{"id":"https://openalex.org/W2792649521","doi":"https://doi.org/10.1137/18m1173708","title":"On Cycles of Pairing-Friendly Elliptic Curves","display_name":"On Cycles of Pairing-Friendly Elliptic Curves","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2792649521","doi":"https://doi.org/10.1137/18m1173708","mag":"2792649521"},"language":"en","primary_location":{"id":"doi:10.1137/18m1173708","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1173708","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1803.02067","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101591310","display_name":"Alessandro Chiesa","orcid":"https://orcid.org/0000-0002-3029-2353"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alessandro Chiesa","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059391636","display_name":"Lynn Chua","orcid":"https://orcid.org/0000-0002-5252-5277"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lynn Chua","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5020153944","display_name":"Matthew Weidner","orcid":"https://orcid.org/0000-0003-0701-7676"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matthew Weidner","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101591310"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1445,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54738423,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"3","issue":"2","first_page":"175","last_page":"192"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9991000294685364,"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":0.9785000085830688,"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/elliptic-curve","display_name":"Elliptic curve","score":0.7698918581008911},{"id":"https://openalex.org/keywords/pairing","display_name":"Pairing","score":0.7697051167488098},{"id":"https://openalex.org/keywords/supersingular-elliptic-curve","display_name":"Supersingular elliptic curve","score":0.7003178596496582},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.6459509134292603},{"id":"https://openalex.org/keywords/tripling-oriented-doche\u2013icart\u2013kohel-curve","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","score":0.5971319079399109},{"id":"https://openalex.org/keywords/edwards-curve","display_name":"Edwards curve","score":0.554621696472168},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5499123334884644},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.5256620049476624},{"id":"https://openalex.org/keywords/twists-of-curves","display_name":"Twists of curves","score":0.48603254556655884},{"id":"https://openalex.org/keywords/elliptic-curve-point-multiplication","display_name":"Elliptic curve point multiplication","score":0.4710614085197449},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4638068675994873},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4506363272666931},{"id":"https://openalex.org/keywords/modular-elliptic-curve","display_name":"Modular elliptic curve","score":0.4275626838207245},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33806583285331726},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28337740898132324},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1954217553138733},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1861284077167511},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.07665380835533142},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.07656082510948181},{"id":"https://openalex.org/keywords/quarter-period","display_name":"Quarter period","score":0.07597494125366211},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06428202986717224}],"concepts":[{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.7698918581008911},{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.7697051167488098},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.7003178596496582},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.6459509134292603},{"id":"https://openalex.org/C37055786","wikidata":"https://www.wikidata.org/wiki/Q7843607","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","level":5,"score":0.5971319079399109},{"id":"https://openalex.org/C92727272","wikidata":"https://www.wikidata.org/wiki/Q3001190","display_name":"Edwards curve","level":5,"score":0.554621696472168},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5499123334884644},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.5256620049476624},{"id":"https://openalex.org/C131182338","wikidata":"https://www.wikidata.org/wiki/Q7858596","display_name":"Twists of curves","level":5,"score":0.48603254556655884},{"id":"https://openalex.org/C117121985","wikidata":"https://www.wikidata.org/wiki/Q78380999","display_name":"Elliptic curve point multiplication","level":3,"score":0.4710614085197449},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4638068675994873},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4506363272666931},{"id":"https://openalex.org/C73683783","wikidata":"https://www.wikidata.org/wiki/Q2728886","display_name":"Modular elliptic