11
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Properties of the full class of quaternary bent-functions of two variables

Pages 2569-2582 | Received 01 Jul 2020, Published online: 13 Jun 2021

References

  • Rothaus O.S. On “bent” functions, J. Comb. Theory Ser. A, USA: Academic Press Inc, 1976, No. 20(3), pp. 300-305.
  • Mazurkov M.I., Sokolov A.V., Barabanov N.A. The Key Sequences Generator Based on Bent Functions Dual Couples, Proceedings of Odessa Polytechnic University, 2013, No. 3, pp. 150-156.
  • Sokolov A.V. Constructive Method for the Synthesis of Nonlinear S-Boxes Satisfying the Strict Avalanche Criterion, Radioelectronics and Communications Systems, 2013, Vol. 56, No. 8, pp. 415-423. doi: 10.3103/S0735272713080049
  • Paterson K.G. Sequences for OFDM and Multi-code CDMA: two problems in algebraic coding theory, Sequences and their applications. Seta 2001. Second Int. Conference (Bergen, Norway, May 13–17, 2001). Proc. Berlin: Springer, 2002, pp. 46-71.
  • Mazurkov M.I., Sokolov A.V. The Regular Rules of Constructing the Complete Class of Bent-Sequences of Length 16, Proceedings of Odessa Polytechnic University, 2013, No.2 (41), pp. 231-237.
  • Qingshu Meng, Min Yang, Huanguo Zhang, Jingsong Cui. A Novel Algorithm Enumerating Bent Functions, Discrete Mathematics, 2008, Vol. 308, Issue 23, pp. 5576-5584. doi: 10.1016/j.disc.2007.10.024
  • Langevin P., Leander G. Counting All Bent Functions in Dimension Eight 99270589265934370305785861242880, Designs, Codes and Cryptography, 2011, No. 59, pp. 193-205. doi: 10.1007/s10623-010-9455-z
  • Enaul Haq Shaik, Nakkeeran Rangaswamy (2017) Implementation of 1×2 decoder and XOR-XNOR logic functions on a PhC structure, Journal of Information and Optimization Sciences, 38:6, pp. 953-960, DOI: 10.1080/02522667.2017.1372142.
  • Zhdanov O.N., Sokolov A.V. Block Symmetric Cryptographic Algorithm Based on Principles of Variable Block Length and Many-Valued Logic, Far East Journal of Electronics and Communications, 2015, Vol. 16, No. 3, pp. 573-589. doi: 10.17654/EC016030573
  • Schmidt K. Quaternary Constant-Amplitude Codes for Multicode CDMA, IEEE International Symposium on Information Theory, Nice, 2007, pp. 2781-2785.
  • Gnatyuk S.O., Zhmurko T.O., Kіnzeryavy V.M., Siyilova N.A. Method for Quality Evaluation of Trit Pseudorandom Sequence to Cryptographic Applications. Information Technology and Security, 2015, Vol. 3, No 2(5), pp. 108-116.
  • Mazurkov M.I., Sokolov A.V., Barabanov N.A. Synthesis Method for Bent-Sequences in the Vilenkin-Chrestenson Basis, Radioelectronics and Communications Systems, Vol. 59, No. 11, pp. 510-517. doi: 10.3103/S0735272716110054
  • Sokolov A.V., Zhdanov O.N. Regular Synthesis Method of a Complete Class of Ternary Bent-Sequences and Their Nonlinear Properties, Journal of Telecommunication, Electronic and Computer Engineering, Vol. 8, No. 9, pp. 39-43.
  • Sokolov A.V. Synthesis Method of Ternary Bent-Functions of Three Variables, Radio Electronics, Computer Science, Control, 2020, No. 1, pp. 82-89. doi: 10.15588/1607-3274-2020-1-9
  • Sokolov A.V., Zhdanov O.N. Cryptographic Constructions Based on Many-Valued Logic Functions. Monograph, Moscow, Scientific Thought, p. 192.
  • Sokolov A.V., Krasota N.I. Very Nonlinear Permutations: Synthesis Methods for S-Boxes with Maximal 4-Nonlinearity, Proceedings of ONAT named after O.S. Popov, 2017, No. 1, pp. 145-154.
  • Sokolov A.V., Overchuk Yu.S. On the Possibility of Synthesizing the Algebraic Normal Form of Quaternary Functions Over a Field GF(4), The First International Scientific-Practical Conference “Problems of Cybersecurity of Information and Telecommunication Systems”, 2018, pp. 384-388.
  • Zhdanov O.N., Sokolov A.V. A Synthesis Method of Basic Ternary Bent-Squares Based on the Triad Shift Operator, System Analysis and Applied Information Science, 2017, No. 1, pp. 77-85.
  • Sokolov A.V., Zhdanov O.N., Barabanov N.A. Pseudo-random Key Sequence Generator Based on Triple Sets of Bent-Functions, Problems of Physics, Mathematics and Technics, 2016, No. 1 (26), pp. 85-91.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.