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Theoretical Foundations for the Analytical Computation of Coefficients of Basic Numbers of Krestenson’s Transformation

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Abstract

This paper presents theoretical foundations for the analytical transformation of coefficients of basic numbers of Krestenson’s transformation, which significantly reduces the number of operations required to convert numbers from a residue number system to the decimal number system. An appropriate selection of modules makes it possible to efficiently use all processor registers.

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References

  1. A. A. Melnik, Computer Architecture [in Russian], Volynsk. Oblast. Tipogr., Lutsk (2008).

    Google Scholar 

  2. V. K. Zadiraka and O. S. Oleksyuk, Computer Arithmetic of Multidigit Numbers [in Ukrainian], Vyshcha Shkola, Kyiv (2008).

    Google Scholar 

  3. N. Ferguson and B. Schneier, Practical Cryptography [Russian translation], Izd. Dom “Williams,” Moscow (2005).

    Google Scholar 

  4. V. Zadiraka and O. Oleksyuk, Computer Cryptology [in Ukrainian], Vyshcha Shkola, Kyiv (2002).

    Google Scholar 

  5. Ya. N. Nykolaychuk, Theory of Information Sources [in Russian], OOO “Terno-Graf,” Ternopil (2010).

    Google Scholar 

  6. Z. L. Rabinovich and V. A. Ramanauskas, Standard Computer Operations [in Russian], Tekhnika, Kyiv (1980).

    Google Scholar 

  7. I. Ya. Akushskii and D. I. Yuditskii, Machine Arithmetic in Residue Classes [in Russian], Sov. Radio, Moscow (1968).

    Google Scholar 

  8. V. A. Torgashev, A Residue Number System and Computer Reliability [in Russian], Sov. Radio, Moscow (1973).

    Google Scholar 

  9. Ya. N. Nykolaychuk, O. I. Volynskii, and S. V. Kulyna, “Theoretical foundations of construction and the structure of special processors in the Krestenson basis,” Vestn. Khmeln. Nats. Un-ta, 1, No. 3, 85–90 (2007).

    Google Scholar 

  10. N. I. Chervyakov, A. I. Galushkin, A. A. Evdokimov, A. V. Lavrinenko, and I. N. Lavrinenko, Application of Artificial Neural Networks and Residue Number Systems in Cryptography [in Russian], Fizmatlit, Moscow (2012).

    Google Scholar 

  11. A. A. Bukhshtab, Number Theory [in Russian], Prosveshcheniye, Moscow (1966).

    Google Scholar 

  12. O. I. Borodin, Number Theory [in Russian], Vyshcha Shkola, Kyiv (1970).

    Google Scholar 

  13. Ya. M. Nykolaychuk, “Developing the theory and complexes of technological tools for the formation, transmission, and processing of digital messages in local computer networks of automated systems,” DPhil, V. M. Glushkov Institute of Cybernetics of AS of UkrSSR, Kyiv (1991).

  14. M. N. Kasyanchuk, “Theory and mathematical regularities of a perfect form of a residue number system,” in: Proc. Intern. Symposium “Issues of optimization of computations (IOC–XXXV),” Vol. 1, Kyiv–Katsiveli (2009), pp. 306–310.

  15. M. Kasyanchuk, “Conception of theoretical tenets of a perfect form of the Krestenson transformation and its practical application,” Optoelectronic Information and Power Technologies, No. 2 (20), 43–48 (2010).

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Correspondence to Ya. M. Nykolaychuk.

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Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 3–8, September–October, 2014.

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Nykolaychuk, Y.M., Kasianchuk, M.M. & Yakymenko, I.Z. Theoretical Foundations for the Analytical Computation of Coefficients of Basic Numbers of Krestenson’s Transformation. Cybern Syst Anal 50, 649–654 (2014). https://doi.org/10.1007/s10559-014-9654-0

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  • DOI: https://doi.org/10.1007/s10559-014-9654-0

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