{"id":"https://openalex.org/W3004947130","doi":"https://doi.org/10.1145/3373207.3404044","title":"Efficient ECM factorization in parallel with the lyness map","display_name":"Efficient ECM factorization in parallel with the lyness map","publication_year":2020,"publication_date":"2020-07-20","ids":{"openalex":"https://openalex.org/W3004947130","doi":"https://doi.org/10.1145/3373207.3404044","mag":"3004947130"},"language":"en","primary_location":{"id":"doi:10.1145/3373207.3404044","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3373207.3404044","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2002.03811","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064714239","display_name":"Andrew N. W. Hone","orcid":"https://orcid.org/0000-0001-9780-7369"},"institutions":[{"id":"https://openalex.org/I20581793","display_name":"University of Kent","ror":"https://ror.org/00xkeyj56","country_code":"GB","type":"education","lineage":["https://openalex.org/I20581793"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Andrew Hone","raw_affiliation_strings":["University of Kent, Canterbury, UK","University of Kent:"],"affiliations":[{"raw_affiliation_string":"University of Kent, Canterbury, UK","institution_ids":["https://openalex.org/I20581793"]},{"raw_affiliation_string":"University of Kent:","institution_ids":["https://openalex.org/I20581793"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064714239"],"corresponding_institution_ids":["https://openalex.org/I20581793"],"apc_list":null,"apc_paid":null,"fwci":0.2783,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62247087,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2020","issue":null,"first_page":"234","last_page":"240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9825999736785889,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9789999723434448,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7001803517341614},{"id":"https://openalex.org/keywords/scalar-multiplication","display_name":"Scalar multiplication","score":0.6652619242668152},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.6362007856369019},{"id":"https://openalex.org/keywords/homogeneous-coordinates","display_name":"Homogeneous coordinates","score":0.5763826966285706},{"id":"https://openalex.org/keywords/elliptic-curve-point-multiplication","display_name":"Elliptic curve point multiplication","score":0.5408940315246582},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.4618268609046936},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.4449625611305237},{"id":"https://openalex.org/keywords/plane-curve","display_name":"Plane curve","score":0.4299643337726593},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36171168088912964},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.323735773563385},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2518007457256317}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7001803517341614},{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.6652619242668152},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6362007856369019},{"id":"https://openalex.org/C106402246","wikidata":"https://www.wikidata.org/wiki/Q528525","display_name":"Homogeneous coordinates","level":2,"score":0.5763826966285706},{"id":"https://openalex.org/C117121985","wikidata":"https://www.wikidata.org/wiki/Q78380999","display_name":"Elliptic curve point multiplication","level":3,"score":0.5408940315246582},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4618268609046936},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.4449625611305237},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.4299643337726593},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36171168088912964},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.323735773563385},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2518007457256317}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1145/3373207.3404044","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3373207.3404044","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:kar.kent.ac.uk:81862","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3373207.3404044>)","pdf_url":null,"source":{"id":"https://openalex.org/S4377196264","display_name":"Kent Academic Repository (University of Kent)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20581793","host_organization_name":"University of Kent","host_organization_lineage":["https://openalex.org/I20581793"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:arXiv.org:2002.03811","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.03811","pdf_url":"https://arxiv.org/pdf/2002.03811","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3004947130","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2002.03811.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"mag:3045864854","is_oa":false,"landing_page_url":"https://eprint.iacr.org/2020/238.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2764847869","display_name":"IACR Cryptology ePrint Archive","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4322614454"],"host_organization_lineage_names":["Cryptology ePrint Archive"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Cryptology ePrint Archive","raw_type":null},{"id":"doi:10.48550/arxiv.2002.03811","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2002.03811","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2002.03811","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.03811","pdf_url":"https://arxiv.org/pdf/2002.03811","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7699999809265137,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G116005921","display_name":null,"funder_award_id":"IEC\\R3\\193024","funder_id":"https://openalex.org/F4320324741","funder_display_name":"Royal Scientific Society"},{"id":"https://openalex.org/G2642690241","display_name":"Cluster algebras with periodicity and discrete dynamics over finite fields","funder_award_id":"EP/M004333/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4536800330","display_name":null,"funder_award_id":"EP/M004333/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320965","display_name":"University of New South Wales","ror":"https://ror.org/03r8z3t63"},{"id":"https://openalex.org/F4320324741","display_name":"Royal Scientific Society","ror":"https://ror.org/029nath19"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W561022122","https://openalex.org/W1510727262","https://openalex.org/W1539740938","https://openalex.org/W1839854938","https://openalex.org/W1971605365","https://openalex.org/W1972442530","https://openalex.org/W1988429563","https://openalex.org/W2002913120","https://openalex.org/W2005317356","https://openalex.org/W2005936791","https://openalex.org/W2020278779","https://openalex.org/W2042115984","https://openalex.org/W2057721651","https://openalex.org/W2059283472","https://openalex.org/W2059326407","https://openalex.org/W2062730276","https://openalex.org/W2074337527","https://openalex.org/W2083291746","https://openalex.org/W2091826091","https://openalex.org/W2151084238","https://openalex.org/W2154290215","https://openalex.org/W2167803419","https://openalex.org/W2171599245","https://openalex.org/W2502666551","https://openalex.org/W2509575576","https://openalex.org/W2594174595","https://openalex.org/W2612824548","https://openalex.org/W2766583826","https://openalex.org/W2962714280","https://openalex.org/W2962737260","https://openalex.org/W4232316670","https://openalex.org/W4247971810","https://openalex.org/W4248639047","https://openalex.org/W4292508377"],"related_works":["https://openalex.org/W3045864854","https://openalex.org/W2154290215","https://openalex.org/W2403854924","https://openalex.org/W2951901236","https://openalex.org/W2183188494","https://openalex.org/W1981187928","https://openalex.org/W2350488341","https://openalex.org/W2396152686","https://openalex.org/W2160936837","https://openalex.org/W1551133258","https://openalex.org/W2028957991","https://openalex.org/W2079603294","https://openalex.org/W1553224946","https://openalex.org/W2381466209","https://openalex.org/W2067780672","https://openalex.org/W2356093108","https://openalex.org/W2029912047","https://openalex.org/W2167229579","https://openalex.org/W2197430430","https://openalex.org/W2460729544"],"abstract_inverted_index":{"The":[0],"Lyness":[1,50],"map":[2,6,51],"is":[3,71],"a":[4,19,28,40,54,62,77],"birational":[5],"in":[7,76,82],"the":[8,14,49,74,83],"plane":[9],"which":[10,70],"provides":[11],"one":[12,23,72],"of":[13,18,25,39,48,56,64,73,79],"simplest":[15],"discrete":[16],"analogues":[17],"Hamiltonian":[20],"system":[21],"with":[22],"degree":[24],"freedom,":[26],"having":[27],"conserved":[29],"quantity":[30],"and":[31,59],"an":[32,37,67],"invariant":[33],"symplectic":[34],"form.":[35],"As":[36],"example":[38],"symmetric":[41],"Quispel-Roberts-Thompson":[42],"(QRT)":[43],"map,":[44],"each":[45],"generic":[46],"orbit":[47],"lies":[52],"on":[53,66],"curve":[55,69],"genus":[57],"one,":[58],"corresponds":[60],"to":[61],"sequence":[63],"points":[65],"elliptic":[68],"fibres":[75],"pencil":[78],"biquadratic":[80],"curves":[81],"plane.":[84]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}