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)


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.


Elliptic curves polynomial interpolation division polynomials 


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

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

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