4 papers
Kummer surfaces for primality testing
Eduardo Ruíz Duarte, Marc Paul Noordman
We use the arithmetic of the Kummer surface associated to the Jacobian of a hyperelliptic curve to study the primality of integers of the form . We provide an algorithm…
A proof of the Hasse-Weil inequality for genus 2 à la Manin
Eduardo Ruíz Duarte, Jaap Top
We prove the Hasse-Weil inequality for genus 2 curves given by an equation of the form y^2 = f(x) with f a polynomial of degree 5, using arguments that mimic the elementary proof o…
Geometric primality tests using curves of genus 1 & 2
Eduardo Ruiz Duarte
We revisit and generalize some geometric techniques behind deterministic primality testing for some integer sequences using curves of genus 1 over finite rings. Subsequently we dev…
Explicit endomorphism of the Jacobian of a hyperelliptic function field of genus 2 using base field operations
Eduardo Ruiz Duarte, Octavio Páez Osuna
We present an efficient endomorphism for the Jacobian of a curve of genus 2 (hyperelliptic) for divisors having a Non disjoint support. This extends the work of Costello and La…