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On Degrees of Polynomial Interpolations Related to Elliptic Curve Cryptography

  • Takakazu Satoh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3969)

Abstract

We study two topics on degrees of polynomials which interpolate cryptographic functions. The one is concerned with elliptic curve discrete logarithm (ECDL) on curves with an endomorphism of degree 2 or 3. For such curves, we obtain a better lower bound of degrees for polynomial interpolation of ECDL. The other deals with degrees of polynomial interpolations of embeddings of a subgroup of the multiplicative group of a finite field to an elliptic curve.

Keywords

Elliptic curves polynomial interpolation division polynomials 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Takakazu Satoh
    • 1
  1. 1.Department of MathematicsTokyo Institute of TechnologyTokyoJapan

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