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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v78.i10.20
pages 853-868

COMBINING AND FILTERING FUNCTIONS BASED ON THE NONLINEAR FEEDBACK SHIFT REGISTERS

A. A. Kuznetsov
V. Karazin National University of Kharkiv, 4 Svobody Sq., Kharkiv 61022, Ukraine
A. V. Potii
V. Karazin National University of Kharkiv, 4 Svobody Sq., Kharkiv 61022, Ukraine
N. A. Poluyanenko
Institute of Information Technologies, 12 Bakulina St., Kharkiv 61166, Ukraine
S. G. Vdovenko
Ivan Chernyakhovsky National Defense University of Ukraine, 28 Povitroflotskyi Ave., Kyiv 03049, Ukraine

RÉSUMÉ

Strong cryptography of stream ciphers is determined, among other things, by the ability of a generated pseudorandom sequence to resist analytical attacks. One of the main components of the pseudorandom stream cipher sequence generating algorithm are Boolean functions for combining and filtering. The paper considers the possibility of applying nonlinear-feedback shift registers that generate a maximum length sequence as a combining or filtering function. This work examines the main indicators of cryptographic strength of such functions, as: balance, the prohibitions presence, correlation immunity and nonlinearity. The study analyzes and demonstrates correlation experimental immunity and nonlinearity values for all nonlinear feedback shift registers, that generate a maximum length sequence, for register sizes up to 6 cells inclusively, and registers sizes up to 9 cells inclusively with algebraic degree of the polynomial under 2. The possibility of optimizing the process of selecting the Boolean functions according to the criteria of maximum correlation immunity and nonlinearity with various algebraic degree and minimization of the number of monomials in the polynomial are studied.

RÉFÉRENCES

  1. Gorodilova, A.A., (2016) From cryptanalysis to cryptographic property of a Boolean function, Applied Discrete Mathematics, 3(33), pp.16-44, (in Russian).

  2. Pankratova, I.A., (2014) Boolean Functions in Cryptography: a Handbook, Tomsk, Russia: Tomsk State University Publishing House, 88 p., (in Russian).

  3. Mukhachev, V.A. and Khoroshko, V.A., (2005) Methods of Practical Cryptography, Kyiv, Ukraine: OOO Poligraf-Consulting, 215 p., (in Russian).

  4. Potii, A.V. and Poluyanenko, N.A., (2017) Computation of the number of forming polynomials for non-linear feedback shift register and non-linearity of an arbitrary order, Internat. sci. conf. on the issues of optimization of computations (POO-XLIV), Kamianets-Podilskyi, Ukraine.

  5. Khachatryan, L.G., (1991) Methods for constructing de Bruijn sequences, Discrete Mathematics, 3(4), pp. 62-78, (in Russian).

  6. Knuth, D., (1969) The Art of Computer Programming. Vol. II. Seminumerical Algorithms, USA, Commonwealth of Massachusetts: Addison-Wesley, p.634.

  7. Logachev, O.A., Salnikov, A.A., Smyshlyaev, S.V., and Yashchenko, V.V., (2012) Boolean Functions in Coding Theory and Cryptography, Moscow, Russia: MCNMO, 584 p., (in Russian).

  8. Smyshlyaev, S.V., (2010) On cryptographic weaknesses of some classes of binary sequence transformations, Applied Discrete Mathematics, 1, pp. 5-15, (in Russian).

  9. Tokareva, N.N., (2010) Generalization of bent functions. A survey, Discrete analysis and studying of operations, 17(1), pp.33-62, (in Russian).

  10. Tokareva, N.N., (2011) Nonlinear Boolean Functions: Bent Functions and their Generalizations, LAP LAMBERT Academic Publishing (Saarbrucken, Germany), 180 p. ISBN: 978-3-8433-0904-2.

  11. Agafonova, I.B., (2007) Cryptographic Properties of nonlinear Boolean Functions, Seminar on discrete harmonic analysis and geometrical modeling, SPb., Russia: DHA & CAGD, pp. 1-24.

  12. Shevelev, Yu.P., (2003) Discrete Mathematics. Part. 1: Theory of Sets. Boolean Algebra (Automatic Learning Technology "Symbol"), Tomsk, Russia: Tomsk State University of Control Systems and Radio Electronics, 118 p., (in Russian).

  13. Moldovyan, A.A., (2002) Cryptography. Fast Ciphers, SPb., Russia: BHV-Peterburg, 496 p., (in Rusian).

  14. Tarannikov, Yu.V., (2002) On correlation immune and resilient Boolean functions, Mathematical Issues of Cybernetics, 11, pp. 91-148, (in Russian).


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