{"id":{"repo_id":"uwo","oai_identifier":"oai:uwo.scholaris.ca:20.500.14721/18464"},"canonical_url":"https://search.dev.ndltd.org/etd/uwo/oai:uwo.scholaris.ca:20.500.14721/18464","repository":{"repo_id":"uwo","name":"Western University","base_url":"https://uwo.scholaris.ca/server/oai/request"},"display":{"title":"Point Counting On Genus 2 Curves","abstract":"For cryptographic purposes, counting points on the jacobian variety of a given hyperelliptic curve is of great importance. There has been several approaches to obtain the cardinality of such a group, specially for hyperelliptic curves of genus 2. The best known algorithm for counting points on genus 2 curves over prime fields of large characteristic is a variant of Schoof’s genus 1 algorithm. Following a recent work of Gaudry and Schost, we show how to speed up the current state of the art genus 2 point counting algorithm by proposing various computational improvements to its basic arithmetical ingredients.","abstract_html":"For cryptographic purposes, counting points on the jacobian variety of a given hyperelliptic curve is of great importance. There has been several approaches to obtain the cardinality of such a group, specially for hyperelliptic curves of genus 2. The best known algorithm for counting points on genus 2 curves over prime fields of large characteristic is a variant of Schoof’s genus 1 algorithm. Following a recent work of Gaudry and Schost, we show how to speed up the current state of the art genus 2 point counting algorithm by proposing various computational improvements to its basic arithmetical ingredients.","abstract_has_math":false,"creators":["Doliskani, Javad Nazari"],"institution":null,"degree_name":"M Sc","degree_level":null,"degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":[],"advisors":["Schost, Eric"],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-01","date_published":"2011-01-01","updated_at":"2026-07-27T21:56:13Z","subjects":["Point counting","Hyperelliptic curves","Schoof’s algorithm","Elliptic curves"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/20.500.14721/18464","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Schost, Eric"]},{"key":"dc:creator","label":"Author","values":["Doliskani, Javad Nazari"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-06-25T18:50:32Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-06-25T18:50:32Z"]},{"key":"dc:date.issued","label":"Date","values":["2011-01-01"]},{"key":"dc:type","label":"Dc Type","values":["thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M Sc"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Point counting","Hyperelliptic curves","Schoof’s algorithm","Elliptic curves"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/20.500.14721/18464"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["For cryptographic purposes, counting points on the jacobian variety of a given hyperelliptic curve is of great importance. There has been several approaches to obtain the cardinality of such a group, specially for hyperelliptic curves of genus 2. The best known algorithm for counting points on genus 2 curves over prime fields of large characteristic is a variant of Schoof’s genus 1 algorithm. Following a recent work of Gaudry and Schost, we show how to speed up the current state of the art genus 2 point counting algorithm by proposing various computational improvements to its basic arithmetical ingredients."]},{"key":"dc:title","label":"Title","values":["Point Counting On Genus 2 Curves"]}]}],"canonical_facts":{"dc:contributor.advisor":["Schost, Eric"],"dc:creator":["Doliskani, Javad Nazari"],"dc:date.accessioned":["2025-06-25T18:50:32Z"],"dc:date.available":["2025-06-25T18:50:32Z"],"dc:date.issued":["2011-01-01"],"dc:description.abstract":["For cryptographic purposes, counting points on the jacobian variety of a given hyperelliptic curve is of great importance. There has been several approaches to obtain the cardinality of such a group, specially for hyperelliptic curves of genus 2. The best known algorithm for counting points on genus 2 curves over prime fields of large characteristic is a variant of Schoof’s genus 1 algorithm. Following a recent work of Gaudry and Schost, we show how to speed up the current state of the art genus 2 point counting algorithm by proposing various computational improvements to its basic arithmetical ingredients."],"dc:identifier.uri":["https://hdl.handle.net/20.500.14721/18464"],"dc:subject":["Point counting","Hyperelliptic curves","Schoof’s algorithm","Elliptic curves"],"dc:title":["Point Counting On Genus 2 Curves"],"dc:type":["thesis"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_name":["M Sc"]},"updated_at":"2026-07-27T21:56:13Z"}