{"id":"https://openalex.org/W4403123695","doi":"https://doi.org/10.1109/access.2024.3473901","title":"Integer Modular Multiplication With Barrett Reduction and Its Variants for Homomorphic Encryption Applications: A Comprehensive Review and an Empirical Study","display_name":"Integer Modular Multiplication With Barrett Reduction and Its Variants for Homomorphic Encryption Applications: A Comprehensive Review and an Empirical Study","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4403123695","doi":"https://doi.org/10.1109/access.2024.3473901"},"language":"en","primary_location":{"id":"doi:10.1109/access.2024.3473901","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2024.3473901","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"type":"review","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2024.3473901","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072652326","display_name":"Ardianto Satriawan","orcid":"https://orcid.org/0000-0001-5400-0995"},"institutions":[{"id":"https://openalex.org/I191879574","display_name":"Inha University","ror":"https://ror.org/01easw929","country_code":"KR","type":"education","lineage":["https://openalex.org/I191879574"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Ardianto Satriawan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Inha University, Incheon, South Korea","Department of Electrical and Computer Engineering, Inha University, Incheon, Korea"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Inha University, Incheon, South Korea","institution_ids":["https://openalex.org/I191879574"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Inha University, Incheon, Korea","institution_ids":["https://openalex.org/I191879574"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017341036","display_name":"Rella Mareta","orcid":null},"institutions":[{"id":"https://openalex.org/I191879574","display_name":"Inha University","ror":"https://ror.org/01easw929","country_code":"KR","type":"education","lineage":["https://openalex.org/I191879574"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Rella Mareta","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Inha University, Incheon, South Korea","Department of Electrical and Computer Engineering, Inha University, Incheon, Korea"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Inha University, Incheon, South Korea","institution_ids":["https://openalex.org/I191879574"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Inha University, Incheon, Korea","institution_ids":["https://openalex.org/I191879574"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069498930","display_name":"Hanho Lee","orcid":"https://orcid.org/0000-0001-8815-1927"},"institutions":[{"id":"https://openalex.org/I191879574","display_name":"Inha University","ror":"https://ror.org/01easw929","country_code":"KR","type":"education","lineage":["https://openalex.org/I191879574"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Hanho Lee","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Inha University, Incheon, South Korea","Department of Electrical and Computer Engineering, Inha University, Incheon, Korea"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Inha University, Incheon, South Korea","institution_ids":["https://openalex.org/I191879574"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Inha University, Incheon, Korea","institution_ids":["https://openalex.org/I191879574"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072652326"],"corresponding_institution_ids":["https://openalex.org/I191879574"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":5.6994,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.96193892,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"12","issue":null,"first_page":"147283","last_page":"147300"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9958000183105469,"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":0.9958000183105469,"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":0.9934999942779541,"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":0.9617000222206116,"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/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.8986074924468994},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.7107031941413879},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6370449066162109},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.5940364003181458},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5884988903999329},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.557051956653595},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.532220721244812},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.5241004228591919},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4104020297527313},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37648096680641174},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3037921190261841},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.12830954790115356},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08701536059379578},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.0718022882938385}],"concepts":[{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.8986074924468994},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.7107031941413879},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6370449066162109},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.5940364003181458},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5884988903999329},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.557051956653595},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.532220721244812},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.5241004228591919},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4104020297527313},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37648096680641174},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3037921190261841},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.12830954790115356},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08701536059379578},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0718022882938385},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2024.3473901","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2024.3473901","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4b72f57636634cbf9918159c581d5bdc","is_oa":true,"landing_page_url":"https://doaj.org/article/4b72f57636634cbf9918159c581d5bdc","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":"IEEE