[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8,"_9":10},"actionData","errors","root",{"_243":244},"routes/_layout",{"_11":163},"routes/entity.$type.$id",{"_11":12,"_13":14,"_15":16,"_17":18,"_19":20,"_21":22,"_23":24,"_25":26,"_27":28},"dehydratedState",{"_73":74,"_75":76},"type","paper","id","paper_W2296489817","section","authors","entity",{"_15":16,"_29":30,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":38,"_39":-5,"_40":41,"_42":43,"_44":45,"_46":47,"_48":-5,"_49":50,"_51":30,"_52":53,"_54":55,"_56":57,"_58":59,"_60":61,"_18":-5,"_62":63,"_64":65,"_66":67,"_68":30,"_69":-5},"canonical","https://www.hugmap.com/entity/paper/paper_W2296489817/authors","siteBaseUrl","https://www.hugmap.com","sectionCount",1,"jsonLd","{\"@context\":\"https://schema.org\",\"@graph\":[{\"name\":\"Optimal Pairings\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W2296489817/authors\",\"@type\":\"ScholarlyArticle\",\"headline\":\"Optimal Pairings\",\"datePublished\":\"2010-01-01\",\"isPartOf\":{\"@type\":\"Periodical\",\"name\":\"IEEE Transactions on Information Theory\"}},{\"@type\":\"CollectionPage\",\"name\":\"Optimal Pairings 作者\",\"description\":\"Optimal Pairings 在 HugMap 中的作者，共 1 条，含结构化关联信息与详情链接。\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W2296489817/authors\",\"inLanguage\":\"zh-CN\"},{\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"首页\",\"item\":\"https://www.hugmap.com/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"论文\",\"item\":\"https://www.hugmap.com/search?type=paper\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Optimal Pairings\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W2296489817\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"作者\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W2296489817/authors\"}]}]}","name","Optimal Pairings","nameZh","aliases","description","descriptionZh","status","active","externalIds","{\"openalex\":\"W2296489817\",\"doi\":\"10.1109/tit.2009.2034881\"}","properties","source","openalex","createdAt","2026-05-20T13:40:18.198873751","updatedAt","2026-05-20T13:41:37.184469105","doi","10.1109/tit.2009.2034881","arxivId","openalexId","W2296489817","title","abstractText","In this paper, we introduce the concept of an optimal pairing, which by definition can be computed using only log ₂ r /¿( k ) basic Miller iterations, with r the order of the groups involved and k the embedding degree. We describe an algorithm to construct optimal ate pairings on all parametrized families of pairing friendly elliptic curves. Finally, we conjecture that any nondegenerate pairing on an elliptic curve without efficiently computable endomorphisms different from powers of Frobenius requires at least log ₂ r /¿( k ) basic Miller iterations.","publishedDate","2010-01-01","publishedYear",2010,"venue","IEEE Transactions on Information Theory","citationCount",330,"keywords",[70,71,72],"pdfUrl","https://www.cosic.esat.kuleuven.be/publications/article-1039.pdf","topVenue",false,"displayName","displayDescription","Cryptography and Residue Arithmetic","Coding theory and cryptography","Polynomial and algebraic