{"id":"https://openalex.org/W4308575787","doi":"https://doi.org/10.1109/vlsi-soc54400.2022.9939657","title":"High-Level Synthesis design approach for Number-Theoretic Multiplier","display_name":"High-Level Synthesis design approach for Number-Theoretic Multiplier","publication_year":2022,"publication_date":"2022-10-03","ids":{"openalex":"https://openalex.org/W4308575787","doi":"https://doi.org/10.1109/vlsi-soc54400.2022.9939657"},"language":"en","primary_location":{"id":"doi:10.1109/vlsi-soc54400.2022.9939657","is_oa":false,"landing_page_url":"https://doi.org/10.1109/vlsi-soc54400.2022.9939657","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IFIP/IEEE 30th International Conference on Very Large Scale Integration (VLSI-SoC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://zenodo.org/record/7413465","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036765642","display_name":"Alexander El-Kady","orcid":null},"institutions":[{"id":"https://openalex.org/I4210135709","display_name":"Industrial Systems Institute","ror":"https://ror.org/02sy6k521","country_code":"GR","type":"nonprofit","lineage":["https://openalex.org/I4210135709"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Alexander El-Kady","raw_affiliation_strings":["R.C. Athena,Industrial Systems Institute,Platani-Patras,Greece,26504"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"R.C. Athena,Industrial Systems Institute,Platani-Patras,Greece,26504","institution_ids":["https://openalex.org/I4210135709"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073797976","display_name":"Apostolos P. Fournaris","orcid":"https://orcid.org/0000-0002-4758-2349"},"institutions":[{"id":"https://openalex.org/I4210135709","display_name":"Industrial Systems Institute","ror":"https://ror.org/02sy6k521","country_code":"GR","type":"nonprofit","lineage":["https://openalex.org/I4210135709"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Apostolos P. Fournaris","raw_affiliation_strings":["R.C. Athena,Industrial Systems Institute,Platani-Patras,Greece,26504"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"R.C. Athena,Industrial Systems Institute,Platani-Patras,Greece,26504","institution_ids":["https://openalex.org/I4210135709"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084883489","display_name":"Evangelos Haleplidis","orcid":"https://orcid.org/0009-0002-7689-6483"},"institutions":[{"id":"https://openalex.org/I4210135709","display_name":"Industrial Systems Institute","ror":"https://ror.org/02sy6k521","country_code":"GR","type":"nonprofit","lineage":["https://openalex.org/I4210135709"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Evangelos Haleplidis","raw_affiliation_strings":["R.C. Athena,Industrial Systems Institute,Platani-Patras,Greece,26504"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"R.C. Athena,Industrial Systems Institute,Platani-Patras,Greece,26504","institution_ids":["https://openalex.org/I4210135709"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021252086","display_name":"Vassilis Paliouras","orcid":"https://orcid.org/0000-0002-1414-7500"},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Vassilis Paliouras","raw_affiliation_strings":["University of Patras,Electrical and Computer Engineering Department,Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Patras,Electrical and Computer Engineering Department,Greece","institution_ids":["https://openalex.org/I174878644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5025,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63346135,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9991000294685364,"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/T11130","display_name":"Coding theory and cryptography","score":0.9986000061035156,"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/computer-science","display_name":"Computer science","score":0.6885649561882019},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.5252090096473694},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.516602635383606},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4821838438510895},{"id":"https://openalex.org/keywords/loop-unrolling","display_name":"Loop unrolling","score":0.45927295088768005},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4493711590766907},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4269619584083557},{"id":"https://openalex.org/keywords/high-level-synthesis","display_name":"High-level synthesis","score":0.4267841875553131},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.4137204885482788},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33692672848701477},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.28390783071517944},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2784859240055084},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.143130362033844},{"id":"https://openalex.org/keywords/compiler","display_name":"Compiler","score":0.11875832080841064},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.11833533644676208},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11113938689231873}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6885649561882019},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.5252090096473694},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.516602635383606},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4821838438510895},{"id":"https://openalex.org/C76970557","wikidata":"https://www.wikidata.org/wiki/Q1869750","display_name":"Loop unrolling","level":3,"score":0.45927295088768005},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4493711590766907},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4269619584083557},{"id":"https://openalex.org/C58013763","wikidata":"https://www.wikidata.org/wiki/Q5754574","display_name":"High-level