{"id":"https://openalex.org/W4414017194","doi":"https://doi.org/10.46586/tches.v2025.i4.848-872","title":"Fast AVX-512 Implementation of the Optimal Ate Pairing on BLS12-381","display_name":"Fast AVX-512 Implementation of the Optimal Ate Pairing on BLS12-381","publication_year":2025,"publication_date":"2025-09-05","ids":{"openalex":"https://openalex.org/W4414017194","doi":"https://doi.org/10.46586/tches.v2025.i4.848-872"},"language":"en","primary_location":{"id":"doi:10.46586/tches.v2025.i4.848-872","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tches.v2025.i4.848-872","pdf_url":"https://tches.iacr.org/index.php/TCHES/article/download/12431/12159","source":{"id":"https://openalex.org/S4210207404","display_name":"IACR Transactions on Cryptographic Hardware and Embedded Systems","issn_l":"2569-2925","issn":["2569-2925"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"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 Transactions on Cryptographic Hardware and Embedded Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://tches.iacr.org/index.php/TCHES/article/download/12431/12159","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101350065","display_name":"Hao Cheng","orcid":"https://orcid.org/0000-0002-4539-3034"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]},{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Cheng","raw_affiliation_strings":["School of Cyber Science and Technology, Shandong University, Qingdao, China; State Key Laboratory of Cryptography and Digital Economy Security, Shandong University, Qingdao, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China","Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China","School of Cyber Science and Technology, Shandong University, Qingdao, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Cyber Science and Technology, Shandong University, Qingdao, China; State Key Laboratory of Cryptography and Digital Economy Security, Shandong University, Qingdao, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China","institution_ids":["https://openalex.org/I4210132990"]},{"raw_affiliation_string":"Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China","institution_ids":["https://openalex.org/I154099455","https://openalex.org/I4210132990"]},{"raw_affiliation_string":"School of Cyber Science and Technology, Shandong University, Qingdao, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085923495","display_name":"Georgios Fotiadis","orcid":"https://orcid.org/0000-0001-9699-3817"},"institutions":[{"id":"https://openalex.org/I163151358","display_name":"Cyprus University of Technology","ror":"https://ror.org/05qt8tf94","country_code":"CY","type":"education","lineage":["https://openalex.org/I163151358"]},{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]},{"id":"https://openalex.org/I4210104221","display_name":"Limassol General Hospital","ror":"https://ror.org/00v7z6m55","country_code":"CY","type":"healthcare","lineage":["https://openalex.org/I4210104221","https://openalex.org/I4210137065"]}],"countries":["CY","LU"],"is_corresponding":false,"raw_author_name":"Georgios Fotiadis","raw_affiliation_strings":["=nil; Foundation, Limassol, Cyprus; DCS and SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg","DCS and SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg","Foundation, Limassol, Cyprus"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"=nil; Foundation, Limassol, Cyprus; DCS and SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg","institution_ids":["https://openalex.org/I186903577"]},{"raw_affiliation_string":"DCS and SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg","institution_ids":["https://openalex.org/I186903577"]},{"raw_affiliation_string":"Foundation, Limassol, Cyprus","institution_ids":["https://openalex.org/I163151358","https://openalex.org/I4210104221"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089125756","display_name":"Johann Gro\u00dfsch\u00e4dl","orcid":"https://orcid.org/0009-0006-3210-3102"},"institutions":[{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]}],"countries":["LU"],"is_corresponding":false,"raw_author_name":"Johann Gro\u00dfsch\u00e4dl","raw_affiliation_strings":["DCS and SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DCS and SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082511819","display_name":"Daniel Page","orcid":"https://orcid.org/0000-0002-6366-7641"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Daniel Page","raw_affiliation_strings":["School of Computer Science, University of Bristol, Bristol, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Bristol, Bristol, UK","institution_ids":["https://openalex.org/I36234482"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7823,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.8869289,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"2025","issue":"4","first_page":"848","last_page":"872"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9975000023841858,"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":0.9975000023841858,"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/T11181","display_name":"Advanced Data Storage Technologies","score":0.9641000032424927,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.5854390859603882},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4787799119949341},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.436318039894104},{"id":"https://openalex.org/keywords/nuclear-physics","display_name":"Nuclear physics","score":0.3751492202281952},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.37085670232772827},{"id":"https://openalex.org/keywords/superconductivity","display_name":"Superconductivity","score":0.07859727740287781}],"concepts":[{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.5854390859603882},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4787799119949341},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.436318039894104},{"id":"https://openalex.org/C185544564","wikidata":"https://www.wikidata.org/wiki/Q81197","display_name":"Nuclear physics","level":1,"score":0.3751492202281952},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.37085670232772827},{"id":"https://openalex.org/C54101563","wikidata":"https://www.wikidata.org/wiki/Q124131","display_name":"Superconductivity","level":2,"score":0.07859727740287781},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.46586/tches.v2025.i4.848-872","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tches.v2025.i4.848-872","pdf_url":"https://tches.iacr.org/index.php/TCHES/article/download/12431/12159","source":{"id":"https://openalex.org/S4210207404","display_name":"IACR Transactions on Cryptographic Hardware and Embedded Systems","issn_l":"2569-2925","issn":["2569-2925"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"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 Transactions on Cryptographic Hardware and Embedded Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:25f095e0c0ac4e799e671f5d0c13ff48","is_oa":true,"landing_page_url":"https://doaj.org/article/25f095e0c0ac4e799e671f5d0c13ff48","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Transactions on Cryptographic Hardware and Embedded Systems, Vol 2025, Iss 4 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46586/tches.v2025.i4.848-872","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tches.v2025.i4.848-872","pdf_url":"https://tches.iacr.org/index.php/TCHES/article/download/12431/12159","source":{"id":"https://openalex.org/S4210207404","display_name":"IACR Transactions on Cryptographic Hardware and Embedded Systems","issn_l":"2569-2925","issn":["2569-2925"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"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 Transactions on Cryptographic Hardware and Embedded Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4613589738","display_name":null,"funder_award_id":"16326754","funder_id":"https://openalex.org/F4320321038","funder_display_name":"Fonds National de la Recherche Luxembourg"}],"funders":[{"id":"https://openalex.org/F4320321038","display_name":"Fonds National de la Recherche Luxembourg","ror":"https://ror.org/039z13y21"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414017194.pdf","grobid_xml":"https://content.openalex.org/works/W4414017194.