computation","mutations",[],"queries",[77],{"_78":79,"_80":81,"_82":83,"_84":85},"dehydratedAt",1783008311935,"state",{"_87":88,"_89":26,"_90":91,"_92":-5,"_93":94,"_95":94,"_96":94,"_97":-5,"_98":-5,"_99":67,"_35":100,"_101":102},"queryKey",[86,19,14,16],"queryHash","[\"portal\",\"entity\",\"paper\",\"paper_W2296489817\"]","portal","data",{"_19":20,"_103":104,"_105":106,"_107":108,"_109":110,"_111":112,"_18":113},"dataUpdateCount","dataUpdatedAt",1783008311934,"error","errorUpdateCount",0,"errorUpdatedAt","fetchFailureCount","fetchFailureReason","fetchMeta","isInvalidated","success","fetchStatus","idle","entityType","Paper","taxonomies",[130,131,132],"events",[],"articles",[],"technologies",[],[114],{"_15":115,"_29":116,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":117,"_39":-5,"_40":41,"_42":118,"_44":119,"_120":121,"_51":-5,"_122":-5,"_123":-5,"_124":-5,"_60":-5,"_125":-5,"_126":-5,"_127":-5,"_128":-5,"_129":-5,"_68":116,"_69":-5},"person_A5032574536","Fréderik Vercauteren","{\"openalex\":\"A5032574536\",\"orcid\":\"0000-0002-7208-9599\"}","2026-05-14T14:14:58.192067477","2026-05-22T10:47:36.207706976","orcid","0000-0002-7208-9599","affiliation","researchArea","paperCount","homepage","linkedin","twitter","github","hindex",{"_15":157,"_29":72,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":158,"_39":-5,"_40":41,"_42":159,"_44":160,"_137":138,"_139":-5,"_140":141,"_142":161,"_144":162,"_146":94,"_147":148,"_149":94,"_150":-5,"_68":72,"_69":-5},{"_15":151,"_29":71,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":152,"_39":-5,"_40":41,"_42":153,"_44":154,"_137":138,"_139":-5,"_140":141,"_142":155,"_144":156,"_146":94,"_147":148,"_149":94,"_150":-5,"_68":71,"_69":-5},{"_15":133,"_29":70,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":134,"_39":-5,"_40":41,"_42":135,"_44":136,"_137":138,"_139":-5,"_140":141,"_142":143,"_144":145,"_146":94,"_147":148,"_149":94,"_150":-5,"_68":70,"_69":-5},"tax_rd_T11693","{\"openalex_topic\":\"T11693\"}","2026-05-14T00:38:40.255799588","2026-05-23T12:39:45.260499977","taxonomyType","RESEARCH_DOMAIN","code","level",3,"parentId","tax_rd_1710","path","Physical Sciences/Computer Science/Information Systems/Cryptography and Residue Arithmetic","sortOrder","isLeaf",true,"entityCount","children","tax_rd_T11130","{\"openalex_topic\":\"T11130\"}","2026-05-14T00:38:28.617637813","2026-05-23T12:17:43.257915081","tax_rd_1702","Physical Sciences/Computer Science/Artificial Intelligence/Coding theory and cryptography","tax_rd_T11435","{\"openalex_topic\":\"T11435\"}","2026-05-14T00:32:34.27305505","2026-05-23T12:27:09.28297263","tax_rd_1703","Physical Sciences/Computer Science/Computational Theory and Mathematics/Polynomial and algebraic computation",{"_73":164,"_75":165},[],[166],{"_78":167,"_80":168,"_82":169,"_84":170},1783008310785,{"_87":172,"_89":26,"_90":167,"_92":-5,"_93":94,"_95":94,"_96":94,"_97":-5,"_98":-5,"_99":67,"_35":100,"_101":102},[86,171],"[\"portal\",\"industries\"]","industries",[173,174,175,176,177,178,179,180,181,182,183,184],{"_15":236,"_29":237,"_31":-5,"_32":238,"_33":239,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":188,"_42":-5,"_44":-5,"_137":189,"_139":-5,"_140":26,"_142":190,"_144":240,"_146":94,"_147":67,"_149":94,"_150":-5,"_68":237,"_69":239},{"_15":232,"_29":233,"_31":-5,"_32":-5,"_33":234,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":188,"_42":-5,"_44":-5,"_137":189,"_139":-5,"_140":26,"_142":190,"_144