synthesis","level":3,"score":0.4267841875553131},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.4137204885482788},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33692672848701477},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.28390783071517944},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2784859240055084},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.143130362033844},{"id":"https://openalex.org/C169590947","wikidata":"https://www.wikidata.org/wiki/Q47506","display_name":"Compiler","level":2,"score":0.11875832080841064},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.11833533644676208},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11113938689231873},{"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},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/vlsi-soc54400.2022.9939657","is_oa":false,"landing_page_url":"https://doi.org/10.1109/vlsi-soc54400.2022.9939657","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IFIP/IEEE 30th International Conference on Very Large Scale Integration (VLSI-SoC)","raw_type":"proceedings-article"},{"id":"pmh:oai:zenodo.org:7413465","is_oa":true,"landing_page_url":"https://zenodo.org/record/7413465","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferencePaper"}],"best_oa_location":{"id":"pmh:oai:zenodo.org:7413465","is_oa":true,"landing_page_url":"https://zenodo.org/record/7413465","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferencePaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1580045882","https://openalex.org/W2061171222","https://openalex.org/W2079219927","https://openalex.org/W2117639037","https://openalex.org/W2151163104","https://openalex.org/W2544862116","https://openalex.org/W2791664942","https://openalex.org/W2801068370","https://openalex.org/W2952334088","https://openalex.org/W2961927607","https://openalex.org/W2968983325","https://openalex.org/W2981801946","https://openalex.org/W2995910517","https://openalex.org/W3004368054","https://openalex.org/W3013574053","https://openalex.org/W3065439923","https://openalex.org/W3108669911","https://openalex.org/W3109801878","https://openalex.org/W3172595455","https://openalex.org/W3205147040","https://openalex.org/W3215302011","https://openalex.org/W6782191061"],"related_works":["https://openalex.org/W2921149022","https://openalex.org/W3003393365","https://openalex.org/W3157069154","https://openalex.org/W2267745769","https://openalex.org/W2398354748","https://openalex.org/W2156848920","https://openalex.org/W2604781201","https://openalex.org/W2082085231","https://openalex.org/W4360994686","https://openalex.org/W2126613634"],"abstract_inverted_index":{"Lattice-based":[0],"cryptography":[1],"(LBC)":[2],"performs":[3],"polynomial":[4,17,36,168],"multiplication":[5,18,37,71],"using":[6,106],"the":[7,16,30,52,59,65,69,93,159,199,211,213,219,225,235,238,248,260,265],"Number":[8],"Theoretic":[9],"Transform":[10],"(NTT),":[11],"in":[12,72,110,138,161,210,244,264],"order":[13,139,245],"to":[14,22,33,67,140,151,188,224,246,282,288],"reduce":[15,247],"complexity":[19,99],"from":[20,198],"O(n2)":[21],"O(n":[23],"log":[24],"n).":[25],"Although":[26],"NTT-based":[27,70,167],"multipliers":[28],"offer":[29,85],"fastest":[31],"way":[32],"compute":[34],"a":[35,48,87,146,165,180,190],"product":[38],"for":[39,122],"high-degree":[40],"polynomials":[41],"(with":[42],"non-trivial":[43],"bit-length":[44],"coefficients),":[45],"they":[46,90],"constitute":[47],"significant":[49,205],"part":[50],"of":[51,218,237],"overall":[53],"LBC":[54,61,266],"scheme":[55,269],"delay":[56],"thus":[57],"becoming":[58],"main":[60],"efficiency":[62],"bottleneck.":[63],"Therefore,":[64],"need":[66],"optimize":[68],"an":[73,143,172],"easy,":[74],"automatic":[75],"yet":[76,202],"efficient":[77,192],"manner":[78],"is":[79,227,242],"significant.":[80],"High-Level":[81],"synthesis":[82],"(HLS)":[83],"tools":[84],"such":[86],"capability":[88],"since":[89],"can":[91,196],"hide":[92],"Register":[94],"Transfer":[95],"Level":[96],"(RTL)-based":[97],"design":[98,117,147,178,187,194],"(typically":[100],"realized":[101],"by":[102,258],"hardware":[103],"description":[104,124],"languages)":[105],"high":[107,206],"level":[108],"descriptions":[109],"C,":[111],"C++":[112],"or":[113],"openCL.":[114],"However,":[115],"this":[116,156],"approach":[118],"requires":[119],"careful":[120],"modifications":[121],"high-level":[123],"code":[125,232],"like":[126],"loop":[127,129,133,136],"reordering,":[128],"flattening,":[130],"removing":[131],"dependencies,":[132],"pipelining":[134],"and":[135,215,234,280],"unrolling":[137],"produce":[141],"through":[142],"HLS":[144,173,182,200,240],"tool":[145],"with":[148,179],"performance":[149],"comparable":[150],"RTL":[152],"hand-crafted":[153],"designs.":[154],"In":[155],"paper,":[157,212],"extending":[158],"work":[160,254],"[1]":[162],"we":[163],"propose":[164],"complete":[166],"multiplier":[169,193,263],"that":[170,195],"combines":[171],"optimized":[174],"Cooley-Tukey":[175],"(CT)":[176],"NTT":[177,220,262],"proposed,":[181],"optimized,":[183],"Gentleman-Sande":[184],"(GS)":[185],"Inverse-NTT":[186],"create":[189],"highly":[191],"benefit":[197],"flexibility":[201],"still":[203],"achieve":[204,283],"speed.":[207],"More":[208],"specifically,":[209],"read":[214],"write":[216],"access":[217],"processing":[221],"elements":[222],"(PE)":[223],"memory":[226],"significantly":[228,284],"increased":[229],"though":[230],"appropriate":[231],"redesign":[233],"use":[236],"dependence":[239],"pragma":[241],"proposed":[243,253,261],"dependencies":[249],"between":[250],"PEs.":[251],"The":[252],"has":[255],"been":[256],"evaluated":[257],"introducing":[259],"Dilithium":[267],"digital-signature":[268],"(polynomial":[270],"degree":[271],"n":[272],"=":[273,278],"256,":[274],"coefficient":[275],"modulus":[276],"Q":[277],"8380417)":[279],"managed":[281],"higher":[285],"speed":[286],"compared":[287],"other":[289],"similar":[290],"works.":[291]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}