Access, Vol 12, Pp 147283-147300 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2024.3473901","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2024.3473901","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3993613658","display_name":null,"funder_award_id":"IITP-2021-0-02052","funder_id":"https://openalex.org/F4320328359","funder_display_name":"Ministry of Science and ICT, South Korea"},{"id":"https://openalex.org/G4080862803","display_name":null,"funder_award_id":"RS-2024-00432449","funder_id":"https://openalex.org/F4320328359","funder_display_name":"Ministry of Science and ICT, South Korea"},{"id":"https://openalex.org/G5865046914","display_name":null,"funder_award_id":"2021R1A2C1011232","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320328359","display_name":"Ministry of Science and ICT, South Korea","ror":"https://ror.org/01wpjm123"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":68,"referenced_works":["https://openalex.org/W56544557","https://openalex.org/W1498685334","https://openalex.org/W1573824426","https://openalex.org/W1582291092","https://openalex.org/W1987159704","https://openalex.org/W2004814164","https://openalex.org/W2021394614","https://openalex.org/W2028888780","https://openalex.org/W2048994663","https://openalex.org/W2069441027","https://openalex.org/W2083368929","https://openalex.org/W2089900865","https://openalex.org/W2107953479","https://openalex.org/W2130423410","https://openalex.org/W2177209050","https://openalex.org/W2226167778","https://openalex.org/W2530820605","https://openalex.org/W2587454507","https://openalex.org/W2738531374","https://openalex.org/W2768174108","https://openalex.org/W2791664942","https://openalex.org/W2792565434","https://openalex.org/W2794556148","https://openalex.org/W2898822637","https://openalex.org/W2934302500","https://openalex.org/W2953289753","https://openalex.org/W2963480066","https://openalex.org/W2966077459","https://openalex.org/W3005730048","https://openalex.org/W3115372621","https://openalex.org/W3133130051","https://openalex.org/W3189815475","https://openalex.org/W3194129464","https://openalex.org/W4210722209","https://openalex.org/W4224245284","https://openalex.org/W4225377307","https://openalex.org/W4231896027","https://openalex.org/W4282979900","https://openalex.org/W4308516229","https://openalex.org/W4323065961","https://openalex.org/W4382119118","https://openalex.org/W4382564403","https://openalex.org/W4383220377","https://openalex.org/W4383899661","https://openalex.org/W4385187193","https://openalex.org/W4385414976","https://openalex.org/W4385569630","https://openalex.org/W4386121344","https://openalex.org/W4386608731","https://openalex.org/W4387019087","https://openalex.org/W4387053951","https://openalex.org/W4387121228","https://openalex.org/W4388022921","https://openalex.org/W4388405929","https://openalex.org/W4391164410","https://openalex.org/W4391183464","https://openalex.org/W4393647697","https://openalex.org/W4394698520","https://openalex.org/W4399409036","https://openalex.org/W4400230650","https://openalex.org/W4403123001","https://openalex.org/W6606067566","https://openalex.org/W6607864507","https://openalex.org/W6753995509","https://openalex.org/W6769118982","https://openalex.org/W6852731070","https://openalex.org/W6856640624","https://openalex.org/W6939767756"],"related_works":["https://openalex.org/W2539930818","https://openalex.org/W4393118461","https://openalex.org/W4390664647","https://openalex.org/W3012147850","https://openalex.org/W2361290373","https://openalex.org/W4302768783","https://openalex.org/W2782264914","https://openalex.org/W2904069009","https://openalex.org/W2792736654","https://openalex.org/W2355149595"],"abstract_inverted_index":{"Modular":[0],"arithmetic":[1],"calculations,":[2],"such":[3],"as":[4],"modular":[5,23,30,42,46,53],"addition":[6,24],"and":[7,17,65,73,81,84],"multiplication,":[8],"are":[9],"fundamental":[10],"building":[11],"blocks":[12],"to":[13,35],"Post-Quantum":[14],"Cryptography":[15],"(PQC)":[16],"Homomorphic":[18],"Encryption":[19],"(HE)":[20],"systems.":[21],"While":[22],"has":[25],"straightforward":[26],"hardware":[27],"implementations,":[28],"integer":[29,41],"multiplication":[31,43,54],"is":[32],"more":[33],"challenging":[34],"implement.":[36],"This":[37],"work":[38],"focuses":[39],"on":[40],"with":[44],"Barrett":[45,52],"reduction,":[47],"or":[48],"in":[49],"short,":[50],"the":[51,78],"(BMM)":[55],"technique,":[56],"presenting":[57],"an":[58],"overview":[59],"of":[60,77],"its":[61],"original":[62],"algorithm,":[63],"variants,":[64],"subsequent":[66],"optimizations.":[67],"The":[68],"study":[69],"offers":[70],"comparative":[71],"examples":[72],"a":[74],"comprehensive":[75],"analysis":[76],"theoretical":[79],"complexity":[80],"both":[82],"empirical":[83],"experimental":[85],"results":[86],"for":[87],"each":[88],"BMM":[89],"variant.":[90]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5}],"updated_date":"2025-12-27T23:08:20.325037","created_date":"2025-10-10T00:00:00"}
