SpringerLink
Log in

Symmetric Cryptoalgorithms in the Residue Number System

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

This paper presents theoretical backgrounds of the symmetric encryption based on the residue number system. The peculiarities of this approach are that in the case of restoring a decimal number based on its residuals using the Chinese remainder theorem, multiplication occurs by arbitrarily chosen coefficients (keys). It is established that cryptostability of the developed methods is determined by the number of modules and their bit size. In addition, the described methods are found to allow to almost indefinitely increase the block of plain text for encryption, which eliminates the necessity to use different encryption modes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Shevchuk and Ya. Pastukh, “Improve the security of social media accounts,” in: Proc. 9th Intern. Conf. on Advanced Computer Information Technologies (ACIT-2019) (Ceske Budejovice, Czech Republic, 5–7 June, 2019). Ceske Budejovice (2019), pp. 439–442. https://doi.org/10.1109/ACITT.2019.8779963.

  2. V. A. Andrijchuk, I. P. Kuritnyk, M. M. Kasyanchuk, M. P. Karpinski, “Modern algorithms and methods of the person biometric identification,” in: Proc. Third IEEE Intern. Workshop on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS-2005) (Sofia, Bulgaria, 5–7 Sept, 2005). IEEE (2005), pp. 403–406. https://doi.org/10.1109/IDAACS.2005.283012.

  3. L. Sousa, S. Antão, and P. Martins, “Combining residue arithmetic to design efficient cryptographic circuits and systems,” IEEE Circuits and Systems Magazine, Vol. 15, No. 4, 6–32 (2016). https://doi.org/10.1109/MCAS.2016.2614714.

    Article  Google Scholar 

  4. D. S. A. Elminaam, H. M. A. Kader, and M. M. Hadhoud, “Performance evaluation of symmetric encryption algorithms,” Intern. J. of Comp. Sci. and Network Security, Vol. 8, No. 12, 280–286 (2008).

    Google Scholar 

  5. M. A. Al-Shabi, “A survey on symmetric and asymmetric cryptography algorithms in information security,” Intern. J. of Scientific and Research Publications, Vol. 9, Iss. 3, 576–589 (2019). https://doi.org/10.29322/IJSRP.9.03.2019.p8779.

  6. M. K. Rusia and M. Rusia, “A literature survey on efficiency and security of symmetric cryptography,” Intern. J. of Comp. Sci. and Network, Vol. 6, Iss. 3, 425–429 (2017).

  7. R. Goel, R. R. Sinha, and O. P. Rishi, “Novel data encryption algorithm,” Intern. J. of Comp. Sci. Issues, Vol. 8, Iss. 4, No. 2, 561–565 (2011).

  8. S. A. Gubka, A. S. Gubka, N. Yu. Nosova, “Modernization symmetric encryption algorithms,” Radioelectronic and Computer Systems, No. 1, 61–65 (2011).

  9. V. Pikh, V. Kimak, and B. Krulikovskyi, “Synthesis of high-performance components of spectral analyzers and special processors for data encryption in Rademacher–Krestenson’s theoretical-numerical basis,” in: Proc. XIII Intern. Conf. “The Experience of Designing and Application of CAD Systems in Microelectronics (CADSM-2015)” (Polyana-Svalyava, Ukraine, 23–25 Feb, 2015), Polyana-Svalyava (2015), pp. 182–184.

  10. P. V. Ananda Mohan, Residue Number Systems: Theory and Applications, Birkhuser, Basel (2016).

    Book  Google Scholar 

  11. V. Zadiraka, Ya. Nykolaichuk, and Yu. Franko, Computer Technologies in Information Security, Kart-Blansh, Ternopil (2015).

  12. L. Djath, K. Bigou, A. Tisserand, “Hierarchical approach in RNS base extension for asymmetric cryptography,” in: Proc. IEEE 26th Symp. on Computer Arithmetic (ARITH) (Kyoto, Japan, 10–12 June, 2019), IEEE (2019), pp. 46–53. https://doi.org/10.1109/ARITH.2019.00016.

  13. I. R. Fadulilahi, E. K. Bankas, and J. B. A. K. Ansuura, “Efficient algorithm for RNS implementation of RSA,” International J. of Computer Applications, Vol. 127, No. 5, 14–19 (2015). https://doi.org/10.5120/ijca2015906381.

    Article  Google Scholar 

  14. I. Yakymenko, M. Kasyanchuk, Ya. Nykolaychuk, “Matrix algorithms of processing of the information flow in computer systems based on theoretical and numerical Krestenson’s basis,” in: Proc. X Intern. Conf. “Modern Problems of Radio Engineering, Telecommunications and Computer Science (TCSET-2010)” (L’viv–Slavske, Ukraine, 23–27 Feb, 2010), IEEE (2010), p. 241.

  15. G. Saldamli and C. K. Koc, “Spectral modular exponentiation,” in: Proc. 18th IEEE Symposium on Computer Arithmetic (ARITH 07) (Montepellier, France, 25–27 June, 2007), IEEE (2007), pp. 123–130. https://doi.org/10.1109/ARITH.2007.34.