curve","level":4,"score":0.4275626838207245},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33806583285331726},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28337740898132324},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1954217553138733},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1861284077167511},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.07665380835533142},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.07656082510948181},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.07597494125366211},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06428202986717224},{"id":"https://openalex.org/C54101563","wikidata":"https://www.wikidata.org/wiki/Q124131","display_name":"Superconductivity","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/18m1173708","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1173708","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1803.02067","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.02067","pdf_url":"https://arxiv.org/pdf/1803.02067","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:2792649521","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1803.02067","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":"doi:10.48550/arxiv.1803.02067","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1803.02067","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:1803.02067","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.02067","pdf_url":"https://arxiv.org/pdf/1803.02067","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/10","display_name":"Reduced inequalities","score":0.699999988079071}],"awards":[],"funders":[{"id":"https://openalex.org/F4320309411","display_name":"University of California Berkeley","ror":"https://ror.org/01an7q238"},{"id":"https://openalex.org/F4320333609","display_name":"Center for Long-Term Cybersecurity, University of California Berkeley","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2792649521.pdf","grobid_xml":"https://content.openalex.org/works/W2792649521.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1534733761","https://openalex.org/W1553083934","https://openalex.org/W1632722589","https://openalex.org/W1751074114","https://openalex.org/W1972442530","https://openalex.org/W1976677460","https://openalex.org/W1979485530","https://openalex.org/W1992402139","https://openalex.org/W1998368731","https://openalex.org/W2021553056","https://openalex.org/W2046569422","https://openalex.org/W2048054397","https://openalex.org/W2060770809","https://openalex.org/W2064804790","https://openalex.org/W2065422049","https://openalex.org/W2086042811","https://openalex.org/W2094556471","https://openalex.org/W2111310412","https://openalex.org/W2115148615","https://openalex.org/W2146075438","https://openalex.org/W2154290215","https://openalex.org/W2322172566","https://openalex.org/W2520031446","https://openalex.org/W2949714594","https://openalex.org/W2964305900","https://openalex.org/W3103821194"],"related_works":["https://openalex.org/W3178388692","https://openalex.org/W2794946234","https://openalex.org/W152994624","https://openalex.org/W1606363966","https://openalex.org/W2952273294","https://openalex.org/W2060617325","https://openalex.org/W158399888","https://openalex.org/W2950305215","https://openalex.org/W1606497022","https://openalex.org/W152760121","https://openalex.org/W140978788","https://openalex.org/W1497868643","https://openalex.org/W3011736806","https://openalex.org/W2952704881","https://openalex.org/W190585531","https://openalex.org/W1579045487","https://openalex.org/W1998927873","https://openalex.org/W1561702390","https://openalex.org/W2163690335","https://openalex.org/W3014116874"],"abstract_inverted_index":{"A":[0],"cycle":[1,75],"of":[2,8,18,28,31,33,43,67,76,80,91,98,104,118,129,144],"elliptic":[3,9,44,132],"curves":[4,10,45,119,133,145],"is":[5,23,50],"a":[6,37,73],"list":[7],"over":[11],"finite":[12],"fields":[13],"such":[14],"that":[15,110,127,138],"the":[16,26,29,34,65,86,121,148],"number":[17],"points":[19],"on":[20],"one":[21],"curve":[22,49],"equal":[24],"to":[25],"size":[27],"field":[30],"definition":[32],"next,":[35],"in":[36,46,58,63],"cyclic":[38],"way.":[39],"We":[40,71,94,108,136],"study":[41],"cycles":[42,89,97,112,128,142],"which":[47],"every":[48],"pairing-friendly.":[51],"These":[52],"have":[53],"recently":[54],"found":[55],"notable":[56],"applications":[57],"pairing-based":[59],"cryptography,":[60],"for":[61,88,101],"instance,":[62],"improving":[64],"scalability":[66],"distributed":[68],"ledger":[69],"technologies.":[70],"construct":[72],"new":[74],"length":[77,99],"4":[78],"consisting":[79,90,143],"MNT":[81,92],"curves,":[82],"and":[83,126],"characterize":[84],"all":[85],"possibilities":[87],"curves.":[93],"rule":[95],"out":[96],"2":[100],"particular":[102],"choices":[103],"small":[105],"embedding":[106],"degrees.":[107],"show":[109,137],"long":[111],"cannot":[113,134],"be":[114],"constructed":[115],"from":[116,146],"families":[117],"with":[120],"same":[122],"complex":[123],"multiplication":[124],"discriminant,":[125],"composite":[130],"order":[131],"exist.":[135],"there":[139],"are":[140],"no":[141],"only":[147],"Freeman":[149],"or":[150],"Barreto--Naehrig":[151],"families.":[152]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}