On degrees of polynomial interpolations related to elliptic curve cryptography

Authors:
Takakazu Satoh
Affiliations:
Department of Mathematics, Tokyo Institute of Technology, Tokyo, Japan
Venue:
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Year:
2005

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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.