{"id":"https://openalex.org/W4403175113","doi":"https://doi.org/10.62056/ae0fhbmo","title":"Computing Orientations from the Endomorphism Ring of Supersingular Curves and Applications","display_name":"Computing Orientations from the Endomorphism Ring of Supersingular Curves and Applications","publication_year":2024,"publication_date":"2024-10-07","ids":{"openalex":"https://openalex.org/W4403175113","doi":"https://doi.org/10.62056/ae0fhbmo"},"language":"en","primary_location":{"id":"doi:10.62056/ae0fhbmo","is_oa":true,"landing_page_url":"https://doi.org/10.62056/ae0fhbmo","pdf_url":"https://cic.iacr.org/p/1/3/5/pdf","source":{"id":"https://openalex.org/S4394708374","display_name":"IACR Communications in Cryptology","issn_l":"3006-5496","issn":["3006-5496"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320989","host_organization_name":"International Association for Cryptologic Research","host_organization_lineage":["https://openalex.org/P4310320989"],"host_organization_lineage_names":["International Association for Cryptologic Research"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Communications in Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://cic.iacr.org/p/1/3/5/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092685334","display_name":"Jonathan Komada Eriksen","orcid":"https://orcid.org/0009-0000-3040-2965"},"institutions":[{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Jonathan Eriksen","raw_affiliation_strings":["Norwegian University of Science and Technology"],"raw_orcid":"https://orcid.org/0009-0000-3040-2965","affiliations":[{"raw_affiliation_string":"Norwegian University of Science and Technology","institution_ids":["https://openalex.org/I204778367"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012789036","display_name":"Antonin Leroux","orcid":"https://orcid.org/0009-0002-3737-0075"},"institutions":[{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Antonin Leroux","raw_affiliation_strings":["DGA-MI","Universit\u00e9 de Rennes"],"raw_orcid":"https://orcid.org/0009-0002-3737-0075","affiliations":[{"raw_affiliation_string":"DGA-MI","institution_ids":[]},{"raw_affiliation_string":"Universit\u00e9 de Rennes","institution_ids":["https://openalex.org/I56067802"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6016,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.9216544,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994000196456909,"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":0.9994000196456909,"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/T11130","display_name":"Coding theory and cryptography","score":0.9929999709129333,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9836999773979187,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.661048412322998},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4366387128829956},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3969828486442566}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.661048412322998},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4366387128829956},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3969828486442566}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.62056/ae0fhbmo","is_oa":true,"landing_page_url":"https://doi.org/10.62056/ae0fhbmo","pdf_url":"https://cic.iacr.org/p/1/3/5/pdf","source":{"id":"https://openalex.org/S4394708374","display_name":"IACR Communications in Cryptology","issn_l":"3006-5496","issn":["3006-5496"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320989","host_organization_name":"International Association for Cryptologic Research","host_organization_lineage":["https://openalex.org/P4310320989"],"host_organization_lineage_names":["International Association for Cryptologic Research"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Communications in Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04851270v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04851270","pdf_url":"https://hal.science/hal-04851270v1/file/2024-146.