Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 214, pp. 19.
Endomorphisms on elliptic curves for optimal subspaces and applications
to differential equations and nonlinear cryptography
Oana Adriana Ticleanu
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.
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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