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Application of modular computing technology to nonlinear encryption in cryptographic systems of informational security

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EN
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In the present paper, we deal with the methodology of nonlinear encryption on the basis of parallel modular computing structures. The use of the minimal redundant modular number system and the interval-modular form of representation of an integer number defined by its modular code creates the computer-arithmetical basis of a cryptographic procedure under consideration. The proposed encryption algorithm is based on the index method of realization of the modular multiplicative operations.
Twórcy
  • Jan Długosz University in Częstochowa, Institute of Technical Education and Safety, al. Armii Krajowej 13/15, 42-200 Częstochowa, Poland
Bibliografia
  • [1] J. Buchmann, Introduction to Cryptography. Springer, New York, 2004.
  • [2] N. Koblitz, Algebraic Aspects of Cryptography. Springer, New York, 2004.
  • [3] D.R. Stinson, Cryptography. Theory and Practice. Chapman & Hall/CRC Press, Boca Raton, 2006.
  • [4] J. Katz, Y. Lindell, Introduction to Modern Cryptography. Chapman & Hall/CRC Press, Boca Raton, 2008.
  • [5] W. Mao, Modern Cryptography. Theory and Practice. Prentice Hall PTR, Upper Saddle River, NJ, 2003.
  • [6] A.A. Kolyada, I.T. Pak, Modular Structures of Pipeline Digital Information Processing. University Press, Minsk, 1992 (in Russian).
  • [7] A.F. Chernyavsky, V.V. Danilevich, A.A. Kolyada, M.Y. Selyaninov, High-speed Methods and Systems of Digital Information Processing. Belarusian State University Press, Minsk, 1996 (in Russian).
  • [8] P.V. Ananda Mohan, Residue Number Systems: Algorithms and Architectures. Kluwer Academic Publishers, 2002.
  • [9] A. Omondi, B. Premkumar, Residue Number Systems: Theory and Implementation. Imperial College Press, London, 2007.
  • [10] P. Kornerup, D.W. Matula, Finite Precision Number Systems and Arithmetic. Cambridge University Press, Cambridge, 2010.
  • [11] I.M. Vinogradov, Fundamentals of Number Theory. Nauka, Moscow, 1981 (in Russian).
  • [12] M. Selyaninov, Modular technique of parallel information processing. Scientific Issues of Jan Długosz University in Czestochowa, Mathematics XIII (2008), 43–52.
  • [13] M. Selyaninov, Construction of modular number system with arbitrary finite ranges. Scientific Issues of Jan Długosz University in Częstochowa, Mathematics XIV (2009), 105–115.
  • [14] M. Selianinau, High- speed modular structures for parallel computing in the space of orthogonal projections. Scientific Issues, Jan Długosz University of Częstochowa, Ser. Technical and IT Education, V, (2010), 87-96.
  • [15] M. Selianinau, Modular principles of high-speed adaptive filtration of discrete signals. Scientific Issues, Jan Długosz University of Częstochowa, Ser. Technical and IT Education, VI, (2011), 75-84.
  • [16] M. Selyaninov, Modular technique of high-speed parallel computing on the sets of polynomials. Scientific Issues of Jan Długosz University in Czestochowa, Mathematics XVII (2012), 69-76.
  • [17] M. Selyaninov, Application of modular computing technique for high-speed implementation of cyclic convolution. Scientific Issues of Jan Długosz University in Częstochowa, Mathematics XIX (2014), 213-222.
  • [18] A.A. Kolyada, M.Y. Selyaninov, On the formation of the integral characteristics of the codes of residue number systems with the symmetrical range. Cybernetics 4 (1986), 20–24 (in Russian).
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Bibliografia
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bwmeta1.element.baztech-d5afb707-b334-4bb9-b4b4-9688ac6fc8af
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