{"id":"https://openalex.org/W4405242258","doi":"https://doi.org/10.46586/tches.v2025.i1.275-313","title":"A High-performance NTT/MSM Accelerator for Zero-knowledge Proof Using Load-balanced Fully-pipelined Montgomery Multiplier","display_name":"A High-performance NTT/MSM Accelerator for Zero-knowledge Proof Using Load-balanced Fully-pipelined Montgomery Multiplier","publication_year":2024,"publication_date":"2024-12-09","ids":{"openalex":"https://openalex.org/W4405242258","doi":"https://doi.org/10.46586/tches.v2025.i1.275-313"},"language":"en","primary_location":{"id":"doi:10.46586/tches.v2025.i1.275-313","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tches.v2025.i1.275-313","pdf_url":"https://tches.iacr.org/index.php/TCHES/article/download/11930/11789","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/11930/11789","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074559377","display_name":"Xiangren Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangren Chen","raw_affiliation_strings":["Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101695003","display_name":"Bohan Yang","orcid":"https://orcid.org/0000-0002-5204-1707"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bohan Yang","raw_affiliation_strings":["Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017205152","display_name":"Wenping Zhu","orcid":"https://orcid.org/0000-0002-3276-4019"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenping Zhu","raw_affiliation_strings":["Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006748700","display_name":"Hanning Wang","orcid":"https://orcid.org/0000-0003-1117-2740"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hanning Wang","raw_affiliation_strings":["Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023915372","display_name":"Qichao Tao","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qichao Tao","raw_affiliation_strings":["Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075915565","display_name":"Shuying Yin","orcid":"https://orcid.org/0000-0001-5352-7330"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuying Yin","raw_affiliation_strings":["Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101484570","display_name":"Min Zhu","orcid":"https://orcid.org/0000-0002-9854-7455"},"institutions":[{"id":"https://openalex.org/I4210150385","display_name":"Innovation Team (China)","ror":"https://ror.org/04ttbbx73","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210150385"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Zhu","raw_affiliation_strings":["Wuxi Micro Innovation Integrated Circuit Design Co., Ltd"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wuxi Micro Innovation Integrated Circuit Design Co., Ltd","institution_ids":["https://openalex.org/I4210150385"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036023084","display_name":"Shaojun Wei","orcid":"https://orcid.org/0000-0001-5117-7920"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shaojun Wei","raw_affiliation_strings":["Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100358856","display_name":"Leibo Liu","orcid":"https://orcid.org/0000-0001-7548-4116"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Leibo Liu","raw_affiliation_strings":["Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing National Research Center for Information Science and Technology (BNRist), School of Integrated Circuits, Tsinghua University, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.715,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.86716471,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"2025","issue":"1","first_page":"275","last_page":"313"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9962999820709229,"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":0.9962999820709229,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9943000078201294,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.7207280993461609},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5389273166656494},{"id":"https://openalex.org/keywords/zero-knowledge-proof","display_name":"Zero-knowledge proof","score":0.5207357406616211},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.503154456615448},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.47769811749458313},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.4419298470020294},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33915334939956665},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15239453315734863},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.13315561413764954},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.04860752820968628},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.04792401194572449}],"concepts":[{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.7207280993461609},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5389273166656494},{"id":"https://openalex.org/C176329583","wikidata":"https://www.wikidata.org/wiki/Q191943","display_name":"Zero-knowledge proof","level":3,"score":0.5207357406616211},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.503154456615448},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.47769811749458313},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.4419298470020294},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33915334939956665},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15239453315734863},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.13315561413764954},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.04860752820968628},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.04792401194572449},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.46586/tches.v2025.i1.275-313","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tches.v2025.i1.275-313","pdf_url":"https://tches.iacr.org/index.php/TCHES/article/download/11930/11789","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:80bd397b87084316bb7d8a4a4ac2e643","is_oa":true,"landing_page_url":"https://doaj.org/article/80bd397b87084316bb7d8a4a4ac2e643","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 