{"id":"https://openalex.org/W7123335360","doi":"https://doi.org/10.1109/candar68384.2025.00029","title":"MMzk: 384-bit Low-Resource Montgomery Multiplier on FPGA for zk-SNARK","display_name":"MMzk: 384-bit Low-Resource Montgomery Multiplier on FPGA for zk-SNARK","publication_year":2025,"publication_date":"2025-11-25","ids":{"openalex":"https://openalex.org/W7123335360","doi":"https://doi.org/10.1109/candar68384.2025.00029"},"language":"en","primary_location":{"id":"doi:10.1109/candar68384.2025.00029","doi":"https://doi.org/10.1109/candar68384.2025.00029","is_oa":false,"landing_page_url":"https://doi.org/10.1109/candar68384.2025.00029","pdf_url":null,"source":{"id":"https://openalex.org/S4306420119","display_name":"International Symposium on Computing and Networking","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 Thirteenth International Symposium on Computing and Networking (CANDAR)","raw_type":"proceedings-article"},"parent_works":[],"lineage":["https://openalex.org/W7123335360"],"child_works_count":0,"type":"conference-paper","is_traditional":true,"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/A5122904889","display_name":"Hikaru Okamoto","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I75917431","display_name":"Nara Institute of Science and Technology","ror":"https://ror.org/05bhada84","country_code":"JP","type":"education","lineage":["https://openalex.org/I75917431"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hikaru Okamoto","raw_affiliation_strings":["Nara Institute of Science and Technology,Division of Information Science,Nara,Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nara Institute of Science and Technology,Division of Information Science,Nara,Japan","institution_ids":["https://openalex.org/I75917431"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077262099","display_name":"Vu Trung Duong Le","orcid":"https://orcid.org/0000-0002-0438-3809","observed_orcids":["https://orcid.org/0000-0002-0438-3809"]},"institutions":[{"id":"https://openalex.org/I75917431","display_name":"Nara Institute of Science and Technology","ror":"https://ror.org/05bhada84","country_code":"JP","type":"education","lineage":["https://openalex.org/I75917431"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Vu Trung Duong Le","raw_affiliation_strings":["Nara Institute of Science and Technology,Division of Information Science,Nara,Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nara Institute of Science and Technology,Division of Information Science,Nara,Japan","institution_ids":["https://openalex.org/I75917431"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046015756","display_name":"Hoai Luan Pham","orcid":"https://orcid.org/0000-0002-4272-0132","observed_orcids":["https://orcid.org/0000-0002-4272-0132"]},"institutions":[{"id":"https://openalex.org/I75917431","display_name":"Nara Institute of Science and Technology","ror":"https://ror.org/05bhada84","country_code":"JP","type":"education","lineage":["https://openalex.org/I75917431"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hoai Luan Pham","raw_affiliation_strings":["Nara Institute of Science and Technology,Division of Information Science,Nara,Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nara Institute of Science and Technology,Division of Information Science,Nara,Japan","institution_ids":["https://openalex.org/I75917431"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101402518","display_name":"Van Tinh Nguyen","orcid":"https://orcid.org/0009-0003-9367-9138","observed_orcids":["https://orcid.org/0009-0003-9367-9138","https://orcid.org/0000-0002-6512-5846","https://orcid.org/0000-0003-4631-5270"]},"institutions":[{"id":"https://openalex.org/I131359167","display_name":"Le Quy Don Technical University","ror":"https://ror.org/04wgyjv21","country_code":"VN","type":"education","lineage":["https://openalex.org/I131359167"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Van Tinh Nguyen","raw_affiliation_strings":["Le Quy Don Technical University,Electrical Engineering Department,Ha Noi,Viet Nam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Le Quy Don Technical University,Electrical Engineering Department,Ha Noi,Viet Nam","institution_ids":["https://openalex.org/I131359167"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061486185","display_name":"Yasuhiko NAKASHIMA","orcid":"https://orcid.org/0000-0002-9457-5061","observed_orcids":["https://orcid.org/0000-0002-9457-5061"]},"institutions":[{"id":"https://openalex.org/I75917431","display_name":"Nara