{"id":"https://openalex.org/W4410614225","doi":"https://doi.org/10.1109/tcsi.2025.3570321","title":"A Timing-Constrained Design Methodology for Radix- 2 <sup> <i>k</i> </sup> NTT in Polynomial Arithmetic","display_name":"A Timing-Constrained Design Methodology for Radix- 2 <sup> <i>k</i> </sup> NTT in Polynomial Arithmetic","publication_year":2025,"publication_date":"2025-05-22","ids":{"openalex":"https://openalex.org/W4410614225","doi":"https://doi.org/10.1109/tcsi.2025.3570321"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2025.3570321","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2025.3570321","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/A5064640365","display_name":"Trong-Hung Nguyen","orcid":"https://orcid.org/0009-0001-0952-0534"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Trong-Hung Nguyen","raw_affiliation_strings":["Department of Computer and Network Engineering, The University of Electro-Communications (UEC), Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, The University of Electro-Communications (UEC), Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092636076","display_name":"Duc-Thuan Dam","orcid":"https://orcid.org/0000-0001-8998-9721"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Duc-Thuan Dam","raw_affiliation_strings":["Department of Computer and Network Engineering, The University of Electro-Communications (UEC), Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, The University of Electro-Communications (UEC), Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039121427","display_name":"Phuc-Phan Duong","orcid":"https://orcid.org/0009-0004-4534-9879"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Phuc-Phan Duong","raw_affiliation_strings":["Department of Computer and Network Engineering, The University of Electro-Communications (UEC), Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, The University of Electro-Communications (UEC), Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031277423","display_name":"Tuan-Kiet Dang","orcid":"https://orcid.org/0000-0003-2616-2510"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tuan-Kiet Dang","raw_affiliation_strings":["Department of Computer and Network Engineering, The University of Electro-Communications (UEC), Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, The University of Electro-Communications (UEC), Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025387024","display_name":"Trong-Thuc Hoang","orcid":"https://orcid.org/0000-0002-4078-0836"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Trong-Thuc Hoang","raw_affiliation_strings":["Department of Computer and Network Engineering, The University of Electro-Communications (UEC), Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, The University of Electro-Communications (UEC), Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042912660","display_name":"Cong\u2010Kha Pham","orcid":"https://orcid.org/0000-0001-5255-4919"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Cong-Kha Pham","raw_affiliation_strings":["Department of Computer and Network Engineering, The University of Electro-Communications (UEC), Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, The University of Electro-Communications (UEC), Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5064640365"],"corresponding_institution_ids":["https://openalex.org/I20529979"],"apc_list":null,"apc_paid":null,"fwci":2.435,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.86409228,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"72","issue":"12","first_page":"7794","last_page":"7807"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10904","display_name":"Embedded Systems Design Techniques","score":0.9876000285148621,"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"}},"topics":[{"id":"https://openalex.org/T10904","display_name":"Embedded Systems Design Techniques","score":0.9876000285148621,"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"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9843000173568726,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9836999773979187,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/arithmetic","display_name":"Arithmetic","score":0.7543236017227173},{"id":"https://openalex.org/keywords/radix","display_name":"Radix (gastropod)","score":0.7521628141403198},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5667785406112671},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5663764476776123},{"id":"https://openalex.org/keywords/adder","display_name":"Adder","score":0.42553484439849854},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34560292959213257},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3224678635597229},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.13550621271133423},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10072708129882812}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.7543236017227173},{"id":"https://openalex.org/C2779091547","wikidata":"https://www.wikidata.org/wiki/Q287565","display_name":"Radix (gastropod)","level":2,"score":0.7521628141403198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5667785406112671},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5663764476776123},{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.42553484439849854},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34560292959213257},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3224678635597229},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.13550621271133423},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10072708129882812},{"id":"https://openalex.org/C82876162","wikidata":"https://www.wikidata.org/wiki/Q17096504","display_name":"Latency (audio)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2025.3570321","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2025.3570321","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W179223734","https://openalex.org/W913176383","https://openalex.org/W1525538795","https://openalex.org/W1669999576","https://openalex.org/W2069441027","https://openalex.org/W2152926062","https://openalex.org/W2467320551","https://openalex.org/W2768174108","https://openalex.org/W2899140612","https://openalex.org/W2942255051","https://openalex.org/W3088315145","https://openalex.org/W3135053459","https://openalex.org/W3185075495","https://openalex.org/W3216360301","https://openalex.org/W3216842157","https://openalex.org/W4210722209","https://openalex.org/W4225986329","https://openalex.org/W4226075590","https://openalex.org/W4231896027","https://openalex.org/W4254389654","https://openalex.org/W4295872570","https://openalex.org/W4312387659","https://openalex.org/W4312563345","https://openalex.org/W4312578262","https://openalex.org/W4312708589","https://openalex.org/W4360770741","https://openalex.org/W4382119118","https://openalex.org/W4383503838","https://openalex.org/W4384787353","https://openalex.org/W4385237357","https://openalex.org/W4386825228","https://openalex.org/W4387019087","https://openalex.org/W4387129556","https://openalex.org/W4387129570","https://openalex.org/W4388893929","https://openalex.org/W4389252478","https://openalex.org/W4389331617","https://openalex.org/W4389664577","https://openalex.org/W4390603852","https://openalex.org/W4390787935","https://openalex.org/W4390872229","https://openalex.org/W4391092603","https://openalex.org/W4392173973","https://openalex.org/W4392309219","https://openalex.org/W4393144920","https://openalex.org/W4399486438","https://openalex.org/W4400409839","https://openalex.org/W4400770649","https://openalex.org/W4401163376","https://openalex.org/W4402808536","https://openalex.org/W4403277117","https://openalex.org/W4403976928"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4390550886","https://openalex.org/W3217463396","https://openalex.org/W2516396101","https://openalex.org/W2790557758","https://openalex.org/W3204929712","https://openalex.org/W4295102875","https://openalex.org/W2300671402","https://openalex.org/W2013839957","https://openalex.org/W3196607417"],"abstract_inverted_index":{"Polynomial":[0],"modular":[1],"multiplication":[2,29],"is":[3],"the":[4,19,26,40,103,108,145,180,201,223],"most":[5],"complex":[6],"and":[7,14,44,57,96,127,136,151,160,197,210,228],"costly":[8],"operation":[9],"in":[10,182,230],"homomorphic":[11],"encryption":[12],"(HE)":[13],"post-quantum":[15],"cryptography":[16],"(PQC).":[17],"Using":[18],"Number":[20],"Theoretic":[21],"Transform":[22],"(NTT)":[23],"helps":[24],"reduce":[25],"complexity":[27],"of":[28,42,102,158],"to":[30,53,122,207],"quasi-linear":[31],"O(<inline-formula":[32],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[33,124,134,140,162],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[34],"notation=\"LaTeX\">$N\\,\\textup{log}_{2}N$</tex-math></inline-formula>).":[35],"Although":[36],"NTT":[37,84,126,164,181,203],"significantly":[38],"impacts":[39],"performance":[41],"HE":[43,150,227],"PQC,":[45],"existing":[46],"NTT-based":[47,219],"multipliers":[48],"often":[49],"fall":[50],"short":[51],"due":[52],"inefficient":[54],"data":[55],"movement":[56],"large":[58],"memory":[59,91],"overhead.":[60],"Notably,":[61],"deploying":[62],"low-latency":[63],"cryptosystems":[64],"incurs":[65],"more":[66],"significant":[67],"costs":[68],"with":[69],"reduced":[70],"acceleration":[71],"gains.":[72],"To":[73],"overcome":[74],"these":[75],"constraints,":[76],"we":[77,106],"introduce":[78],"a":[79,183],"pioneering":[80],"methodology":[81,119],"called":[82],"timing-constrained":[83],"(TCO-NTT).":[85],"We":[86,143],"propose":[87],"an":[88],"innovative":[89],"time-controlled":[90],"(TCM)":[92],"structure":[93],"that":[94,170],"re-orders":[95],"stores":[97],"coefficients":[98],"within":[99],"each":[100],"stage":[101],"NTT.":[104],"Then,":[105],"employ":[107],"divide-and-conquer":[109],"strategy,":[110],"allowing":[111],"freely":[112],"configurable":[113],"parallelism":[114,159],"levels.":[115],"Besides,":[116],"our":[117,171],"proposed":[118,146,213],"can":[120],"generalize":[121],"radix-2<sup":[123,161],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><i>k</i></sup>":[125,163],"supports":[128],"any":[129],"arbitrary":[130],"polynomial":[131],"degree":[132],"<italic":[133,139],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</i>":[135],"scale":[137],"factor":[138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</i>":[141],"values.":[142],"evaluate":[144],"TCO-NTT":[147,172,214],"on":[148],"typical":[149],"PQC":[152,229],"parameter":[153],"sets":[154,215],"across":[155],"multiple":[156],"levels":[157],"configurations.":[165],"FPGA":[166],"implementation":[167],"results":[168],"demonstrate":[169],"achieves":[173],"minimal":[174],"hardware":[175],"cost":[176],"while":[177],"consistently":[178],"executing":[179],"near-theoretical":[184],"execution":[185],"time.":[186],"Our":[187],"area-time":[188],"product":[189],"(ATP)":[190],"reports":[191],"about":[192],"LUT-ATP":[193],"(LATP),":[194],"FF-ATP":[195],"(FATP),":[196],"BRAM-ATP":[198],"(BATP)":[199],"surpass":[200],"reported-to-date":[202],"designs":[204],"by":[205],"up":[206],"10.2\u00d7,":[208],"17.8\u00d7":[209],"47.2\u00d7.":[211],"The":[212],"new":[216],"records":[217],"for":[218,225],"multiplier":[220],"efficiency,":[221],"laying":[222],"foundation":[224],"implementing":[226],"real-time":[231],"applications.":[232]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-28T02:08:47.144824","created_date":"2025-10-10T00:00:00"}
