Skip to main content
SpringerLink
Log in

Solution Algorithms for Systems of Linear Equations Over Residue Rings

  • SOFTWARE–HARDWARE SYSTEMS
  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

Polynomial algorithms are proposed for constructing the basis of the solution set of a system of linear homogeneous equations or a system of inhomogeneous linear Diophantine equations in the ring of residues modulo some number provided that the prime factorization of the number is known.

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. S. L. Kryvyi, “Algorithms for solving systems of linear Diophantine equations in residue rings,” Cybernetics and Systems Analysis, 43, No. 6, 787–798 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  2. S. L. Kryvyi, “Algorithms for solving systems of linear Diophantine equations in integer domains,” Cybernetics and Systems Analysis, 42, No. 2, 163–176 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  3. S. L. Kryvyi, “Algorithms for solution of systems of linear Diophantine equations in residue fields,” Cybernetics and Systems Analysis, 43, No. 2, 171–178 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  4. G. A. Donets, “Solution of the safe problem on (0,1)-matrices,” Cybernetics and Systems Analysis, 38, No. 1, 83–88 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  5. G. A. Donets and Aghaei Agh Ghamish Yaghoub, “The mathematical safe problem on matrices,” in: Prepr. V. M. Glushkov Institute of Cybernetics of NANU (2013), pp. 124–131.

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    S. L. Kryvyi

Authors
  1. S. L. Kryvyi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. L. Kryvyi.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2016, pp. 149–160.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kryvyi, S.L. Solution Algorithms for Systems of Linear Equations Over Residue Rings. Cybern Syst Anal 52, 791–801 (2016). https://doi.org/10.1007/s10559-016-9880-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-016-9880-8

Keywords

Search

Navigation