{"id":"https://openalex.org/W4377193753","doi":"https://doi.org/10.1142/s1793830923500544","title":"Faster optimal ate pairings for cyclotomic sparse families of pairing-friendly elliptic curves with embedding degrees k = 5,7","display_name":"Faster optimal ate pairings for cyclotomic sparse families of pairing-friendly elliptic curves with embedding degrees k = 5,7","publication_year":2023,"publication_date":"2023-05-22","ids":{"openalex":"https://openalex.org/W4377193753","doi":"https://doi.org/10.1142/s1793830923500544"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830923500544","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830923500544","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5091987151","display_name":"Senegue Gomez Nyamsi","orcid":"https://orcid.org/0000-0002-2954-201X"},"institutions":[{"id":"https://openalex.org/I178331978","display_name":"Universit\u00e9 de Dschang","ror":"https://ror.org/0566t4z20","country_code":"CM","type":"education","lineage":["https://openalex.org/I178331978"]}],"countries":["CM"],"is_corresponding":true,"raw_author_name":"Senegue Gomez Nyamsi","raw_affiliation_strings":["Department of Mathematics and Computer Science, The University of Dschang, P. O. Box 67, Dschang, Cameroon"],"raw_orcid":"https://orcid.org/0000-0002-2954-201X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, The University of Dschang, P. O. Box 67, Dschang, Cameroon","institution_ids":["https://openalex.org/I178331978"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052689003","display_name":"Emmanuel Fouotsa","orcid":"https://orcid.org/0000-0002-7729-0419"},"institutions":[{"id":"https://openalex.org/I263774594","display_name":"University of Bamenda","ror":"https://ror.org/031ahrf94","country_code":"CM","type":"education","lineage":["https://openalex.org/I263774594"]}],"countries":["CM"],"is_corresponding":false,"raw_author_name":"Emmanuel Fouotsa","raw_affiliation_strings":["Department of Mathematics, Higher Teacher Training College, The University of Bamenda, P. O. Box 39, Bambili, Cameroon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Higher Teacher Training College, The University of Bamenda, P. O. Box 39, Bambili, Cameroon","institution_ids":["https://openalex.org/I263774594"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053629811","display_name":"Calvin Tcheka","orcid":"https://orcid.org/0000-0003-3086-7302"},"institutions":[{"id":"https://openalex.org/I178331978","display_name":"Universit\u00e9 de Dschang","ror":"https://ror.org/0566t4z20","country_code":"CM","type":"education","lineage":["https://openalex.org/I178331978"]}],"countries":["CM"],"is_corresponding":false,"raw_author_name":"Calvin Tcheka","raw_affiliation_strings":["Department of Mathematics and Computer Science, The University of Dschang, P. O. Box 67, Dschang, Cameroon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, The University of Dschang, P. O. Box 67, Dschang, Cameroon","institution_ids":["https://openalex.org/I178331978"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091987151"],"corresponding_institution_ids":["https://openalex.org/I178331978"],"apc_list":null,"apc_paid":null,"fwci":0.8221,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.7667855,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"16","issue":"05","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":0.9923999905586243,"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":0.9923999905586243,"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":0.9782999753952026,"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/pairing","display_name":"Pairing","score":0.8575859069824219},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6583173274993896},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5738658905029297},{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.5534404516220093},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.544283390045166},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4557073712348938},{"id":"https://openalex.org/keywords/family-of-curves","display_name":"Family of curves","score":0.41669604182243347},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36235466599464417},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35410451889038086},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3271191716194153},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30652928352355957},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26232513785362244},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.188745379447937},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15208733081817627},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14134874939918518},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07880198955535889}],"concepts":[{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.8575859069824219},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6583173274993896},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5738658905029297},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.5534404516220093},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.544283390045166},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4557073712348938},{"id":"https://openalex.org/C53622353","wikidata":"https://www.wikidata.org/wiki/Q1518913","display_name":"Family of curves","level":2,"score":0.41669604182243347},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36235466599464417},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35410451889038086},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3271191716194153},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30652928352355957},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26232513785362244},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.188745379447937},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15208733081817627},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14134874939918518},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07880198955535889},{"id":"https://openalex.org/C54101563","wikidata":"https://www.wikidata.org/wiki/Q124131","display_name":"Superconductivity","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830923500544","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830923500544","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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":24,"referenced_works":["https://openalex.org/W9592995","https://openalex.org/W129300768","https://openalex.org/W1532836984","https://openalex.org/W1553871775","https://openalex.org/W1905774212","https://openalex.org/W1974049704","https://openalex.org/W2014239329","https://openalex.org/W2114428623","https://openalex.org/W2152924492","https://openalex.org/W2164056221","https://openalex.org/W2170274287","https://openalex.org/W2296489817","https://openalex.org/W2326003419","https://openalex.org/W2736126599","https://openalex.org/W2737042076","https://openalex.org/W2769087919","https://openalex.org/W2789331349","https://openalex.org/W2947480871","https://openalex.org/W3011736806","https://openalex.org/W3037250204","https://openalex.org/W3215995789","https://openalex.org/W4200530946","https://openalex.org/W4283382856","https://openalex.org/W4296870987"],"related_works":["https://openalex.org/W192788341","https://openalex.org/W2400487092","https://openalex.org/W2952575986","https://openalex.org/W179888710","https://openalex.org/W4319323581","https://openalex.org/W2950832472","https://openalex.org/W1553871775","https://openalex.org/W2401618370","https://openalex.org/W2949714594","https://openalex.org/W1904757850"],"abstract_inverted_index":{"Nowadays,":[0],"pairing-based":[1],"cryptography":[2],"researchers":[3],"are":[4],"looking":[5],"for":[6,9,30],"new":[7,15,28],"parameters":[8,29],"standard":[10],"security":[11,106],"levels":[12],"against":[13],"the":[14,70,74,92,96,99,104,131],"number":[16,20],"field":[17,21],"sieve":[18,22],"tower":[19],"algorithm.":[23],"Recently,":[24],"they":[25],"have":[26],"suggested":[27],"well-studied":[31],"pairing-friendly":[32],"curves":[33,54,90,111,139],"with":[34,58],"odd":[35],"embedding":[36,59,113,141],"degrees":[37,60,114,142],"five":[38,61,115,143],"and":[39,62,73,116,125,144],"seven":[40],"resistant":[41],"to":[42,68,109],"this":[43,46],"attack.":[44],"In":[45],"paper,":[47],"we":[48],"define":[49],"optimal":[50,100,132],"ate":[51,101,133],"pairing":[52,102,134],"on":[53,137],"using":[55,77],"sparse":[56],"families":[57,88],"seven.":[63,117],"We":[64],"also":[65],"provide":[66],"details":[67],"perform":[69],"miller":[71],"loop":[72],"final":[75],"exponentiation":[76],"addition":[78],"chain":[79],"process.":[80],"Our":[81],"theoretical":[82],"results":[83],"costs":[84],"indicate":[85],"that":[86],"these":[87],"of":[89,98,112,140],"offer":[91],"best":[93],"performance":[94],"in":[95],"computation":[97],"at":[103],"128-bit":[105],"level":[107],"compared":[108],"Cocks\u2013Pinch":[110,138],"The":[118],"improvement":[119],"is":[120],"about":[121],"[Formula:":[122,126],"see":[123,127],"text]":[124,128],"faster":[129],"than":[130],"previously":[135],"computed":[136],"seven,":[145],"respectively.":[146]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}