  16. I. Z. Yakymenko, M. M. Kasianchuk, S. V. Ivasiev, A. M. Melnyk, and Y. M. Nykolaichuk, “Realization of RSA cryptographic algorithm based on vector-module method of modular exponention,” in: Proc. 14th Intern. Conf. on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET-2018) (L’viv–Slavske, Ukraine, 20–24 Feb, 2018), IEEE (2018). pp. 550–554. https://doi.org/10.1109/TCSET.2018.8336262.

  17. V. Yatskiv, A. Sachenko, N. Yatskiv, P. Bykovyy, and A. Segin, “Compression and transfer of images in wireless sensor networks using the transformation of residue number system,” in: Proc. IEEE 10th Intern. Conf. on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS-2019) (Metz, France, 18–21 Sept, 2019), IEEE (2019), pp. 1111–1114. https://doi.org/10.1109/IDAACS.2019.8924372.

  18. V. A. Krasnobayev, A. S. Yanko, and S. A. Koshman, “A method for arithmetic comparison of data represented in a residue number system,” Cybern. Syst. Analysis, Vol. 52, No. 1, 145–150 (2016). https://doi.org/10.1007/s10559-016-9809-2.

    Article  MATH  Google Scholar 

  19. M. Kasianchuk, I. Yakymenko, I. Pazdriy, and O. Zastavnyy, “Algorithms of findings of perfect shape modules of remaining classes system,” in: Proc. XIII Intern. Conf. “The Experience of Designing and Application of CAD Systems in Microelectronics (CADSM-2015)” (Lviv, Ukraine, 24–27 Feb, 2015), IEEE (2015), pp.168–171. https://doi.org/10.1109/CADSM.2015.7230866.

  20. M. N. Kasianchuk, Ya. N. Nykolaychuk, and I. Z. Yakymenko, “Theory and methods of constructing of modules system of the perfect modified form of the system of residual classes,” J. Autom. Inform. Sci., Vol. 48, No. 8 (2016), pp. 56–63. https://doi.org/10.1615/JAutomatInfScien.v48.i8.60.

  21. V. Shoup, A Computational Introduction to Number Theory and Algebra, Cambridge University Press (2005). https://doi.org/10.1017/CBO9781139165464.

  22. M. Karpinski, S. Rajba, S. Zawislak, K. Warwas, M. Kasianchuk, S. Ivasiev, and I. Yakymenko, “A method for decimal number recovery from its residues based on the addition of the product modules,” in: Proc. 10th IEEE Intern. Conf. on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS-2019) (Metz, France, 18–21 Sept, 2019), IEEE (2019), pp. 13–17. https://doi.org/10.1109/IDAACS.2019.8924395.

  23. Zhengbing Hu, I. A. Dychka, M. Onai, and A. Bartkoviak, “The analysis and investigation of multiplicative inverse searching methods in the ring of integers modulo m,” Intern. J. of Intelligent Systems and Applications, Vol. 8, No. 11, 9–18 (2016). https://doi.org/10.5815/ijisa.2016.11.02.

    Article  Google Scholar 

  24. T. Rajba, A. Klos-Witkowska, S. Ivasiev, I. Yakymenko, and M. Kasianchuk, “Research of time characteristics of search methods of inverse element by the module,” in: Proc. 2017 IEEE 9th Intern. Conf. on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS-2017) (Bucharest, Romania, 21–23 Sept, 2017), IEEE (2017), pp. 82–85. https://doi.org/10.1109/IDAACS.2017.8095054.

  25. S. Dasgupta, C. Papadimitriou, and U. Vazirani, Algorithms, McGraw-Hill Science/Engineering/Math (2006).

  26. H. Jeffrey, P. Jill, and H. Joseph, An Introduction to Mathematical Cryptography, Springer, Berlin (2008).

    MATH  Google Scholar 

  27. A. Bogdanov, D. Khovratovich, and C. Rechberger, “Biclique cryptanalysis of the full AES,” in: Proc. Intern. Conf. on the Theory and Application of Cryptology and Information Security “Advances in Cryptology — ASIACRYPT 2011” (Seoul, Korea, 4–8 Dec, 2011); LNCS, Vol. 7073, 344–371 (2011). https://doi.org/10.1007/978-3-642-25385-0_19.

Download references

Author information

Authors and Affiliations

  1. West Ukrainian National University, Ternopil, Ukraine

    M. M. Kasianchuk, I. Z. Yakymenko & Ya. M. Nykolaychuk

Authors
  1. M. M. Kasianchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Z. Yakymenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ya. M. Nykolaychuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. M. Kasianchuk.

Additional information

Translated from Kibernetyka ta Systemnyi Analiz, No. 2, March–April, 2021, pp. 184–192.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kasianchuk, M.M., Yakymenko, I.Z. & Nykolaychuk, Y.M. Symmetric Cryptoalgorithms in the Residue Number System. Cybern Syst Anal 57, 329–336 (2021). https://doi.org/10.1007/s10559-021-00358-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-021-00358-6

Keywords

Search

Navigation