{"id":"https://openalex.org/W7134887650","doi":"https://doi.org/10.1109/tc.2026.3671958","title":"Optimized NTT Architecture Based on the Plantard Algorithm for ML-KEM and ML-DSA","display_name":"Optimized NTT Architecture Based on the Plantard Algorithm for ML-KEM and ML-DSA","publication_year":2026,"publication_date":"2026-03-10","ids":{"openalex":"https://openalex.org/W7134887650","doi":"https://doi.org/10.1109/tc.2026.3671958"},"language":null,"primary_location":{"id":"doi:10.1109/tc.2026.3671958","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2026.3671958","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"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 Computers","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/A5012854154","display_name":"J.-Y. Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiansheng Chen","raw_affiliation_strings":["College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0002-5743-8188","affiliations":[{"raw_affiliation_string":"College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048802810","display_name":"Bei Wang","orcid":"https://orcid.org/0000-0002-2891-8521"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bei Wang","raw_affiliation_strings":["College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-4760-3362","affiliations":[{"raw_affiliation_string":"College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073590716","display_name":"Ziying Ni","orcid":"https://orcid.org/0000-0001-8300-8865"},"institutions":[{"id":"https://openalex.org/I126231945","display_name":"Queen's University Belfast","ror":"https://ror.org/00hswnk62","country_code":"GB","type":"education","lineage":["https://openalex.org/I126231945"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ziying Ni","raw_affiliation_strings":["Centre for Secure Information Technologies (CSIT), Queen’s University Belfast, Belfast, U.K"],"raw_orcid":"https://orcid.org/0000-0001-8300-8865","affiliations":[{"raw_affiliation_string":"Centre for Secure Information Technologies (CSIT), Queen’s University Belfast, Belfast, U.K","institution_ids":["https://openalex.org/I126231945"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042656524","display_name":"Mengxue Li","orcid":null},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mengxue Li","raw_affiliation_strings":["College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0008-4206-1457","affiliations":[{"raw_affiliation_string":"College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101700624","display_name":"Fei Lyu","orcid":"https://orcid.org/0000-0001-9566-3023"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fei Lyu","raw_affiliation_strings":["College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-2282-1574","affiliations":[{"raw_affiliation_string":"College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011952918","display_name":"Yijun Cui","orcid":"https://orcid.org/0000-0002-6262-2329"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yijun Cui","raw_affiliation_strings":["College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-6262-2329","affiliations":[{"raw_affiliation_string":"College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100641142","display_name":"Wei Liu","orcid":"https://orcid.org/0000-0002-7409-0948"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weiqiang Liu","raw_affiliation_strings":["College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-8398-8648","affiliations":[{"raw_affiliation_string":"College of Integrated Circuits, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":18.952,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.98150372,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"75","issue":"6","first_page":"2141","last_page":"2154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9254999756813049,"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":0.9254999756813049,"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/T10237","display_name":"Cryptography and Data Security","score":0.03449999913573265,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.016499999910593033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.6764000058174133},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6556000113487244},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.6057000160217285},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.48899999260902405},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.46810001134872437},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43619999289512634},{"id":"https://openalex.org/keywords/commutator","display_name":"Commutator","score":0.42010000348091125},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.37450000643730164}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.694100022315979},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.6764000058174133},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6556000113487244},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.6057000160217285},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.48899999260902405},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.46810001134872437},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46389999985694885},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43619999289512634},{"id":"https://openalex.org/C145620117","wikidata":"https://www.wikidata.org/wiki/Q2989763","display_name":"Commutator","level":4,"score":0.42010000348091125},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.37450000643730164},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.3416000008583069},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.31859999895095825},{"id":"https://openalex.org/C157922185","wikidata":"https://www.wikidata.org/wiki/Q173198","display_name":"Logic