Cybernetics and Systems Analysis

, Volume 43, Issue 6, pp 787–798 | Cite as

Algorithms for solving systems of linear diophantine equations in residue rings

Article

Abstract

Algorithms are proposed that construct the basis of the set of solutions to a system of homogeneous or inhomogeneous linear Diophantine equations in a residue ring modulo n when the prime factors of n are known.

Keywords

residue ring linear Diophantine equation basis of a solution set 

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References

  1. 1.
    S. L. Kryvyi, “Algorithms for solving systems of linear Diophantine equations in integer domains,” Cybernetics and Systems Analysis, No. 2, 3–17 (2006).Google Scholar
  2. 2.
    S. L. Kryvyi, “Algorithms for solution of systems of linear Diophantine equations in residue fields,” Cybernetics and Systems Analysis, No. 2, 15–23 (2007).Google Scholar
  3. 3.
    S. L. Kryvyi, “Methods of solution and criteria of consistency of systems of linear Diophantine equations over the set of natural numbers,” Cybernetics and Systems Analysis, No. 4, 12–36 (1999).Google Scholar
  4. 4.
    G. A. Donets, “Solution of the safe problem on (0,1)-matrices,” Cybernetics and Systems Analysis, No. 1, 98–105 (2002).Google Scholar
  5. 5.
    G. A. Donets and Samer I. M. Alshalame, “Solution of the problem of construction of a linear mosaic,” in: Theory of Optimal Solutions, V. M. Glushkov Cybernetic Institute of NASU, Kiev (2005), pp. 15–24.Google Scholar
  6. 6.
    A. V. Cheremushkin, Lectures on Arithmetic Algorithms in Cryptography [in Russian], MTsNMO, Moscow (2002).Google Scholar
  7. 7.
    R. Allen and K. Kennedy, “Automatic translation of FORTRAN programs to vector form,” ACM Trans. on Progr. Languages and Systems, 9, No. 4, 491–542 (1987).MATHCrossRefGoogle Scholar
  8. 8.
    E. Contenjean and H. Devie, “An efficient algorithm for solving systems of Diophantine equations,” Information and Computation, 113, No. 1, 143–172 (1994).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Cybernetics InstituteNational Academy of Sciences of UkraineKievUkraine

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