Endomorphisms on elliptic curves for optimal subspaces and applications to differential equations and nonlinear cryptography

Abstract

Finite spaces are used on elliptic curves cryptography (ECC) to define the necessary parameters for nonlinear asymmetric cryptography, and to optimize certain solutions of differential equations. These finite spaces contain a set of "cryptographic points" which define the strengthens of the chosen field. One of the current research areas on ECC is choosing optimal subspaces which contains most of the interesting points. The present work presents a new way to define the cryptographic strengthens of a particular field, by constructing an endomorphism between the classically studied subspaces and a certain subspace.

Keywords

• Elliptic curves cryptography
• endomorphism of elliptic curves
• Frobenius endomorphism