{"id":"https://openalex.org/W7134961599","doi":"https://doi.org/10.1109/tcsi.2026.3667103","title":"KHNTT: A Configurable and High-Performance Polynomial Multiplication Unit Based on FPGA","display_name":"KHNTT: A Configurable and High-Performance Polynomial Multiplication Unit Based on FPGA","publication_year":2026,"publication_date":"2026-03-10","ids":{"openalex":"https://openalex.org/W7134961599","doi":"https://doi.org/10.1109/tcsi.2026.3667103"},"language":null,"primary_location":{"id":"doi:10.1109/tcsi.2026.3667103","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2026.3667103","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","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/A5060283626","display_name":"Bin Li","orcid":"https://orcid.org/0000-0003-3455-4901"},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]},{"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"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bin Li","raw_affiliation_strings":["Advanced Cryptography and System Security Key Laboratory of Sichuan Province, Chengdu, Sichuan, China","School of Computer and Artificial Intelligence, Zhengzhou University, Zhengzhou, Henan, China"],"raw_orcid":"https://orcid.org/0000-0003-3455-4901","affiliations":[{"raw_affiliation_string":"Advanced Cryptography and System Security Key Laboratory of Sichuan Province, Chengdu, Sichuan, China","institution_ids":["https://openalex.org/I4210132990"]},{"raw_affiliation_string":"School of Computer and Artificial Intelligence, Zhengzhou University, Zhengzhou, Henan, China","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114086083","display_name":"Heru Han","orcid":null},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Heru Han","raw_affiliation_strings":["School of Computer and Artificial Intelligence, Zhengzhou University, Zhengzhou, Henan, China"],"raw_orcid":"https://orcid.org/0009-0007-7967-1753","affiliations":[{"raw_affiliation_string":"School of Computer and Artificial Intelligence, Zhengzhou University, Zhengzhou, Henan, China","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128741703","display_name":"Linying Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Linying Liu","raw_affiliation_strings":["School of Computer and Artificial Intelligence, Zhengzhou University, Zhengzhou, Henan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer and Artificial Intelligence, Zhengzhou University, Zhengzhou, Henan, China","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Shiliang Yu","orcid":"https://orcid.org/0009-0001-9889-7519"},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shiliang Yu","raw_affiliation_strings":["School of Computer and Artificial Intelligence, Zhengzhou University, Zhengzhou, Henan, China"],"raw_orcid":"https://orcid.org/0009-0001-9889-7519","affiliations":[{"raw_affiliation_string":"School of Computer and Artificial Intelligence, Zhengzhou University, Zhengzhou, Henan, China","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128702147","display_name":"Qinglei Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qinglei Zhou","raw_affiliation_strings":["School of Computer and Artificial Intelligence, Zhengzhou University, Zhengzhou, Henan, China"],"raw_orcid":"https://orcid.org/0000-0002-1156-1108","affiliations":[{"raw_affiliation_string":"School of Computer and Artificial Intelligence, Zhengzhou University, Zhengzhou, Henan, China","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082955232","display_name":"Binyong Li","orcid":"https://orcid.org/0000-0003-3615-1129"},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]},{"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Binyong Li","raw_affiliation_strings":["Advanced Cryptography and System Security Key Laboratory of Sichuan Province, Chengdu, Sichuan, China","School of Computer and Artificial Intelligence, Zhengzhou University, Zhengzhou, Henan, China"],"raw_orcid":"https://orcid.org/0000-0003-3615-1129","affiliations":[{"raw_affiliation_string":"Advanced Cryptography and System Security Key Laboratory of Sichuan Province, Chengdu, Sichuan, China","institution_ids":["https://openalex.org/I4210132990"]},{"raw_affiliation_string":"School of Computer and Artificial Intelligence, Zhengzhou University, Zhengzhou, Henan, China","institution_ids":["https://openalex.org/I38877650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5060283626"],"corresponding_institution_ids":["https://openalex.org/I38877650","https://openalex.org/I4210132990"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.36556277,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"73","issue":"5","first_page":"3410","last_page":"3423"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9406999945640564,"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":0.9406999945640564,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.02019999921321869,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11130","display_name":"Coding theory and