Institute of Science and Technology","ror":"https://ror.org/05bhada84","country_code":"JP","type":"education","lineage":["https://openalex.org/I75917431"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yasuhiko Nakashima","raw_affiliation_strings":["Nara Institute of Science and Technology,Division of Information Science,Nara,Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nara Institute of Science and Technology,Division of Information Science,Nara,Japan","institution_ids":["https://openalex.org/I75917431"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5251,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.60249339,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"160","last_page":"166"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9818999767303467,"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":0.9818999767303467,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.003800000064074993,"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.003100000089034438,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/zk-snarks","display_name":"zk-SNARKs","score":0.8870000243186951},{"id":"https://openalex.org/keywords/montgomery-multiplication","display_name":"Montgomery multiplication","score":0.8960000276565552},{"id":"https://openalex.org/keywords/cio","display_name":"CIO","score":0.5170000195503235},{"id":"https://openalex.org/keywords/multi-scalar-multiplication","display_name":"multi-scalar multiplication","score":0.8569999933242798},{"id":"https://openalex.org/keywords/zero-knowledge-proofs","display_name":"zero-knowledge proofs","score":0.8100000023841858},{"id":"https://openalex.org/keywords/fpga-architecture","display_name":"FPGA architecture","score":0.7599999904632568},{"id":"https://openalex.org/keywords/resource-constrained-devices","display_name":"resource-constrained devices","score":0.6510000228881836},{"id":"https://openalex.org/keywords/resource-sharing","display_name":"resource sharing","score":0.765999972820282},{"id":"https://openalex.org/keywords/energy-efficiency","display_name":"energy efficiency","score":0.734000027179718},{"id":"https://openalex.org/keywords/edge-computing","display_name":"edge computing","score":0.7129999995231628},{"id":"https://openalex.org/keywords/blockchain-privacy","display_name":"blockchain privacy","score":0.6639999747276306}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8009999990463257},{"id":"https://openalex.org/C55526617","wikidata":"https://www.wikidata.org/wiki/Q719375","display_name":"Operand","level":2,"score":0.6629999876022339},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.574999988079071},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.5598999857902527},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.5031999945640564},{"id":"https://openalex.org/C118524514","wikidata":"https://www.wikidata.org/wiki/Q173212","display_name":"Computer architecture","level":1,"score":0.4458000063896179},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.43309998512268066},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.38040000200271606},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.357699990272522},{"id":"https://openalex.org/C51332947","wikidata":"https://www.wikidata.org/wiki/Q1172305","display_name":"Shared resource","level":2,"score":0.3361999988555908},{"id":"https://openalex.org/C157764524","wikidata":"https://www.wikidata.org/wiki/Q1383412","display_name":"Throughput","level":3,"score":0.33149999380111694},{"id":"https://openalex.org/C123657996","wikidata":"https://www.wikidata.org/wiki/Q12271","display_name":"Architecture","level":2,"score":0.3287000060081482},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.32659998536109924},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3149999976158142},{"id":"https://openalex.org/C2742236","wikidata":"https://www.wikidata.org/wiki/Q924713","display_name":"Efficient energy use","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.3075999915599823},{"id":"https://openalex.org/C159718280","wikidata":"https://www.wikidata.org/wiki/Q5526353","display_name":"Gas meter prover","level":3,"score":0.29899999499320984},{"id":"https://openalex.org/C206345919","wikidata":"https://www.wikidata.org/wiki/Q20380951","display_name":"Resource (disambiguation)","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C126298526","wikidata":"https://www.wikidata.org/wiki/Q189376","display_name":"Reduced instruction set