{"id":"https://openalex.org/W2079198712","doi":"https://doi.org/10.3934/amc.2010.4.307","title":"Invalid-curve attacks on (hyper)elliptic curve cryptosystems","display_name":"Invalid-curve attacks on (hyper)elliptic curve cryptosystems","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2079198712","doi":"https://doi.org/10.3934/amc.2010.4.307","mag":"2079198712"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2010.4.307","is_oa":false,"landing_page_url":"https://doi.org/10.3934/amc.2010.4.307","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087800081","display_name":"Koray Karabina","orcid":"https://orcid.org/0000-0001-9538-8877"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Koray Karabina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5024282315","display_name":"Berkant Ustao\u011flu","orcid":"https://orcid.org/0000-0002-0411-9389"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Berkant Ustaoglu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7136,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.83561183,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"4","issue":"3","first_page":"307","last_page":"321"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9923999905586243,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.982200026512146,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8230992555618286},{"id":"https://openalex.org/keywords/hyperelliptic-curve","display_name":"Hyperelliptic curve","score":0.7626364827156067},{"id":"https://openalex.org/keywords/hyperelliptic-curve-cryptography","display_name":"Hyperelliptic curve cryptography","score":0.7030115127563477},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.632784903049469},{"id":"https://openalex.org/keywords/hessian-form-of-an-elliptic-curve","display_name":"Hessian form of an elliptic curve","score":0.6289770603179932},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.6123058199882507},{"id":"https://openalex.org/keywords/jacobian-curve","display_name":"Jacobian curve","score":0.5750385522842407},{"id":"https://openalex.org/keywords/tripling-oriented-doche\u2013icart\u2013kohel-curve","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","score":0.45416268706321716},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4536757171154022},{"id":"https://openalex.org/keywords/supersingular-elliptic-curve","display_name":"Supersingular elliptic curve","score":0.4120079278945923},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.38277575373649597},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.30006954073905945},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.2807338237762451},{"id":"https://openalex.org/keywords/quarter-period","display_name":"Quarter period","score":0.14565509557724},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.1296149492263794},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11949402093887329},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.04396602511405945}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8230992555618286},{"id":"https://openalex.org/C11074058","wikidata":"https://www.wikidata.org/wiki/Q850110","display_name":"Hyperelliptic curve","level":3,"score":0.7626364827156067},{"id":"https://openalex.org/C166780011","wikidata":"https://www.wikidata.org/wiki/Q3005926","display_name":"Hyperelliptic curve cryptography","level":5,"score":0.7030115127563477},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.632784903049469},{"id":"https://openalex.org/C104993295","wikidata":"https://www.wikidata.org/wiki/Q17023345","display_name":"Hessian form of an elliptic curve","level":5,"score":0.6289770603179932},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.6123058199882507},{"id":"https://openalex.org/C79993320","wikidata":"https://www.wikidata.org/wiki/Q6119657","display_name":"Jacobian curve","level":5,"score":0.5750385522842407},{"id":"https://openalex.org/C37055786","wikidata":"https://www.wikidata.org/wiki/Q7843607","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","level":5,"score":0.45416268706321716},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4536757171154022},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.4120079278945923},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.38277575373649597},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.30006954073905945},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2807338237762451},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.14565509557724},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.1296149492263794},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11949402093887329},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.04396602511405945},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2010.4.307","is_oa":false,"landing_page_url":"https://doi.org/10.3934/amc.2010.4.307","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W239595814","https://openalex.org/W1488807031","https://openalex.org/W1566347835","https://openalex.org/W1592482282","https://openalex.org/W1602301309","https://openalex.org/W1857035554","https://openalex.org/W1950989567","https://openalex.org/W1969728959","https://openalex.org/W2005317356","https://openalex.org/W2009435168","https://openalex.org/W2013383029","https://openalex.org/W2022862710","https://openalex.org/W2037090944","https://openalex.org/W2064281699","https://openalex.org/W2076965705","https://openalex.org/W2090963060","https://openalex.org/W2092705148","https://openalex.org/W2100059641","https://openalex.org/W2117455301","https://openalex.org/W2135654420","https://openalex.org/W2161850389","https://openalex.org/W2172194269"],"related_works":["https://openalex.org/W2188057592","https://openalex.org/W2496249880","https://openalex.org/W1530096792","https://openalex.org/W4283814357","https://openalex.org/W2563539030","https://openalex.org/W4383499643","https://openalex.org/W2953939619","https://openalex.org/W4390117011","https://openalex.org/W2062791219","https://openalex.org/W2546557231"],"abstract_inverted_index":{"We":[0,15,41],"extend":[1],"the":[2,37,80],"notion":[3],"of":[4,36,39,63],"an":[5],"invalid-curve":[6,27],"attack":[7],"from":[8],"elliptic":[9],"curvesto":[10],"genus":[11,64],"2":[12],"hyperelliptic":[13,54,66],"curves.":[14,55],"also":[16],"show":[17,43],"that":[18,44,76],"invalid":[19],"singular":[20],"(hyper)ellipticcurves":[21],"can":[22],"be":[23],"used":[24],"in":[25,51],"mounting":[26],"attacks":[28],"on":[29,53],"(hyper)elliptic":[30],"curvecryptosystems,":[31],"and":[32],"make":[33],"quantitative":[34],"estimates":[35],"practicality":[38],"theseattacks.":[40],"thereby":[42],"proper":[45],"key":[46],"validation":[47],"is":[48,77],"necessary":[49],"even":[50],"cryptosystemsbased":[52],"As":[56],"a":[57,69,73],"byproduct,":[58],"we":[59],"enumerate":[60],"theisomorphism":[61],"classes":[62],"g":[65],"curves":[67],"over":[68],"finite":[70],"field":[71],"by":[72],"newcounting":[74],"argument":[75],"simpler":[78],"than":[79],"previous":[81],"methods.":[82]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}