Transformations of Cryptographic Schemes Through Interpolation Techniques

Stamatios-Aggelos N. Alexandropoulos (), Gerasimos C. Meletiou (), Dimitrios S. Triantafyllou () and Michael N. Vrahatis ()
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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

A chapter in Computation, Cryptography, and Network Security, 2015, pp 1-17 from Springer

Abstract: 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.

Keywords: Public key cryptography; Discrete logarithm; Diffie Hellman mapping; Polynomial interpolation techniques; Matrix factorization (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-18275-9_1

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DOI: 10.1007/978-3-319-18275-9_1

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