synthesis","level":3,"score":0.3179999887943268},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.3109000027179718},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C14580979","wikidata":"https://www.wikidata.org/wiki/Q876049","display_name":"Very-large-scale integration","level":2,"score":0.29739999771118164},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.2026.3671958","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2026.3671958","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"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 Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","score":0.44442635774612427,"display_name":"Industry, innovation and infrastructure"}],"awards":[{"id":"https://openalex.org/G2424954739","display_name":null,"funder_award_id":"62201234","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3397188688","display_name":null,"funder_award_id":"62371226","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4070429046","display_name":null,"funder_award_id":"62022041","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6928822994","display_name":null,"funder_award_id":"62571233","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7118155122","display_name":null,"funder_award_id":"62134002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7274142727","display_name":null,"funder_award_id":"62425404","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7928980550","display_name":null,"funder_award_id":"62474092","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1498685334","https://openalex.org/W2004814164","https://openalex.org/W2467320551","https://openalex.org/W3135053459","https://openalex.org/W3157961299","https://openalex.org/W3159034445","https://openalex.org/W3185075495","https://openalex.org/W3216360301","https://openalex.org/W3216842157","https://openalex.org/W3217272717","https://openalex.org/W4210722209","https://openalex.org/W4229014338","https://openalex.org/W4285264388","https://openalex.org/W4293143765","https://openalex.org/W4294326371","https://openalex.org/W4364859972","https://openalex.org/W4384947555","https://openalex.org/W4385237357","https://openalex.org/W4387092738","https://openalex.org/W4392309219","https://openalex.org/W4393144920","https://openalex.org/W4394842312","https://openalex.org/W4399396331","https://openalex.org/W4402159598","https://openalex.org/W4403277416","https://openalex.org/W4408236261","https://openalex.org/W4410614225","https://openalex.org/W4410692334","https://openalex.org/W4416342002"],"related_works":[],"abstract_inverted_index":{"Modular":[0],"multiplication":[1,15,25],"is":[2],"a":[3,93,99],"vital":[4],"operation":[5],"in":[6,16,168],"the":[7,28,38,43,47,52,83,109,118,154,196],"Number":[8],"Theoretic":[9],"Transform":[10],"(NTT),":[11],"significantly":[12],"enhancing":[13],"polynomial":[14,32],"Post-Quantum":[17],"Cryptography":[18],"(PQC).":[19],"The":[20,182],"design":[21,92,126,152,185],"efficiency":[22],"of":[23,31,42,164,173,201],"modular":[24],"directly":[26],"influences":[27],"computational":[29],"performance":[30,200],"computation":[33,84],"units.":[34],"This":[35],"work":[36],"marks":[37],"first":[39],"hardware-oriented":[40],"improvement":[41],"Plantard":[44,53],"algorithm,":[45],"optimizing":[46],"NTT":[48,97,151,184],"architecture.":[49],"We":[50],"modify":[51],"algorithm":[54],"and":[55,74,98,111,134,146,166,170,175,179,191,198],"propose":[56],"three":[57],"innovative":[58],"enhanced":[59],"versions":[60],"tailored":[61],"for":[62,71,177],"lattice-based":[63],"cryptography":[64],"(LBC).":[65],"By":[66],"employing":[67],"pre-processed":[68],"twiddle":[69],"factors":[70],"result":[72],"correction":[73],"eliminating":[75],"an":[76],"additional":[77],"constant":[78],"multiplication,":[79],"we":[80,90],"greatly":[81],"simplify":[82],"steps.":[85],"Based":[86],"on":[87,117],"these":[88],"improvements,":[89],"further":[91],"lightweight":[94],"BRAM-free":[95],"iterative":[96,150],"high-speed":[100],"Multi-path":[101],"Delay":[102],"Commutator":[103],"(MDC)":[104],"pipelined":[105,183],"NTT,":[106],"both":[107],"targeting":[108],"ML-KEM":[110,178],"ML-DSA":[112],"parameter":[113],"sets.":[114],"Implementation":[115],"results":[116],"Xilinx":[119],"Artix-7":[120],"platform":[121],"demonstrate":[122],"that":[123],"our":[124,149,202],"Plantard_pre\u03c9":[125],"reduces":[127,187],"slice":[128],"usage":[129],"by":[130,136,189,193],"22%":[131],"to":[132,138,141],"53%":[133],"delay":[135,188],"41.1%":[137],"44.3%":[139],"compared":[140],"existing":[142],"algorithms":[143],"like":[144],"Barrett":[145],"K2RED.":[147],"Furthermore,":[148],"achieves":[153],"minimal":[155],"area-time":[156],"product":[157],"(ATP)":[158],"among":[159],"state-of-the-art":[160],"implementations,":[161],"with":[162],"reductions":[163],"61.3%":[165],"40.8%":[167],"ENS,":[169],"frequency":[171],"increases":[172],"72.7%":[174],"145.4%":[176],"ML-DSA,":[180],"respectively.":[181],"also":[186],"23.7%":[190],"ATP":[192],"4.9%,":[194],"showcasing":[195],"compactness":[197],"superior":[199],"approach.":[203]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2026-03-12T00:00:00"}