{"id":"https://openalex.org/W2890383074","doi":"https://doi.org/10.1007/s13389-018-0195-8","title":"RNS Montgomery reduction algorithms using quadratic residuosity","display_name":"RNS Montgomery reduction algorithms using quadratic residuosity","publication_year":2018,"publication_date":"2018-09-03","ids":{"openalex":"https://openalex.org/W2890383074","doi":"https://doi.org/10.1007/s13389-018-0195-8","mag":"2890383074"},"language":"en","primary_location":{"id":"doi:10.1007/s13389-018-0195-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s13389-018-0195-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s13389-018-0195-8.pdf","source":{"id":"https://openalex.org/S2764800400","display_name":"Journal of Cryptographic Engineering","issn_l":"2190-8508","issn":["2190-8508","2190-8516"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptographic Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s13389-018-0195-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103017325","display_name":"S. Kawamura","orcid":"https://orcid.org/0000-0003-1126-4645"},"institutions":[{"id":"https://openalex.org/I1292669757","display_name":"Toshiba (Japan)","ror":"https://ror.org/0326v3z14","country_code":"JP","type":"company","lineage":["https://openalex.org/I1292669757"]},{"id":"https://openalex.org/I4210106989","display_name":"Photonics Electronics Technology Research Association","ror":"https://ror.org/01fqmah26","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210106989"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Shinichi Kawamura","raw_affiliation_strings":["ECSEC Technical Research Association, Tokyo, Japan","Toshiba Corporation, Kawasaki, Japan"],"raw_orcid":"https://orcid.org/0000-0003-1126-4645","affiliations":[{"raw_affiliation_string":"ECSEC Technical Research Association, Tokyo, Japan","institution_ids":["https://openalex.org/I4210106989"]},{"raw_affiliation_string":"Toshiba Corporation, Kawasaki, Japan","institution_ids":["https://openalex.org/I1292669757"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016988489","display_name":"Yuichi Komano","orcid":"https://orcid.org/0000-0002-5121-3458"},"institutions":[{"id":"https://openalex.org/I1292669757","display_name":"Toshiba (Japan)","ror":"https://ror.org/0326v3z14","country_code":"JP","type":"company","lineage":["https://openalex.org/I1292669757"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yuichi Komano","raw_affiliation_strings":["Toshiba Corporation, Kawasaki, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Toshiba Corporation, Kawasaki, Japan","institution_ids":["https://openalex.org/I1292669757"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030059840","display_name":"Hideo Shimizu","orcid":"https://orcid.org/0000-0002-3457-514X"},"institutions":[{"id":"https://openalex.org/I1292669757","display_name":"Toshiba (Japan)","ror":"https://ror.org/0326v3z14","country_code":"JP","type":"company","lineage":["https://openalex.org/I1292669757"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hideo Shimizu","raw_affiliation_strings":["Toshiba Corporation, Kawasaki, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Toshiba Corporation, Kawasaki, Japan","institution_ids":["https://openalex.org/I1292669757"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074594488","display_name":"Tomoko Yonemura","orcid":null},"institutions":[{"id":"https://openalex.org/I1292669757","display_name":"Toshiba (Japan)","ror":"https://ror.org/0326v3z14","country_code":"JP","type":"company","lineage":["https://openalex.org/I1292669757"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tomoko Yonemura","raw_affiliation_strings":["Toshiba Corporation, Kawasaki, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Toshiba Corporation, Kawasaki, Japan","institution_ids":["https://openalex.org/I1292669757"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5103017325"],"corresponding_institution_ids":["https://openalex.org/I1292669757","https://openalex.org/I4210106989"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":4.5222,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.95348395,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"9","issue":"4","first_page":"313","last_page":"331"},"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":0.9919999837875366,"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":0.9858999848365784,"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/residue-number-system","display_name":"Residue number system","score":0.8367204666137695},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.7453066110610962},{"id":"https://openalex.org/keywords/quadratic-residue","display_name":"Quadratic residue","score":0.6182324886322021},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.548777163028717},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4971485435962677},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.48227551579475403},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4623919725418091},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4084954261779785},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39408186078071594}],"concepts":[{"id":"https://openalex.org/C71480937","wikidata":"https://www.wikidata.org/wiki/Q3086516","display_name":"Residue