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Communications in Cryptology, 2024","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.62056/ae0fhbmo","is_oa":true,"landing_page_url":"https://doi.org/10.62056/ae0fhbmo","pdf_url":"https://cic.iacr.org/p/1/3/5/pdf","source":{"id":"https://openalex.org/S4394708374","display_name":"IACR Communications in Cryptology","issn_l":"3006-5496","issn":["3006-5496"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320989","host_organization_name":"International Association for Cryptologic Research","host_organization_lineage":["https://openalex.org/P4310320989"],"host_organization_lineage_names":["International Association for Cryptologic Research"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Communications in Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6700000166893005}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403175113.pdf","grobid_xml":"https://content.openalex.org/works/W4403175113.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W2107012927","https://openalex.org/W2592544948","https://openalex.org/W2791851483","https://openalex.org/W2811492100","https://openalex.org/W2953643502","https://openalex.org/W3096403266","https://openalex.org/W3096704360","https://openalex.org/W3096999101","https://openalex.org/W3116436840","https://openalex.org/W3116788907","https://openalex.org/W4200380216","https://openalex.org/W4285195271","https://openalex.org/W4310806686","https://openalex.org/W4310806736","https://openalex.org/W4362476350","https://openalex.org/W4390867301","https://openalex.org/W4400041471","https://openalex.org/W4401651827"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109"],"abstract_inverted_index":{"This":[0,18],"work":[1],"introduces":[2],"several":[3,25,118,185],"algorithms":[4,68,261],"related":[5],"to":[6,51,62,69,80,104,209,238],"the":[7,22,28,36,188,204,211,215,218,221,229,239,264,271,286,309],"computation":[8,189,310],"of":[9,14,24,30,46,76,120,129,145,147,169,190,198,203,220,231,241,255,273,311,313],"orientations":[10,243],"in":[11,32,44,160,244,267],"endomorphism":[12,212,245],"rings":[13],"supersingular":[15,236],"elliptic":[16],"curves.":[17],"problem":[19,72,230,240],"is":[20,61,138,150,200,283],"at":[21],"heart":[23],"results":[26,94,186],"regarding":[27,187],"security":[29],"oriented-curves":[31],"isogeny-based":[33],"cryptography.":[34],"Under":[35],"Deuring":[37],"correspondence,":[38],"it":[39,137],"can":[40],"be":[41],"expressed":[42],"purely":[43],"terms":[45],"quaternion":[47],"and":[48,112,124,247,266],"boils":[49],"down":[50],"representing":[52],"integers":[53],"by":[54,95,297],"ternary":[55],"quadratic":[56,74],"forms.":[57],"Our":[58,89],"main":[59],"contribution":[60],"show":[63,249,303],"that":[64,250,305],"there":[65,278],"exist":[66,279],"efficient":[67],"solve":[70],"this":[71,97,199],"for":[73,177,251,276],"orders":[75],"discriminant":[77],"n":[78,153,180],"up":[79],"O":[81,100,105,151,170],"(":[82,101,106,152,171],"p":[83,102,107,158,172],"4":[84,108,156],"/":[85,109,155,157,174],"3":[86,110,154,175],")":[87,103,111,159,176],".":[88,181],"approach":[90],"improves":[91],"upon":[92],"previous":[93],"increasing":[96],"bound":[98],"from":[99,207],"removing":[113,214],"some":[114],"heuristics.":[115],"We":[116,182],"introduce":[117,184],"variants":[119,149],"our":[121,148,259,306],"new":[122,260],"algorithm":[123,282],"provide":[125],"a":[126,167,201,224,252,280,298],"careful":[127],"analysis":[128],"their":[130],"asymptotic":[131,143],"running":[132],"time":[133],"(without":[134],"heuristic":[135,164],"when":[136,292],"possible).":[139],"The":[140,162,195],"best":[141,163],"proven":[142],"complexity":[144,168],"one":[146],"average.":[161],"variant":[165],"has":[166],"1":[173],"big":[178],"enough":[179],"then":[183],"ideals":[191],"between":[192,235],"oriented":[193,296],"orders.":[194],"first":[196],"application":[197],"simplification":[202],"known":[205],"reduction":[206],"vectorization":[208],"computing":[210,232,242],"ring,":[213],"assumption":[216],"on":[217,263],"factorization":[219],"discriminant.":[222],"As":[223],"second":[225],"application,":[226],"we":[227,248,290,302],"relate":[228],"fixed-degree":[233],"isogenies":[234,312],"curves":[237,294],"rings,":[246],"large":[253],"range":[254,272],"degree":[256,274,300],"d":[257,275],",":[258],"improve":[262],"state-of-the-art,":[265],"important":[268],"special":[269,288],"cases,":[270],"which":[277],"polynomial-time":[281],"increased.":[284],"In":[285],"most":[287],"case":[289],"consider,":[291],"both":[293],"are":[295],"small":[299],"endomorphism,":[301],"heuristically":[304],"techniques":[307],"allow":[308],"any":[314],"degree,":[315],"assuming":[316],"they":[317],"exist.":[318]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2}],"updated_date":"2026-08-23T07:36:19.812096","created_date":"2025-10-10T00:00:00"}
