{"id":"https://openalex.org/W4379743214","doi":"https://doi.org/10.1109/tvlsi.2023.3277865","title":"TCPM: A Reconfigurable and Efficient Toom-Cook-Based Polynomial Multiplier Over Rings Using a Novel Compressed Postprocessing Algorithm","display_name":"TCPM: A Reconfigurable and Efficient Toom-Cook-Based Polynomial Multiplier Over Rings Using a Novel Compressed Postprocessing Algorithm","publication_year":2023,"publication_date":"2023-06-07","ids":{"openalex":"https://openalex.org/W4379743214","doi":"https://doi.org/10.1109/tvlsi.2023.3277865"},"language":"en","primary_location":{"id":"doi:10.1109/tvlsi.2023.3277865","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvlsi.2023.3277865","pdf_url":null,"source":{"id":"https://openalex.org/S37538908","display_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","issn_l":"1063-8210","issn":["1063-8210","1557-9999"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","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/A5080354346","display_name":"Jianfei Wang","orcid":"https://orcid.org/0009-0004-0132-3319"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianfei Wang","raw_affiliation_strings":["School of Microelectronics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China"],"raw_orcid":"https://orcid.org/0009-0004-0132-3319","affiliations":[{"raw_affiliation_string":"School of Microelectronics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100719382","display_name":"Chen Yang","orcid":"https://orcid.org/0000-0002-8221-7670"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen Yang","raw_affiliation_strings":["School of Microelectronics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China"],"raw_orcid":"https://orcid.org/0000-0002-8221-7670","affiliations":[{"raw_affiliation_string":"School of Microelectronics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073626581","display_name":"Fahong Zhang","orcid":"https://orcid.org/0009-0008-8613-5323"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fahong Zhang","raw_affiliation_strings":["School of Microelectronics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Microelectronics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046312537","display_name":"Yishuo Meng","orcid":"https://orcid.org/0000-0002-3402-6386"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yishuo Meng","raw_affiliation_strings":["School of Microelectronics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Microelectronics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100728012","display_name":"Yang Su","orcid":"https://orcid.org/0009-0008-5951-8476"},"institutions":[{"id":"https://openalex.org/I4210134428","display_name":"Chinese People's Armed Police Force Engineering University","ror":"https://ror.org/031jzbb03","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210134428"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Su","raw_affiliation_strings":["School of Cryptography Engineering, Engineering University of People&#x2019;s Armed Police, Xi&#x2019;an, China"],"raw_orcid":"https://orcid.org/0000-0003-3619-7936","affiliations":[{"raw_affiliation_string":"School of Cryptography Engineering, Engineering University of People&#x2019;s Armed Police, Xi&#x2019;an, China","institution_ids":["https://openalex.org/I4210134428"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5080354346"],"corresponding_institution_ids":["https://openalex.org/I87445476"],"apc_list":null,"apc_paid":null,"fwci":1.8745,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.88234007,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"31","issue":"8","first_page":"1153","last_page":"1166"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9775000214576721,"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":0.9775000214576721,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9204000234603882,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9146999716758728,"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/computer-science","display_name":"Computer science","score":0.5473969578742981},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5228205919265747},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5194723010063171},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.50213623046875},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.45298442244529724},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4466714859008789},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4153480529785156},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.39760008454322815},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35718467831611633},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.20185163617134094}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5473969578742981},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5228205919265747},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5194723010063171},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.50213623046875},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.45298442244529724},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4466714859008789},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4153480529785156},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.39760008454322815},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35718467831611633},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.20185163617134094},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tvlsi.2023.3277865","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvlsi.2023.3277865","pdf_url":null,"source":{"id":"https://openalex.org/S37538908","display_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","issn_l":"1063-8210","issn":["1063-8210","1557-9999"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/2","display_name":"Zero