computing","level":3,"score":0.27630001306533813},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C156972235","wikidata":"https://www.wikidata.org/wiki/Q1443434","display_name":"Instructions per cycle","level":3,"score":0.25780001282691956}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/candar68384.2025.00029","doi":"https://doi.org/10.1109/candar68384.2025.00029","is_oa":false,"landing_page_url":"https://doi.org/10.1109/candar68384.2025.00029","pdf_url":null,"source":{"id":"https://openalex.org/S4306420119","display_name":"International Symposium on Computing and Networking","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 Thirteenth International Symposium on Computing and Networking (CANDAR)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.428600013256073,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1491543582","https://openalex.org/W1893601685","https://openalex.org/W2144752539","https://openalex.org/W2496825637","https://openalex.org/W2542845775","https://openalex.org/W2943126371","https://openalex.org/W3016585670","https://openalex.org/W4380081638","https://openalex.org/W4387987583","https://openalex.org/W4393207741","https://openalex.org/W4396871399","https://openalex.org/W4409128906"],"related_works":["https://openalex.org/W4401808682","https://openalex.org/W4402196163","https://openalex.org/W4391455296","https://openalex.org/W4414017041","https://openalex.org/W4412623597","https://openalex.org/W7164419097","https://openalex.org/W4408161356","https://openalex.org/W7155714635","https://openalex.org/W7223242573","https://openalex.org/W4405242258"],"abstract_inverted_index":{"Zero-Knowledge":[0,28],"Proof":[1],"(ZKP)":[2],"is":[3,75],"a":[4,9,16,60,109,112,127,141,161],"privacy-preserving":[5],"protocol":[6],"that":[7,132],"allows":[8],"prover":[10],"to":[11,138,166,177,199],"demonstrate":[12],"the":[13,96],"validity":[14],"of":[15,26,32,82,106,143,163,174,188],"statement":[17],"without":[18],"revealing":[19],"its":[20,51],"details.":[21],"A":[22],"widely":[23],"used":[24],"primitive":[25],"ZKP,":[27],"Succinct":[29],"Non-Interactive":[30],"Argument":[31],"Knowledge":[33],"(zk-SNARK),":[34],"has":[35],"attracted":[36],"significant":[37],"attention":[38],"in":[39,78],"edge":[40,43],"computing;":[41],"however,":[42],"devices":[44],"face":[45],"severe":[46],"resource":[47,90,104],"constraints":[48],"when":[49],"processing":[50],"computational":[52],"bottleneck,":[53],"Montgomery":[54,72,219],"multiplication.":[55],"This":[56],"paper":[57],"proposes":[58],"MMzk,":[59],"lightweight":[61],"hardware":[62],"architecture":[63],"optimized":[64],"for":[65,117,213],"384-bit":[66],"Coarsely":[67],"Integrated":[68],"Operand":[69],"Scanning":[70],"(CIOS)":[71],"multiplication,":[73],"which":[74],"primarily":[76],"employed":[77],"multi-scalar":[79],"multiplication":[80,220],"(MSM)":[81],"zk-SNARKs.":[83],"To":[84],"achieve":[85],"both":[86],"high":[87],"performance":[88],"and":[89,111,120,150,170,192,210,217],"efficiency,":[91],"MMzk":[92,133,205],"core":[93,134,206],"operating":[94],"at":[95,136,190],"System-on-Chip":[97],"(SoC)":[98],"level":[99],"integrates":[100],"three":[101],"key":[102],"optimizations:":[103],"sharing":[105],"two":[107],"adders,":[108],"subtractor,":[110],"multiplier;":[113],"effective":[114],"memory":[115,122],"organization":[116],"large-data":[118],"processing;":[119],"double-buffering":[121],"scheduling.":[123],"Implementation":[124],"results":[125,203],"on":[126],"Xilinx":[128],"ZCU102":[129],"SoC":[130],"show":[131],"operates":[135],"up":[137,198],"250MHz":[139,191],"with":[140,155],"utilization":[142],"3,590":[144],"LUTs,":[145],"1,648":[146],"FFs,":[147],"16":[148],"DSPs,":[149],"6":[151],"BRAM36":[152],"blocks.":[153],"Compared":[154],"existing":[156],"FPGA-based":[157],"counterparts,":[158],"it":[159],"achieves":[160],"throughput":[162],"657.53Mbps":[164],"(up":[165,176],"35.9":[167],"times":[168,179],"higher)":[169],"an":[171,185,208],"area":[172],"efficiency":[173,187],"81.48Kbps/eLUT":[175],"9.5":[178],"higher).":[180],"Furthermore,":[181],"real-time":[182],"evaluation":[183],"demonstrates":[184],"energy":[186],"9,030Mbps/W":[189],"67mW,":[193],"surpassing":[194],"modern":[195],"CPUs":[196],"by":[197],"52.9":[200],"times.":[201],"These":[202],"confirm":[204],"as":[207],"energy-efficient":[209],"high-performance":[211],"solution":[212],"zk-SNARK-based":[214],"blockchain":[215],"systems":[216],"other":[218],"applications.":[221]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2026-01-14T00:00:00"}
