Differential operators over particular elliptic curves spaces with cryptographic applications

Abstract

Finding optimal implementations to solve differential equations in the case of boundary conditions is an open problem. In the particular case of using nonsupersingular elliptic curves there are applications in the asymmetric encryption field. Starting from the general implementations, we constructed solutions for the nonsupersingular elliptic curves case. Our developments are of high interest in the domain of nonlinear cryptography and have a good resistance for differential cryptanalysis.

Keywords

• Elliptic curves
• cryptography
• differential equation