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Transformations of Cryptographic Schemes Through Interpolation Techniques

In: Computation, Cryptography, and Network Security

Author

Listed:
  • Stamatios-Aggelos N. Alexandropoulos

    (University of Patras, Computational Intelligence Laboratory (CILab), Department of Mathematics)

  • Gerasimos C. Meletiou

    (A.T.E.I. of Epirus)

  • Dimitrios S. Triantafyllou

    (University of Military Education, Hellenic Army Academy (SSE))

  • Michael N. Vrahatis

    (University of Patras, Computational Intelligence Laboratory (CILab), Department of Mathematics)

Abstract

The problem of transforming cryptographic schemes using interpolation techniques is studied. Firstly, explicit forms for the discrete logarithm and the Diffie–Hellman cryptographic functions are given. Subsequently, the inverse Aitken and Neville interpolation methods for the discrete logarithm and the Lucas logarithm problems are presented. Next, the representation of cryptographic functions through polynomials or algebraic functions as well as a special case of discrete logarithm problem is given. Finally, a study of cryptographic functions using factorization of matrices is analyzed.

Suggested Citation

  • Stamatios-Aggelos N. Alexandropoulos & Gerasimos C. Meletiou & Dimitrios S. Triantafyllou & Michael N. Vrahatis, 2015. "Transformations of Cryptographic Schemes Through Interpolation Techniques," Springer Books, in: Nicholas J. Daras & Michael Th. Rassias (ed.), Computation, Cryptography, and Network Security, pages 1-17, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-18275-9_1
    DOI: 10.1007/978-3-319-18275-9_1
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