On Degrees of Polynomial Interpolations Related to Elliptic Curve Cryptography
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.
KeywordsElliptic curves polynomial interpolation division polynomials
Unable to display preview. Download preview PDF.
- 7.Silverman, J.H.: The arithmetic of elliptic curves. GTM, 106. Springer, Heidelberg (1985)Google Scholar
- 8.Stark, H.M.: Class-numbers of complex quadratic fields, Modular functions of one variable, I. In: Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972. Lect. Notes in Math, vol. 320, pp. 153–174. Springer, Berlin (1973)Google Scholar