Synthesis method for bent sequences in the Vilenkin-Chrestenson basis
DOI:
https://doi.org/10.3103/S0735272716110054Keywords:
bent sequence, Vilenkin-Chrestenson transform, regular methodAbstract
The paper presents a method developed for building a complete class of bent sequences of length N = 9 in the Vilenkin–Chrestenson basis based on employing three reference constructions. The first construction allows the bent sequences of arbitrary length N = 32k, k Î¥ to be built. The resultant bent sequences can be used both in cryptographic applications and as constant amplitude codes in the MC-CDMA technology. A design of the gamma xoring block of graphic and video information based on bent sequences in the Vilenkin–Chrestenson basis was also proposed.References
MAZURKOV, M.I. Broadband Radio Communication Systems. Odessa: Nauka i Tekhnika, 2010 [in Russian], ISBN 978-966-8335-95-2.
MAZURKOV, M.I.; BARABANOV, N.A.; SOKOLOV, A.V. The key sequences generator based on bent functions dual couples. Odes’kyi Politechnichnyi Universystet. Pratsi, 2013, n.3, p.150-156, http://pratsi.opu.ua/articles/show/1017.
SOKOLOV, A.V. Quick key sequences generator based on cellular automata. Odes’kyi Politechnichnyi Universystet. Pratsi, 2014, v.43, n.1, p.180-186, http://pratsi.opu.ua/articles/show/1087.
AMBROSIMOV, A.S. Properties of bent functions of q-valued logic over finite fields. Diskr. Mat., 1994, v.6, n.3, p.50-60, http://mi.mathnet.ru/eng/dm639.
PATERSON, KENNETH G. Sequences for OFDM and multi-code CDMA: two problems in algebraic coding theory. Proc. of 2nd Int. Conf. on Sequences and Their Applications, Seta 2001, May 13-17, 2001, Bergen, Norway. Berlin: Springer, 2002, p.46-71, DOI: http://dx.doi.org/10.1007/978-1-4471-0673-9_4.
MAZURKOV, M.I.; SOKOLOV, A.V.; BARABANOV, N.A. On the effect of the type of orthogonal transform on PAPR of signal spectrum in CDMA systems. Informatics and Mathematical Methods in Simulation, 2015, v.5, n.1, p.28-37.
HNATIUK, S.O.; ZHMURKO, T.O.; KINZERIAVYI, V.M.; SEILOVA, N.A. Method for quality evaluation of trip pseudorandom sequence to cryptographic applications. Information Technology and Security, 2015, v.3, n.2, p.108-116, http://its.iszzi.kpi.ua/article/view/60891.
TRAKHTMAN, A.M.; TRAKHTMAN, V.A. Foundations of the Theory of Discrete Signals over Finite Intervals. Moscow: Sov. Radio, 1975 [in Russian].
SOKOLOV, A.V.; ZHDANOV, O.N.; BARABANOV, N.A. On the existence of triple bent sequences. Proc. of 19th Int. Youth Conf. on Radioelectronics and Youth in the XXI Century, 2015, Kharkiv, Ukraine. Kharkiv: KhNURE, 2015, v.3.
TOKAREVA, N.N. Bent functions: results and applications. A survey. Appl. Discrete Math., 2009, n.1, p.15-37, http://journals.tsu.ru/pdm/en/&journal_page=archive&id=431&article_id=26255.
SCHNEIER, B. Applied Cryptography: Protocols, Algorithms, and Source Code in C. Wiley, 2015.