{"id":"https://openalex.org/W4387019087","doi":"https://doi.org/10.3390/cryptography7040046","title":"A High-Efficiency Modular Multiplication Digital Signal Processing for Lattice-Based Post-Quantum Cryptography","display_name":"A High-Efficiency Modular Multiplication Digital Signal Processing for Lattice-Based Post-Quantum Cryptography","publication_year":2023,"publication_date":"2023-09-25","ids":{"openalex":"https://openalex.org/W4387019087","doi":"https://doi.org/10.3390/cryptography7040046"},"language":"en","primary_location":{"id":"doi:10.3390/cryptography7040046","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography7040046","pdf_url":"https://www.mdpi.com/2410-387X/7/4/46/pdf?version=1695627744","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2410-387X/7/4/46/pdf?version=1695627744","any_repository_has_fulltext":true},"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, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Tokyo 182-8585, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Tokyo 182-8585, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","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, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Tokyo 182-8585, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Tokyo 182-8585, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"last","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, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Tokyo 182-8585, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Tokyo 182-8585, Japan","institution_ids":["https://openalex.org/I20529979"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064640365"],"corresponding_institution_ids":["https://openalex.org/I20529979"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1732},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1732},"fwci":8.2366,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.97621275,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"7","issue":"4","first_page":"46","last_page":"46"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9987999796867371,"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/T10237","display_name":"Cryptography and Data Security","score":0.9987000226974487,"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/digital-signal-processing","display_name":"Digital signal processing","score":0.6967270374298096},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.6795839667320251},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5458089709281921},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.5421692728996277},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.49584683775901794},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.4931463599205017},{"id":"https://openalex.org/keywords/lattice-based-cryptography","display_name":"Lattice-based cryptography","score":0.471583753824234},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.4502817392349243},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.43118253350257874},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.42144322395324707},{"id":"https://openalex.org/keywords/digital-signal-processor","display_name":"Digital signal processor","score":0.41480904817581177},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.41303712129592896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3519653081893921},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.34830713272094727},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.3029148578643799},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23073217272758484},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.1780884861946106},{"id":"https://openalex.org/keywords/quantum-cryptography","display_name":"Quantum cryptography","score":0.1359400451183319},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.07418957352638245},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07190492749214172}],"concepts":[{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.6967270374298096},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.6795839667320251},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5458089709281921},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.5421692728996277},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.49584683775901794},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.4931463599205017},{"id":"https://openalex.org/C137660015","wikidata":"https://www.wikidata.org/wiki/Q6497083","display_name":"Lattice-based cryptography","level":5,"score":0.471583753824234},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.4502817392349243},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.43118253350257874},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.42144322395324707},{"id":"https://openalex.org/C161611012","wikidata":"https://www.wikidata.org/wiki/Q106370","display_name":"Digital signal processor","level":3,"score":0.41480904817581177},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.41303712129592896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3519653081893921},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.34830713272094727},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.3029148578643799},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23073217272758484},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.1780884861946106},{"id":"https://openalex.org/C144901912","wikidata":"https://www.wikidata.org/wiki/Q471906","display_name":"Quantum