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A Note On Certain Maximal Curves
(Taylor & Francis IncPhiladelphia, 2017)
Field of moduli of generalized Fermat curves of type (k, 3) with an application to non-hyperelliptic dessins d'enfants
(2015)
A generalized Fermat curve of type (k, 3), where k >= 2, is a closed Riemann surface admitting a group H congruent to Z(k)(3) as a group of conformal automorphisms so that the quotient orbifold S / H is the Riemann sphere ...
Optimization of the arithmetic of the ideal class group for genus 4 hyperelliptic curves over projective coordinates
(AMER INST MATHEMATICAL SCIENCES, 2010)
A filtering method for the hyperelliptic curve index calculus and its analysis
(AMER INST MATHEMATICAL SCIENCES, 2010)
NUMERICAL UNIFORMIZATION OF HYPERELLIPTIC-M-SYMMETRIC RIEMANN SURFACES
(Universidad Católica del Norte, Departamento de Matemáticas, 2001)
A tower of Riemann surfaces which cannot be defined over their Field of Moduli
(2017)
Explicit examples of both hyperelliptic and non-hyperelliptic curves which cannot be defined over their field of moduli are known in the literature. In this paper, we construct a tower of explicit examples of such kind of ...
An algebraic approach to elliptic and hyperelliptic curve cryptography
(Universidad de los AndesMatemáticasFacultad de CienciasDepartamento de Matemáticas, 2019)
During the past decades, cryptographic methods have radically improved as well as the mathematical tools employed in them. In this work we introduce elliptic curves as building blocks of cryptosystems and review their ...