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

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Information Security and Assurance (ISA 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 200))

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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.

This work was partially supported by the European Union project ABC4Trust (Attribute-based Credentials for Trust) funded within the context of the 7th Research Framework Program (FP7).

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Author information

Authors and Affiliations

  1. A.T.E.I. of Epirus, P.O. Box 110, GR 47100, Arta, Greece

    Gerasimos C. Meletiou

  2. Department of Mathematics, University of Ioannina, GR 45110, Ioannina, Greece

    Yannis C. Stamatiou & Apostolos Tsiakalos

  3. Research Academic Computer Technology Institute, University of Patras, N. Kazantzaki, Rio, Patras, GR 26504, Greece

    Yannis C. Stamatiou

Authors
  1. Gerasimos C. Meletiou
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  2. Yannis C. Stamatiou
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  3. Apostolos Tsiakalos
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Editor information

Editors and Affiliations

  1. Hannam University, 133 Ojeong-dong, Daeduk-gu, 306-791, Daejeon, South Korea

    Tai-hoon Kim

  2. The Ohio State University, 470 Hitchcock Hall, 2070 Neil Avenue, 43210-1275, Columbus, OH, USA

    Hojjat Adeli

  3. Hannam University, 133 Ojeong-dong, Daeduk-gu, 306-791, Daejeon, Korea

    Rosslin John Robles

  4. Hannam University, 133 Ojeong-dong, Daeduk-gu, Daejeon, Korea

    Maricel Balitanas

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Meletiou, G.C., Stamatiou, Y.C., Tsiakalos, A. (2011). Lower Bounds for Interpolating Polynomials for Square Roots of the Elliptic Curve Discrete Logarithm. In: Kim, Th., Adeli, H., Robles, R.J., Balitanas, M. (eds) Information Security and Assurance. ISA 2011. Communications in Computer and Information Science, vol 200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23141-4_17

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  • DOI: https://doi.org/10.1007/978-3-642-23141-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23140-7

  • Online ISBN: 978-3-642-23141-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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