, Univ. J. Math. Appl., vol. 1, no. 1, pp. 29–32, 2018, doi: 10.32323/ujma.393155.
ISNAD Sattarov, Alijon Bozorbayevicha - Abdurahimov, Bakhtiyor Fayzievich. “An Algorithm for Constructing S-Boxes for Block Symmetric Encryption”. Universal Journal of Mathematics and Applications 1/1 (March 2018), 29-32. https://doi.org/10.32323/ujma.393155.
JAMA Sattarov AB, Abdurahimov BF. An algorithm for constructing S-boxes for block symmetric encryption. Univ. J. Math. Appl. 2018;1:29–32.
MLA Sattarov, Alijon Bozorbayevicha and Bakhtiyor Fayzievich Abdurahimov. “An Algorithm for Constructing S-Boxes for Block Symmetric Encryption”. Universal Journal of Mathematics and Applications, vol. 1, no. 1, 2018, pp. 29-32, doi:10.32323/ujma.393155.
Vancouver Sattarov AB, Abdurahimov BF. An algorithm for constructing S-boxes for block symmetric encryption. Univ. J. Math. Appl. 2018;1(1):29-32.

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