Electron. J. Diff. Equ., Vol. 2015 (2015), No. 214, pp. 1-9.

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

Oana Adriana Ticleanu

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.

Submitted April 9, 2015. Published August 17, 2015.
Math Subject Classifications: 12H20, 35R03, 11G05.
Key Words: Elliptic curves cryptography; endomorphism of elliptic curves; Frobenius endomorphism.

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Oana Adriana Ticleanu
University of Craiova
Street: A. I. Cuza 13
200585 Craiova, Romania
email: oana.ticleanu@inf.ucv.ro

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