number system","level":2,"score":0.8367204666137695},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.7453066110610962},{"id":"https://openalex.org/C12817185","wikidata":"https://www.wikidata.org/wiki/Q878259","display_name":"Quadratic residue","level":2,"score":0.6182324886322021},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.548777163028717},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4971485435962677},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.48227551579475403},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4623919725418091},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4084954261779785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39408186078071594},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s13389-018-0195-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s13389-018-0195-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s13389-018-0195-8.pdf","source":{"id":"https://openalex.org/S2764800400","display_name":"Journal of Cryptographic Engineering","issn_l":"2190-8508","issn":["2190-8508","2190-8516"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptographic Engineering","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s13389-018-0195-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s13389-018-0195-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s13389-018-0195-8.pdf","source":{"id":"https://openalex.org/S2764800400","display_name":"Journal of Cryptographic Engineering","issn_l":"2190-8508","issn":["2190-8508","2190-8516"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptographic Engineering","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321034","display_name":"New Energy and Industrial Technology Development Organization","ror":"https://ror.org/0055k7a87"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2890383074.pdf","grobid_xml":"https://content.openalex.org/works/W2890383074.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1491543582","https://openalex.org/W1513845308","https://openalex.org/W1517364441","https://openalex.org/W1565956254","https://openalex.org/W1572502182","https://openalex.org/W1608900708","https://openalex.org/W1879275280","https://openalex.org/W1910751411","https://openalex.org/W1923580562","https://openalex.org/W1968875548","https://openalex.org/W1988025868","https://openalex.org/W1992719330","https://openalex.org/W2004814164","https://openalex.org/W2076515953","https://openalex.org/W2097953324","https://openalex.org/W2100264217","https://openalex.org/W2109996716","https://openalex.org/W2132249288","https://openalex.org/W2132341963","https://openalex.org/W2155095649","https://openalex.org/W2176190288","https://openalex.org/W2530710018","https://openalex.org/W2594864105"],"related_works":["https://openalex.org/W1579872621","https://openalex.org/W2912881334","https://openalex.org/W2584805892","https://openalex.org/W1553103133","https://openalex.org/W1968471781","https://openalex.org/W1973181769","https://openalex.org/W2784975415","https://openalex.org/W2964271806","https://openalex.org/W4300187176","https://openalex.org/W2890383074"],"abstract_inverted_index":{"The":[0],"residue":[1],"number":[2,71],"system":[3,38],"(RNS)":[4],"is":[5,30,56,80,86,138],"a":[6,21,35,58,67,90,103],"method":[7],"for":[8,39,145],"representing":[9],"an":[10,13],"integer":[11],"as":[12,82],"n-tuple":[14],"of":[15,54,66,72],"its":[16,99],"residues":[17],"with":[18,131],"respect":[19],"to":[20,33,111],"given":[22],"base.":[23],"Since":[24],"RNS":[25,46,95,146],"has":[26],"inherent":[27],"parallelism,":[28],"it":[29,109,137],"actively":[31],"researched":[32],"implement":[34],"faster":[36],"processing":[37],"public-key":[40],"cryptography.":[41],"This":[42,85,107],"paper":[43],"proposes":[44],"new":[45,91,122],"Montgomery":[47],"reduction":[48],"algorithms,":[49,118],"Q-RNSs,":[50],"the":[51,64,70,77,94,121,149],"main":[52],"part":[53],"which":[55],"twice":[57],"matrix":[59],"multiplication.":[60],"Letting":[61],"n":[62],"be":[63],"size":[65],"base":[68],"set,":[69],"unit":[73],"modular":[74],"multiplications":[75],"in":[76],"proposed":[78],"algorithms":[79,123],"evaluated":[81],"$$(2n^2+n)$$":[83],".":[84],"achieved":[87],"by":[88],"posing":[89],"restriction":[92],"on":[93],"base,":[96],"namely,":[97],"that":[98,140],"elements":[100],"should":[101],"have":[102,127],"certain":[104],"quadratic":[105,150],"residuosity.":[106],"makes":[108],"possible":[110],"remove":[112],"some":[113],"multiplication":[114],"steps":[115],"from":[116],"conventional":[117,132],"and":[119,126],"thus":[120],"are":[124,142],"simpler":[125],"higher":[128],"regularity":[129],"compared":[130],"ones.":[133],"From":[134],"our":[135],"experiments,":[136],"confirmed":[139],"there":[141],"sufficient":[143],"candidates":[144],"bases":[147],"meeting":[148],"residuosity":[151],"requirements.":[152]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