cryptography","level":4,"score":0.1359400451183319},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.07418957352638245},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07190492749214172},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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":2,"locations":[{"id":"doi:10.3390/cryptography7040046","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography7040046","pdf_url":"https://www.mdpi.com/2410-387X/7/4/46/pdf?version=1695627744","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:421ae8d7ab3c4e8a945f15cda8bf1711","is_oa":true,"landing_page_url":"https://doaj.org/article/421ae8d7ab3c4e8a945f15cda8bf1711","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cryptography, Vol 7, Iss 4, p 46 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/cryptography7040046","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography7040046","pdf_url":"https://www.mdpi.com/2410-387X/7/4/46/pdf?version=1695627744","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4387019087.pdf"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W179223734","https://openalex.org/W1498685334","https://openalex.org/W1669999576","https://openalex.org/W2004814164","https://openalex.org/W2051009455","https://openalex.org/W2061171222","https://openalex.org/W2064680883","https://openalex.org/W2069441027","https://openalex.org/W2107953479","https://openalex.org/W2295948984","https://openalex.org/W2467320551","https://openalex.org/W2616692762","https://openalex.org/W2913851998","https://openalex.org/W2953289753","https://openalex.org/W2953568773","https://openalex.org/W3013093367","https://openalex.org/W3119074453","https://openalex.org/W3135053459","https://openalex.org/W3135898413","https://openalex.org/W3157575264","https://openalex.org/W3157961299","https://openalex.org/W3159034445","https://openalex.org/W3185075495","https://openalex.org/W3187954618","https://openalex.org/W3212142976","https://openalex.org/W3213547738","https://openalex.org/W3217272717","https://openalex.org/W4207043551","https://openalex.org/W4210722209","https://openalex.org/W4226075590","https://openalex.org/W4226101078","https://openalex.org/W4240339612","https://openalex.org/W4246927843","https://openalex.org/W4250492047","https://openalex.org/W4285264388","https://openalex.org/W4285302767","https://openalex.org/W4294326371","https://openalex.org/W4312559487","https://openalex.org/W4312563345","https://openalex.org/W4313496496","https://openalex.org/W4364859972","https://openalex.org/W4383899661","https://openalex.org/W4384947555","https://openalex.org/W4385237357","https://openalex.org/W4386178380","https://openalex.org/W6631311870","https://openalex.org/W6799280137","https://openalex.org/W6839324823"],"related_works":["https://openalex.org/W1994292126","https://openalex.org/W2405527256","https://openalex.org/W4249848495","https://openalex.org/W2041904473","https://openalex.org/W2136650617","https://openalex.org/W2391901421","https://openalex.org/W1650124897","https://openalex.org/W2146721459","https://openalex.org/W2041380856","https://openalex.org/W4387019087"],"abstract_inverted_index":{"The":[0,78],"Number":[1],"Theoretic":[2],"Transform":[3],"(NTT)":[4],"has":[5],"been":[6],"widely":[7],"used":[8,39],"to":[9,44,153,158,186],"speed":[10,96],"up":[11],"polynomial":[12],"multiplication":[13,55,66,84,161],"in":[14,135,151,162],"lattice-based":[15,90,198],"post-quantum":[16],"algorithms.":[17],"All":[18],"NTT":[19,30],"operands":[20],"use":[21],"modular":[22,25,65,75,86,202],"arithmetic,":[23],"especially":[24],"multiplication,":[26],"which":[27],"significantly":[28],"influences":[29],"hardware":[31,37,183],"implementation":[32],"efficiency.":[33],"Until":[34],"now,":[35],"most":[36],"implementations":[38],"Digital":[40],"Signal":[41],"Processing":[42],"(DSP)":[43],"multiply":[45],"two":[46],"integers":[47],"and":[48,74,85,97,114,127],"optimally":[49],"perform":[50],"modulo":[51],"computations":[52],"from":[53],"the":[54,69,95,101,121,132,136,144,147,163,168,193],"product.":[56],"This":[57],"paper":[58],"presents":[59],"a":[60,93,159,171,182],"customized":[61],"Lattice-DSP":[62],"(L-DSP)":[63],"for":[64,89,106,111,117,177,197],"based":[67],"on":[68,167,181],"Karatsuba":[70],"algorithm,":[71],"Vedic":[72],"multiplier,":[73],"reduction":[76,87],"methods.":[77],"proposed":[79,169],"L-DSP":[80],"performs":[81],"both":[82],"integer":[83],"simultaneously":[88],"cryptography.":[91],"As":[92],"result,":[94],"area":[98],"efficiency":[99],"of":[100,124,146],"L-DSPs":[102],"are":[103],"283":[104],"MHz":[105,110,116],"77":[107],"SLICEs,":[108,113,156],"272":[109],"87":[112],"256":[115],"101":[118],"SLICEs":[119],"with":[120],"parameters":[122],"q":[123],"3329,":[125],"7681,":[126],"12,289,":[128],"respectively.":[129],"In":[130],"addition,":[131],"N\u22121":[133],"multiplier":[134],"Inverse-NTT":[137],"(INTT)":[138],"calculation":[139],"is":[140,179,192],"also":[141],"eliminated,":[142],"reducing":[143],"size":[145],"Butterfly":[148],"Unit":[149],"(BU)":[150],"CRYSTAL-Kyber":[152,178],"about":[154],"104":[155],"equivalent":[157,185],"conventional":[160],"other":[164],"studies.":[165],"Based":[166],"DSP,":[170],"Point-Wise":[172],"Matrix":[173],"Multiplication":[174],"(PWMM)":[175],"architecture":[176],"designed":[180,196],"footprint":[184],"386":[187],"SLICEs.":[188],"Furthermore,":[189],"this":[190],"research":[191],"first":[194],"DSP":[195],"Post-quantum":[199],"Cryptography":[200],"(PQC)":[201],"multiplication.":[203]},"counts_by_year":[{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":8}],"updated_date":"2026-02-28T09:26:25.869077","created_date":"2025-10-10T00:00:00"}