Hasse-Weil inequality and primality tests in the context of curves of genus 2

Eduardo Ruíz Duarte

Research output: ThesisThesis fully internal (DIV)

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Abstract

This thesis is focused on the Hasse-Weil bound and some applications of it.
We provide a different proof for the genus 2 case inspired by an elementary
proof for the genus 1 case presented by Manin in 1956.

Moreover, we use this inequality to develop deterministic primality testing
algorithms using elliptic curves. Further we provide an algorithm to find
primes using Jacobians of genus 2 curves over finite rings, also using the Hasse-Weil bound.

A detailed treatment of the function field of the Jacobian of a genus 2 curve is covered.
We include the construction of interesting infinite families of symmetric functions on the Jacobian. These functions, among other things, will allow us to easily represent explicitly an endomorphism that is used for the genus 2 primality test.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • University of Groningen
Supervisors/Advisors
  • Top, Jaap, Supervisor
  • Waalkens, Holger, Supervisor
Award date25-May-2018
Place of Publication[Groningen]
Publisher
Print ISBNs978-94-034-0700-5
Electronic ISBNs978-94-034-0699-2
Publication statusPublished - 2018

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