Analysis of Isomorphism Classes of a Family of Elliptic Curves Over Finite Fields
Zhao Wei *
College of Science, North China University of Technology, Beijing 100144, P. R. China.
*Author to whom correspondence should be addressed.
Abstract
Doche et al. constructed a family of elliptic curves (DIK elliptic curves) and proposed more efficient tripling formulas leading to a fast scalar multiplication algorithm. In this paper we present a direct method to compute the number of \(\bar{F}\)q-isomorphism classes (isomorphism over \(\bar{F}\)q ) and \(\bar{F}\)q isomorphism classes of DIK family of elliptic curves defined over a finite field \(\bar{F}\)q. We give the explicit formulae for the number of \(\bar{F}\)q-isomorphism and an estimate formulae for the number of isomorphism classes. These result can be used in the elliptic curve cryptosystems.
Keywords: Elliptic curves, isomorphism classes, cryptography