Elliptic curves generation for isogeny-based cryptosystems

Abstract

Methods of generating supersingular and ordinary elliptic curves for isogeny-based cryptosystems have been studied. The influence of the class field polynomial on the time of generating ordinary elliptic curves has been analyzed and the comparative time of generating curves using Weber and Hilbert polynomials have been presented. Parameters that influence on the cryptographic security of isogeny-based cryptosystems have been considered.