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885"],"abstract_inverted_index":{"Non-degenerate":[0],"bilinear":[1],"maps":[2],"on":[3,159,244],"elliptic":[4],"curves,":[5],"commonly":[6],"referred":[7],"to":[8,47,109,180,202,342],"as":[9,34,217,219],"pairings,":[10],"have":[11,75],"many":[12],"applications":[13],"including":[14],"short":[15],"signature":[16],"schemes,":[17],"zero-knowledge":[18],"proofs":[19],"and":[20,62,95,129,196,215,229,252],"remote":[21],"attestation":[22],"protocols.":[23],"Computing":[24],"a":[25,70,135,150,188],"state-of-the-art":[26,93],"pairing":[27,38,73,124,158,238],"at":[28],"the":[29,35,40,48,59,66,79,88,107,114,121,155,165,168,208,269,273,284,289,297,327],"128-bit":[30],"security":[31],"level,":[32],"such":[33,134],"optimal":[36,122,156],"ate":[37,123,157],"over":[39],"curve":[41],"BLS12-381,":[42],"is":[43,101,167,311,336],"very":[44],"costly":[45],"due":[46],"high":[49],"complexity":[50],"of":[51,53,83,87,92,116,120,154,164,170,199,305,333],"some":[52,226],"its":[54],"sub-operations:":[55],"most":[56],"notable":[57],"are":[58,140,178],"Miller":[60],"loop":[61],"final":[63,285],"exponentiation.":[64,286],"In":[65],"past":[67],"ten":[68],"years,":[69],"few":[71],"optimized":[72],"implementations":[74],"been":[76],"introduced":[77],"in":[78,187,207,283,349],"literature,":[80],"but":[81],"none":[82],"those":[84],"took":[85],"advantage":[86],"vector":[89],"(SIMD)":[90],"extensions":[91],"Intel":[94,246],"AMD":[96],"CPUs,":[97],"especially":[98],"AVX-512;":[99],"this":[100],"surprising,":[102],"because":[103],"doing":[104],"so":[105],"offers":[106],"potential":[108],"reach":[110],"significant":[111],"speed-ups.":[112],"Consequently,":[113],"questions":[115,147],"1)":[117],"how":[118,230],"computation":[119],"can":[125,138],"be":[126],"effectively":[127],"vectorized,":[128],"2)":[130],"what":[131],"execution":[132,233,303],"time":[133,304],"vectorized":[136],"implementation":[137,153,166,295,322],"achieve":[139],"still":[141],"open.":[142],"This":[143],"paper":[144],"addresses":[145],"said":[146],"by":[148,325,338],"introducing":[149],"carefully-optimized":[151],"AVX-512":[152],"BLS12-381.":[160],"A":[161],"central":[162],"feature":[163],"use":[169],"8-way":[171],"Integer":[172],"Fused":[173],"Multiply-Add":[174],"(IFMA)":[175],"instructions,":[176,348],"which":[177,240,310,345],"capable":[179],"execute":[181],"eight":[182],"52":[183],"x":[184],"52-bit":[185],"multiplications":[186],"SIMD-parallel":[189],"fashion.":[190],"We":[191,235],"introduce":[192],"new":[193],"vectorization":[194],"strategies":[195],"describe":[197],"optimizations":[198],"existing":[200],"ones":[201],"speed":[203],"up":[204],"arithmetic":[205],"operations":[206],"extension":[209],"fields":[210],"Fp4":[211],",":[212,214],"Fp6":[213],"Fp12":[216],"well":[218],"certain":[220],"higher-level":[221],"functions.":[222],"Furthermore,":[223],"we":[224,241],"discuss":[225],"parallelization":[227],"bottlenecks":[228],"they":[231],"impact":[232],"time.":[234],"benchmarked":[236],"our":[237],"software,":[239],"call":[242],"avxbls,":[243],"an":[245,302],"Core":[247],"i3-1005G1":[248],"(\u201cIce":[249],"Lake\u201d)":[250],"CPU":[251],"found":[253],"that":[254],"it":[255],"needs":[256],"1,":[257,263],"265,":[258],"314":[259],"clock":[260,266],"cycles":[261],"(resp.":[262,277,314],"195,":[264],"236":[265],"cycles)":[267],"for":[268],"full":[270],"pairing,":[271],"with":[272],"Granger-Scott":[274],"cyclotomic":[275,279],"squaring":[276],"compressed":[278],"squaring)":[280],"being":[281],"used":[282],"For":[287],"comparison,":[288],"non-vectorized":[290],"(i.e.,":[291],"scalar)":[292],"x64":[293],"assembly":[294],"from":[296],"widely-used":[298],"blst":[299],"library":[300],"has":[301],"2,":[306],"351,":[307],"615":[308],"cycles,":[309],"1.86":[312],"times":[313],"1.97":[315],"times)":[316],"slower.":[317],"avxbls":[318],"also":[319],"outperforms":[320],"Longa\u2019s":[321],"(CHES":[323],"2023)":[324],"almost":[326],"same":[328],"factor.":[329],"The":[330],"practical":[331],"importance":[332],"these":[334],"results":[335],"amplified":[337],"Intel\u2019s":[339],"recent":[340],"announcement":[341],"support":[343],"AVX10,":[344],"includes":[346],"IFMA":[347],"all":[350],"future":[351],"CPUs.":[352]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}