Skip to main content
SpringerLink
Log in

Application of Commutative Rings with Unity for Construction of Symmetric Encryption System

  • CYBERNETICS
  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

A method for constructing a symmetric cryptosystem based on the properties of finite associative-commutative rings with unity is proposed. Algorithms with polynomial time and memory complexity for constructing addition and multiplication tables for these rings are presented. Examples of using this system, as well as its extension by the model of a mathematical safe for subscriber identification are considered. Conditions for using the discrete logarithm function in rings are provided. The advantages of the graph task of the safe in comparison with the matrix task are shown.

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

Access this article

Log in via an institution

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. L. A. Kaluzhnin, Introduction to General Algebra [in Russian], Nauka, Moscow (1973).

  2. D. J. Cooke and H. E. Bez, Computer Mathematics, Cambridge University Press (1984).

  3. S. L. Kryvyi, “A cryptosystem based on Abelian groups and rings,” Problemy Programmir., No. 2–3, 270–277 (2020).

  4. N. Koblitz, A Course in Number Theory and Cryptography (Graduate Texts in Mathematics, 114), Springer (1994).

  5. A. V. Cheremushkin, Lectures in Arithmetic Algorithms in Cryptography [in Russian], MTsNMO, Moscow (2002).

  6. G. A. Donets, “Solution of the safe problem on (0, 1)-matrices,” Cybern. Syst. Analysis, Vol. 38, No. 1, 83–88 (2002). https://doi.org/10.1023/A:1015596100010.

  7. S. L. Kryvyi, Numerical methods to solve problems on a mathematical safe,” Cybern. Syst. Analysis, Vol. 55, No. 5, 714–730 (2019). https://doi.org/10.1007/s10559-019-00182-z.

  8. S. L. Kryvyi, “Algorithms for solving systems of linear Diophantine equations in residue rings,” Cybern. Syst. Analysis, Vol. 43, No. 6, 787–798 (2007). https://doi.org/10.1007/s10559-007-0103-1.

  9. K. Rosen, J. Michaels, J. Gross, J. Grossman, and D. Shier (eds.), Handbook of Discrete and Combinatorial Mathematics, CRC Press, Ch. 2.4, p. 219 (2000).

  10. A. G. Korobeinikov and Yu. A. Gatchin, Mathematical Fundamentals of Cryptology [in Russian], ITMO, St. Petersburg (2004).

  11. A. P. Alferov, A. Yu. Zubov, A. S. Kuz’min, and A. V. Cheremushkin, Fundamentals of Cryptography [in Russian], Helios ARV, Moscow (2001).

Download references

Author information

Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    S. Kryvyi

Authors
  1. S. Kryvyi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Kryvyi.

Additional information

Translated from Kibernetyka ta Systemnyi Analiz, No. 3, May–June, 2022, pp. 3–16.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kryvyi, S. Application of Commutative Rings with Unity for Construction of Symmetric Encryption System. Cybern Syst Anal 58, 319–330 (2022). https://doi.org/10.1007/s10559-022-00464-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-022-00464-z

Keywords

Search

Navigation