":235,"_146":94,"_147":67,"_149":94,"_150":-5,"_68":233,"_69":234},{"_15":226,"_29":227,"_31":-5,"_32":228,"_33":229,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":188,"_42":-5,"_44":-5,"_137":189,"_139":-5,"_140":26,"_142":190,"_144":230,"_146":94,"_147":67,"_149":94,"_150":-5,"_68":227,"_69":229},{"_15":222,"_29":223,"_31":-5,"_32":-5,"_33":224,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":188,"_42":-5,"_44":-5,"_137":189,"_139":-5,"_140":26,"_142":190,"_144":225,"_146":94,"_147":67,"_149":94,"_150":-5,"_68":223,"_69":224},{"_15":218,"_29":219,"_31":-5,"_32":-5,"_33":220,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":188,"_42":-5,"_44":-5,"_137":189,"_139":-5,"_140":26,"_142":190,"_144":221,"_146":94,"_147":67,"_149":94,"_150":-5,"_68":219,"_69":220},{"_15":212,"_29":213,"_31":-5,"_32":214,"_33":215,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":188,"_42":-5,"_44":-5,"_137":189,"_139":-5,"_140":26,"_142":190,"_144":216,"_146":94,"_147":67,"_149":94,"_150":-5,"_68":213,"_69":215},{"_15":208,"_29":209,"_31":-5,"_32":-5,"_33":210,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":188,"_42":-5,"_44":-5,"_137":189,"_139":-5,"_140":26,"_142":190,"_144":211,"_146":94,"_147":148,"_149":94,"_150":-5,"_68":209,"_69":210},{"_15":204,"_29":205,"_31":-5,"_32":-5,"_33":206,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":188,"_42":-5,"_44":-5,"_137":189,"_139":-5,"_140":26,"_142":190,"_144":207,"_146":94,"_147":67,"_149":94,"_150":-5,"_68":205,"_69":206},{"_15":200,"_29":201,"_31":-5,"_32":-5,"_33":202,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":188,"_42":-5,"_44":-5,"_137":189,"_139":-5,"_140":26,"_142":190,"_144":203,"_146":94,"_147":67,"_149":94,"_150":-5,"_68":201,"_69":202},{"_15":196,"_29":197,"_31":-5,"_32":-5,"_33":198,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":188,"_42":-5,"_44":-5,"_137":189,"_139":-5,"_140":26,"_142":190,"_144":199,"_146":94,"_147":67,"_149":94,"_150":-5,"_68":197,"_69":198},{"_15":192,"_29":193,"_31":-5,"_32":-5,"_33":194,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":188,"_42":-5,"_44":-5,"_137":189,"_139":-5,"_140":26,"_142":190,"_144":195,"_146":94,"_147":67,"_149":94,"_150":-5,"_68":193,"_69":194},{"_15":185,"_29":186,"_31":-5,"_32":-5,"_33":187,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":188,"_42":-5,"_44":-5,"_137":189,"_139":-5,"_140":26,"_142":190,"_144":191,"_146":94,"_147":67,"_149":94,"_150":-5,"_68":186,"_69":187},"tax_ind_smartphone","智能手机","Smartphone","manual","INDUSTRY","tax_ind_root","科技行业/智能手机","tax_ind_robot","机器人","Robotics","科技行业/机器人","tax_ind_wearable","智能穿戴","Smart Wearables","科技行业/智能穿戴","tax_ind_energy","新能源与智能制造","New Energy & Smart Manufacturing","科技行业/新能源与智能制造","tax_ind_biotech","生物科技","Biotech","科技行业/生物科技","tax_ind_quantum","量子计算","Quantum Computing","科技行业/量子计算","tax_ind_blockchain","区块链",[217],"Blockchain","科技行业/区块链","Web3","tax_ind_enterprise","企业软件","Enterprise Software","科技行业/企业软件","tax_ind_security","网络安全","Cybersecurity","科技行业/网络安全","tax_ind_semi","半导体",[231],"Semiconductor","科技行业/半导体","芯片","tax_ind_cloud","云计算","Cloud Computing","科技行业/云计算","tax_ind_ai","人工智能",[241,242],"Artificial Intelligence","科技行业/人工智能","AI","AI 技术","env",{"_245":24},"SITE_BASE_URL"]

Optimal Pairings 论文

Optimal Pairings · 作者