Constructive and destructive facets of Weil descent on elliptic curves

摘要: In this paper we look in detail at the curves which arise method of Galbraith and Smart for producing Weil restriction an elliptic curve over a finite field characteristic 2 composite degree. We explain how can be used to construct hyperelliptic cryptosystems could as secure based on original curve. On other hand, show that same technique may provide way attacking cryptosystem using recent advances study discrete logarithm problem curves. We examine resulting higher genus some propose additional check systems defined fields so make them immune from methods paper.