hunger","score":0.4399999976158142}],"awards":[{"id":"https://openalex.org/G7748210645","display_name":null,"funder_award_id":"2020Z066070001","funder_id":"https://openalex.org/F4320322857","funder_display_name":"Aeronautical Science Foundation of China"},{"id":"https://openalex.org/G963865091","display_name":null,"funder_award_id":"62176206","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"},{"id":"https://openalex.org/F4320322857","display_name":"Aeronautical Science Foundation of China","ror":"https://ror.org/02wq41p38"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1498685334","https://openalex.org/W1649758727","https://openalex.org/W1880212920","https://openalex.org/W2001121794","https://openalex.org/W2048994663","https://openalex.org/W2098290658","https://openalex.org/W2138391902","https://openalex.org/W2177209050","https://openalex.org/W2226167778","https://openalex.org/W2415881634","https://openalex.org/W2791664942","https://openalex.org/W2792565434","https://openalex.org/W2796314191","https://openalex.org/W2866028610","https://openalex.org/W2922452168","https://openalex.org/W2934510082","https://openalex.org/W2942255051","https://openalex.org/W2949507333","https://openalex.org/W2979557494","https://openalex.org/W3013348637","https://openalex.org/W3019884349","https://openalex.org/W3023641472","https://openalex.org/W3028867652","https://openalex.org/W3092489368","https://openalex.org/W3121011012","https://openalex.org/W3207326900","https://openalex.org/W3212142976","https://openalex.org/W4210403826","https://openalex.org/W4221138287","https://openalex.org/W4225321568","https://openalex.org/W4225468027","https://openalex.org/W4286542608","https://openalex.org/W4366377472","https://openalex.org/W6629789561","https://openalex.org/W6636949950","https://openalex.org/W6762012821","https://openalex.org/W6778434676","https://openalex.org/W6784137253","https://openalex.org/W6810564138"],"related_works":["https://openalex.org/W2111241003","https://openalex.org/W4200391368","https://openalex.org/W3093936885","https://openalex.org/W2210979487","https://openalex.org/W2074043759","https://openalex.org/W3042736233","https://openalex.org/W2082487009","https://openalex.org/W2373535795","https://openalex.org/W2994146737","https://openalex.org/W1886625815"],"abstract_inverted_index":{"Polynomial":[0],"multiplication":[1,105,200],"over":[2,106,201],"rings":[3,202],"is":[4,99,119,138,145],"a":[5,40,110,148,152,159,174,191,204,207,212,224,230],"significant":[6],"bottleneck":[7],"of":[8,78,84,88,125,206,209],"ring":[9],"learning":[10],"with":[11,33,147,203,248],"error":[12],"(RLWE)-based":[13],"encryption.":[14],"To":[15],"speed":[16,102],"it":[17,144],"up,":[18],"three":[19],"algorithms":[20],"are":[21,52],"widely":[22],"used,":[23],"i.e.,":[24],"number":[25,77],"theoretic":[26],"transform":[27],"(NTT),":[28],"Schoolbook,":[29],"and":[30,35,45,56,69,80,93,112,127,158,167,171],"Toom-Cook.":[31],"Compared":[32],"Schoolbook":[34],"NTT,":[36],"Toom-Cook":[37,49,71],"can":[38,164,189],"achieve":[39],"better":[41],"trade-off":[42],"between":[43],"performance":[44],"flexibility.":[46],"However,":[47],"in":[48],"postprocessing,":[50],"there":[51],"many":[53],"redundant":[54],"steps":[55,79],"calculations":[57],"that":[58,74],"have":[59],"not":[60],"been":[61],"eliminated.":[62],"Therefore,":[63],"we":[64],"propose":[65],"an":[66],"efficient,":[67],"compressed,":[68],"fused":[70],"postprocessing":[72,137],"algorithm":[73],"reduces":[75],"the":[76,85,123,130,133,180,249],"at":[81,223],"least":[82],"33.33%":[83],"arithmetic":[86],"operations":[87],"postprocessing.":[89],"A":[90],"highly":[91],"reconfigurable":[92,149],"efficient":[94,113],"Toom-Cook-based":[95],"polynomial":[96,104,154,199],"multiplier":[97],"(TCPM)":[98],"proposed":[100],"to":[101,121,238],"up":[103],"rings.":[107],"In":[108,141],"TCPM,":[109],"high-throughput":[111],"heterogeneous":[114],"processing":[115],"element":[116],"(PE)":[117],"array":[118,135,185],"designed":[120],"exploit":[122],"parallelism":[124],"Toom-Cook,":[126],"based":[128],"on":[129,173,179],"compressed":[131],"algorithm,":[132],"PE":[134,161],"for":[136],"scaled":[139],"down.":[140],"addition,":[142],"as":[143],"provided":[146],"evaluation":[150],"module,":[151],"flexible":[153],"data":[155],"storage":[156],"module":[157],"universal":[160],"array,":[162],"TCPM":[163,188],"efficiently":[165],"map":[166],"execute":[168],"Toom-Cook-2,":[169],"3,":[170],"4":[172],"unified":[175],"hardware":[176],"architecture.":[177],"Implemented":[178],"Xilinx":[181],"VC709":[182],"field-programmable":[183],"gate":[184],"(FPGA)":[186],"platform,":[187],"perform":[190],"Toom-Cook-4-based":[192],"<inline-formula":[193,216,231,239],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[194,217,232,240],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[195,218,233,241],"<tex-math":[196,219,234,242],"notation=\"LaTeX\">$256\\times256$":[197],"</tex-math></inline-formula>":[198,222,237,245],"modulus":[205],"power":[208],"two":[210],"or":[211],"prime":[213],"every":[214],"3.28":[215],"notation=\"LaTeX\">$\\mu":[220],"\\text{s}$":[221],"360-MHz":[225],"clock":[226],"frequency.":[227],"It":[228],"achieves":[229],"notation=\"LaTeX\">$2.47\\times":[235],"$":[236,244],"notation=\"LaTeX\">$50.11\\times":[243],"speedup":[246],"compared":[247],"previous":[250],"designs.":[251]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