1 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46586/tches.v2025.i1.275-313","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tches.v2025.i1.275-313","pdf_url":"https://tches.iacr.org/index.php/TCHES/article/download/11930/11789","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/G2825495846","display_name":null,"funder_award_id":"62274102","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3006266431","display_name":null,"funder_award_id":"2023YFB4403500","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405242258.pdf","grobid_xml":"https://content.openalex.org/works/W4405242258.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1870614684","https://openalex.org/W194387157","https://openalex.org/W2000850689","https://openalex.org/W59628553","https://openalex.org/W1483984920","https://openalex.org/W2376228871","https://openalex.org/W3021720713","https://openalex.org/W3137461547","https://openalex.org/W2952570804","https://openalex.org/W4281295723"],"abstract_inverted_index":{"Zero-knowledge":[0],"proof":[1,57,88],"(ZKP)":[2],"is":[3,60],"an":[4],"attractive":[5],"cryptographic":[6],"paradigm":[7],"that":[8,213],"allows":[9],"a":[10,17,141,154,220],"party":[11],"to":[12,181,237,331],"prove":[13],"the":[14,64,87,105,119,130,148,165,171,184,190,206,227,239,249,258,267,291,304,308,332],"correctness":[15],"of":[16,51,121,134,186,202,260],"given":[18],"statement":[19],"without":[20],"revealing":[21],"any":[22],"additional":[23],"information.":[24],"It":[25],"offers":[26],"both":[27,136,215],"computation":[28,38,229,242],"integrity":[29],"and":[30,40,70,96,116,132,138,143,157,169,197,209,217,230,255,263,282,298,313,318,335],"privacy,":[31],"witnessing":[32],"many":[33],"celebrated":[34],"deployments,":[35],"such":[36],"as":[37,99],"outsourcing":[39],"cryptocurrencies.":[41],"Recent":[42],"general-purpose":[43],"ZKP":[44,109],"schemes,":[45],"e.g.,":[46],"zero-knowledge":[47],"succinct":[48],"non-interactive":[49],"argument":[50],"knowledge":[52],"(zk-SNARK),":[53],"suffer":[54],"from":[55],"time-consuming":[56],"generation,":[58],"which":[59,286],"mainly":[61],"bottlenecked":[62],"by":[63,163],"large-scale":[65],"number":[66],"theoretic":[67],"transformation":[68],"(NTT)":[69],"multi-scalar":[71],"point":[72],"multiplication":[73],"(MSM).":[74],"To":[75],"boost":[76],"its":[77],"wide":[78],"application,":[79],"great":[80],"interest":[81],"has":[82],"been":[83],"shown":[84],"in":[85,219],"expediting":[86],"generation":[89],"on":[90,104,266],"various":[91],"platforms":[92],"like":[93],"GPU,":[94],"FPGA":[95],"ASIC.So":[97],"far":[98],"we":[100,127,152,176,204],"know,":[101],"current":[102],"works":[103],"hardware":[106,145,211],"designs":[107],"for":[108,114,253,271,316],"employ":[110],"two":[111],"separated":[112],"data-paths":[113],"NTT":[115,137,216,254,317],"MSM,":[117],"overlooking":[118],"potential":[120],"resource":[122],"reusage.":[123],"In":[124],"this":[125],"work,":[126],"particularly":[128],"explore":[129],"feasibility":[131],"profit":[133],"implementing":[135],"MSM":[139,218,319],"with":[140,243],"unified":[142,309],"high-performance":[144],"architecture.":[146],"For":[147],"crucial":[149],"operator":[150],"design,":[151],"propose":[153],"dual-precision,":[155],"load-balanced":[156],"fully-pipelined":[158],"Montgomery":[159],"multiplier":[160,262],"(LBFP":[161],"MM)":[162],"introducing":[164],"new":[166],"mixed-radix":[167],"technique":[168],"improving":[170],"prior":[172],"quotient-decoupled":[173],"strategy.":[174],"Collectively,":[175],"also":[177,321],"integrate":[178],"orthogonal":[179],"ideas":[180],"further":[182],"enhance":[183],"performance":[185],"LBFP":[187,293],"MM,":[188],"including":[189],"customized":[191],"constant":[192],"multiplication,":[193],"truncated":[194],"LSB/MSB":[195],"multiplication/addition":[196],"Karatsuba":[198],"technique.":[199],"On":[200],"top":[201],"that,":[203],"present":[205],"unified,":[207],"scalable":[208],"highperformance":[210],"architecture":[212,265],"conducts":[214],"versatile":[221],"pipelined":[222],"execution":[223],"mechanism,":[224],"intensively":[225],"sharing":[226],"common":[228],"memory":[231,241,245],"resource.":[232],"The":[233],"proposed":[234,292],"accelerator":[235,310],"manages":[236],"overlap":[238],"on-chip":[240,326],"off-chip":[244],"access,":[246],"considerably":[247],"reducing":[248],"overall":[250,264,325],"cycle":[251],"counts":[252],"MSM.We":[256],"showcase":[257],"implementation":[259],"modular":[261],"BLS12-381":[268],"elliptic":[269],"curve":[270],"zk-SNARK.":[272],"Extensive":[273],"experiments":[274],"are":[275],"carried":[276],"out":[277],"under":[278],"TSMC":[279],"28nm":[280],"synthesis":[281],"similar":[283],"simulation":[284],"set,":[285],"demonstrate":[287],"impressive":[288],"improvements:":[289],"(1)":[290],"MM":[294],"obtains":[295],"1.8x":[296],"speed-up":[297],"1.3x":[299],"less":[300],"area":[301,327],"cost":[302],"versus":[303],"state-of-the-art":[305],"design;":[306],"(2)":[307],"achieves":[311],"12.1x":[312],"5.8x":[314],"acceleration":[315],"while":[320],"consumes":[322],"4.3x":[323],"lower":[324],"overhead,":[328],"when":[329],"compared":[330],"most":[333],"related":[334],"advanced":[336],"work":[337],"PipeZK.":[338]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4}],"updated_date":"2026-07-17T09:13:05.818461","created_date":"2025-10-10T00:00:00"}
