Regular Synthesis Method of a Complete Class of Ternary Bent-Sequences and Their Nonlinear Properties
Keywords:Bent-Sequence, Many-Valued Logic, VilenkinChristenson Transform, Nonlinearity,
AbstractA regular synthesis method of the full class of ternary bent-sequences based on their representation in the form of 3-bent-squares is developed. The formula for the nonlinearity estimation of ternary sequences, based on their VilenkinChristenson spectral coefficients is introduced. The distribution of nonlinearity of the full code of length N=9 is researched.
M.I. Mazurkov, V.Ya. Chechel'nitskii, “The classes of equivalent and generative perfect binary arrays for CDMA-technologies,” Radioelectron. Commun. Syst., vol. 46, no. 5, pp. 48-57, 2003.
M.I. Mazurkov, A.V. Sokolov, “Synthesis methods of pseudo-random binary sequences with the property of the k-gram distribution for encryption tasks,” Works of the Odessa polytechnic univer., no. 1(38), pp.188-198, 2012.
M. I. Mazurkov, A.V. Sokolov, “Constructive method for synthesis of complete classes of multilevel de Bruijn sequences,” Radioelectron. Commun. Syst., vol. 56, no. 1, pp. 36-41, 2013.
M. I. Mazurkov, A. V. Sokolov, “Nonlinear transformations based on complete classes of isomorphic and automorphic representations of field GF(256),” Radioelectron. Commun. Syst., vol. 56, no. 11, pp. 513-521, 2013.
O.S. Rothaus, “On “bent” functions,” J. Comb. Theory Ser. A. — USA: Academic Press Inc, no. 20(3), pp. 300-305, 1976.
K.G. Paterson, “Sequences For OFDM and Multi-code CDMA: two problems in algebraic coding theory”, Sequences and their applications. Seta 2001. Second Int. Conference. Proc. Berlin: Springer, pp. 46–71, 2002.
A.V. Sokolov, “Constructive method for the synthesis of nonlinear Sboxes satisfying the strict avalanche criterion”, Radioelectron. Commun. Syst., vol. 56, no. 8, pp. 415-423, 2013.
M.I. Mazurkov, N.A. Barabanov, A.V. Sokolov, “The key sequences generator based on bent functions dual couples,” Works of the Odessa Polytechnic Univer., vol. 3(42), pp. 150-156, 2013.
A.V.Sokolov, “The cellular automata key sequences generator,” Works of the Odessa Polytechnic University, vol. 1 (43), pp. 180-186, 2014.
L. Bolc, P. Borowik, “Many-valued Logics 2: Automated reasoning and practical applications,” Springer Science & Business Media, 2003, p. 303.
M.I. Mazurkov, A.V. Sokolov, N.A. Barabanov, “On the effect of the type of orthogonal transform on PAPR of signal spectrum in CDMA systems,” Informatics and Math. Methods in Sim., vol. 5, no. 1, pp. 28-37, 2015.
O.N. Zhdanov, A.V. Sokolov, “Algorithm of construction of optimal according to criterion of zero correlation non-binary S-boxes,” PFMT, no. 3(24), pp. 94-97, 2015.
A.V. Sokolov, O.N. Zhdanov, N.A. Barabanov, “Pseudo-random key sequence generator based on triple sets of bent-functions,” PFMT, no. 1 (26), pp. 85-91, 2016.
S.O. Gnatyuk, T.S. Zhmurko, V.M. Kіnzeryavy, N.A. Seylova, “Method of trit pseudorandom sequences generating for quantum cryptography systems,” Inf. Sec., vol. 22, no. 2, pp. 140-147, 2015.
A.M. Trakhtman, V.A. Trakhtman, “Elements of the Theory of
Discrete Signals on Finite Intervals,” Moscow, Sov. Radio, 1975 p. 208.
A.V. Sokolov, O.N. Zhdanov, O.A. Ayvazian “Synthesis methods of algebraic normal form of many-valued logic functions,” System analysis and applied inform. sc., no.1, pp. 69-76, 2016.
S.V. Agievich “On the representation of bent functions by bent rectangles,” Probabilistic Methods in Discrete Mathematics: roceedings of the Fifth International Petrozavodsk Conference. Utrecht, Boston: VSP, pp. 121-135, 2002.
N. Tokareva “Bent Functions: Results and Applications to Cryptography,” Academic Press, 2015, p. 220.
W. Maier, O. Staffelbach “Nonlinearity criteria for cryptographic functions,” In Advances in Cryptology, EUROCRYPT’89, vol.434, Lecture
Notes in Computer Science, Springer-Verlag, pp.549-562, 1990.
G.B. Arfken, H. J. Weber, “Mathematical Methods for Physicists,” Harcourt: San Diego, 2005, p. 1182.
How to Cite
TRANSFER OF COPYRIGHT AGREEMENT
The manuscript is herewith submitted for publication in the Journal of Telecommunication, Electronic and Computer Engineering (JTEC). It has not been published before, and it is not under consideration for publication in any other journals. It contains no material that is scandalous, obscene, libelous or otherwise contrary to law. When the manuscript is accepted for publication, I, as the author, hereby agree to transfer to JTEC, all rights including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the author(s) specifically retain(s):
- All proprietary right other than copyright, such as patent rights
- The right to make further copies of all or part of the published article for my use in classroom teaching
- The right to reuse all or part of this manuscript in a compilation of my own works or in a textbook of which I am the author; and
- The right to make copies of the published work for internal distribution within the institution that employs me
I agree that copies made under these circumstances will continue to carry the copyright notice that appears in the original published work. I agree to inform my co-authors, if any, of the above terms. I certify that I have obtained written permission for the use of text, tables, and/or illustrations from any copyrighted source(s), and I agree to supply such written permission(s) to JTEC upon request.