cryptography","score":0.011300000362098217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.5971999764442444},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.4941999912261963},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48660001158714294},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.45210000872612},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.40790000557899475},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.40630000829696655},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.3939000070095062}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7318999767303467},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.5971999764442444},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.49790000915527344},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.4941999912261963},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48660001158714294},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.45210000872612},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.40790000557899475},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.40630000829696655},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.3939000070095062},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.384799987077713},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.34880000352859497},{"id":"https://openalex.org/C142962650","wikidata":"https://www.wikidata.org/wiki/Q240838","display_name":"Reconfigurable computing","level":3,"score":0.3199000060558319},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.30979999899864197},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C151635116","wikidata":"https://www.wikidata.org/wiki/Q193878","display_name":"Chinese remainder theorem","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2732999920845032},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C134835016","wikidata":"https://www.wikidata.org/wiki/Q690265","display_name":"Lookup table","level":2,"score":0.2556999921798706}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2026.3667103","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2026.3667103","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W2007466965","https://openalex.org/W2902661060","https://openalex.org/W2982379075","https://openalex.org/W2995995168","https://openalex.org/W3048071914","https://openalex.org/W3065439923","https://openalex.org/W3135053459","https://openalex.org/W3137525851","https://openalex.org/W3157961299","https://openalex.org/W3169003396","https://openalex.org/W3179259833","https://openalex.org/W3185075495","https://openalex.org/W3216234213","https://openalex.org/W3216360301","https://openalex.org/W4213069811","https://openalex.org/W4226216812","https://openalex.org/W4226334377","https://openalex.org/W4293143765","https://openalex.org/W4295872570","https://openalex.org/W4312563345","https://openalex.org/W4312578262","https://openalex.org/W4318273611","https://openalex.org/W4364859951","https://openalex.org/W4384787353","https://openalex.org/W4385327521","https://openalex.org/W4387129570","https://openalex.org/W4389331617","https://openalex.org/W4396995605","https://openalex.org/W4402804765","https://openalex.org/W4402808536","https://openalex.org/W4403277117","https://openalex.org/W4403291154","https://openalex.org/W4410614225","https://openalex.org/W4415124224"],"related_works":[],"abstract_inverted_index":{"Polynomial":[0],"multiplication":[1,28,143,197],"is":[2],"a":[3,23,76,125,177,200],"critical":[4],"performance":[5],"bottleneck":[6],"in":[7,11,194,217],"lattice-based":[8],"cryptographic":[9],"schemes,":[10],"which":[12,57],"efficient":[13],"and":[14,25,36,66,91,98,108,135,152,199],"flexible":[15,146],"hardware":[16],"implementations":[17],"are":[18,112],"essential.":[19],"This":[20],"paper":[21],"presents":[22],"high-performance":[24],"reconfigurable":[26],"polynomial":[27,44,85,142,154,196],"unit":[29,80,144],"that":[30],"integrates":[31],"the":[32,40,48,59,95,149,160,195,218,223],"cooptimization":[33],"of":[34,43,82,148,156,226],"algorithmic":[35],"architectural":[37,99],"optimizations.":[38],"As":[39],"core":[41],"operation":[42],"multiplication,":[45],"we":[46,74,116],"propose":[47],"Karatsuba-based":[49],"high-efficiency":[50],"radix-4":[51,78],"number":[52],"theoretic":[53],"transform":[54],"(KHNTT)":[55],"algorithm,":[56,73],"reduces":[58],"computational":[60,96,224],"complexity":[61],"by":[62],"leveraging":[63,222],"low-bit-width":[64],"arithmetic":[65],"parallel":[67],"processing":[68],"techniques.":[69],"Based":[70],"on":[71],"this":[72],"develop":[75],"unified":[77],"butterfly":[79,150],"capable":[81],"supporting":[83],"modular":[84,106],"operations":[86],"under":[87],"various":[88,157],"parameter":[89],"configurations,":[90],"to":[92,130,185,208],"further":[93],"improve":[94,136],"efficiency":[97],"flexibility,":[100],"key":[101],"algorithm":[102],"modules":[103],"such":[104],"as":[105],"reduction":[107],"data":[109,137],"flow":[110],"scheduling":[111],"deeply":[113],"optimized.":[114],"Furthermore,":[115],"introduce":[117],"an":[118],"iterative":[119],"interleaving":[120],"memory":[121,132],"strategy":[122],"combined":[123],"with":[124,171],"bank":[126],"resource":[127],"sharing":[128],"mechanism":[129],"eliminate":[131],"access":[133,138],"conflicts":[134],"efficiency.":[139],"The":[140,164],"proposed":[141],"allows":[145],"configuration":[147],"units":[151],"supports":[153],"computations":[155],"degrees":[158],"without":[159],"need":[161],"for":[162],"recompilation.":[163],"FPGA":[165],"implementation":[166],"results":[167],"demonstrate":[168],"that,":[169],"compared":[170],"existing":[172],"solutions,":[173],"our":[174],"architecture":[175],"achieves":[176],"<inline-formula":[178,186,201,209],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[179,187,202,210],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[180,188,203,211],"<tex-math":[181,189,204,212],"notation=\"LaTeX\">$1.25\\times":[182],"$</tex-math>":[183,191,206,214],"</inline-formula>":[184,192,207,215],"notation=\"LaTeX\">$5.27\\times":[190],"improvement":[193],"throughput":[198],"notation=\"LaTeX\">$1.14\\times":[205],"notation=\"LaTeX\">$2.7\\times":[213],"enhancement":[216],"area":[219],"efficiency,":[220],"fully":[221],"advantages":[225],"FPGAs.":[227]},"counts_by_year":[],"updated_date":"2026-05-05T06:06:40.768181","created_date":"2026-03-12T00:00:00"}