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Lower Bounds for Interpolating Polynomials for Square Roots of the Elliptic Curve Discrete Logarithm

  • Gerasimos C. Meletiou
  • Yannis C. Stamatiou
  • Apostolos Tsiakalos
Part of the Communications in Computer and Information Science book series (CCIS, volume 200)

Abstract

In this paper we derive lower bounds for the degree of polynomials that approximate the square root of the discrete logarithm for Elliptic Curves with orders of various specific types. These bounds can serve as evidence for the difficulty in the computation of the square root of discrete logarithms for such elliptic curves, with properly chosen parameters that result in the curve having order of any of types studied in this paper. The techniques are potentially applicable to elliptic curves of order of any specific, allowable (by Hasse’s bounds), order type that is of interest for the application in hand.

Keywords

Elliptic Curve Elliptic Curf Discrete Logarithm Discrete Logarithm Problem Quadratic Residue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Gerasimos C. Meletiou
    • 1
  • Yannis C. Stamatiou
    • 2
    • 3
  • Apostolos Tsiakalos
    • 2
  1. 1.A.T.E.I. of EpirusArtaGreece
  2. 2.Department of MathematicsUniversity of IoanninaIoanninaGreece
  3. 3.Research Academic Computer Technology InstituteUniversity of Patras, N. Kazantzaki, RioPatrasGreece

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