Abstract
This thesis is focused on the HasseWeil 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 HasseWeil 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.
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 HasseWeil 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 language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  25May2018 
Place of Publication  [Groningen] 
Publisher  
Print ISBNs  9789403407005 
Electronic ISBNs  9789403406992 
Publication status  Published  2018 