{"id":"https://openalex.org/W3080933033","doi":"https://doi.org/10.1109/access.2020.3019452","title":"Classification of Moduli Sets for Residue Number System With Special Diagonal Functions","display_name":"Classification of Moduli Sets for Residue Number System With Special Diagonal Functions","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3080933033","doi":"https://doi.org/10.1109/access.2020.3019452","mag":"3080933033"},"language":"en","primary_location":{"id":"doi:10.1109/access.2020.3019452","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3019452","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2020.3019452","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026823761","display_name":"Peter Boyvalenkov","orcid":"https://orcid.org/0000-0001-7563-9552"},"institutions":[{"id":"https://openalex.org/I24768866","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03","country_code":"BG","type":"government","lineage":["https://openalex.org/I24768866"]},{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]}],"countries":["BG"],"is_corresponding":true,"raw_author_name":"Peter Boyvalenkov","raw_affiliation_strings":["Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria"],"raw_orcid":"https://orcid.org/0000-0001-7563-9552","affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria","institution_ids":["https://openalex.org/I4210105926","https://openalex.org/I24768866"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018867267","display_name":"N.I. Chervyakov","orcid":"https://orcid.org/0000-0002-4573-2032"},"institutions":[{"id":"https://openalex.org/I210043505","display_name":"North-Caucasus Federal University","ror":"https://ror.org/05g1k4d79","country_code":"RU","type":"education","lineage":["https://openalex.org/I210043505"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Nikolay I. Chervyakov","raw_affiliation_strings":["Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, Stavropol, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, Stavropol, Russia","institution_ids":["https://openalex.org/I210043505"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032223985","display_name":"Pavel Lyakhov","orcid":"https://orcid.org/0000-0003-0487-4779"},"institutions":[{"id":"https://openalex.org/I210043505","display_name":"North-Caucasus Federal University","ror":"https://ror.org/05g1k4d79","country_code":"RU","type":"education","lineage":["https://openalex.org/I210043505"]},{"id":"https://openalex.org/I41518628","display_name":"Saint Petersburg State Electrotechnical University","ror":"https://ror.org/023bq8521","country_code":"RU","type":"education","lineage":["https://openalex.org/I41518628"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Pavel Lyakhov","raw_affiliation_strings":["Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, Stavropol, Russia","Department of Automation and Control Processes, Saint Petersburg Electrotechnical University \"LETI\", Saint Petersburg, Russia"],"raw_orcid":"https://orcid.org/0000-0003-0487-4779","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, Stavropol, Russia","institution_ids":["https://openalex.org/I210043505"]},{"raw_affiliation_string":"Department of Automation and Control Processes, Saint Petersburg Electrotechnical University \"LETI\", Saint Petersburg, Russia","institution_ids":["https://openalex.org/I41518628"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025346936","display_name":"Nataliya Semyonova","orcid":"https://orcid.org/0000-0001-6462-2106"},"institutions":[{"id":"https://openalex.org/I210043505","display_name":"North-Caucasus Federal University","ror":"https://ror.org/05g1k4d79","country_code":"RU","type":"education","lineage":["https://openalex.org/I210043505"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Nataliya Semyonova","raw_affiliation_strings":["Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, Stavropol, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, Stavropol, Russia","institution_ids":["https://openalex.org/I210043505"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056395916","display_name":"Anton Nazarov","orcid":"https://orcid.org/0000-0002-0109-6097"},"institutions":[{"id":"https://openalex.org/I210043505","display_name":"North-Caucasus Federal University","ror":"https://ror.org/05g1k4d79","country_code":"RU","type":"education","lineage":["https://openalex.org/I210043505"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Anton Nazarov","raw_affiliation_strings":["Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, Stavropol, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, Stavropol, Russia","institution_ids":["https://openalex.org/I210043505"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004597011","display_name":"Maria Valueva","orcid":"https://orcid.org/0000-0002-4732-3216"},"institutions":[{"id":"https://openalex.org/I210043505","display_name":"North-Caucasus Federal University","ror":"https://ror.org/05g1k4d79","country_code":"RU","type":"education","lineage":["https://openalex.org/I210043505"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Maria Valueva","raw_affiliation_strings":["Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, Stavropol, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, Stavropol, Russia","institution_ids":["https://openalex.org/I210043505"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042922624","display_name":"Georgi Boyvalenkov","orcid":"https://orcid.org/0000-0001-5384-6200"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Georgi Boyvalenkov","raw_affiliation_strings":["Bosch.IO LTD, Sofia, Bulgaria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bosch.IO LTD, Sofia, Bulgaria","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035058924","display_name":"D. V. Bogaevskiy","orcid":null},"institutions":[{"id":"https://openalex.org/I41518628","display_name":"Saint Petersburg State Electrotechnical University","ror":"https://ror.org/023bq8521","country_code":"RU","type":"education","lineage":["https://openalex.org/I41518628"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Danil Bogaevskiy","raw_affiliation_strings":["Department of Automation and Control Processes, Saint Petersburg Electrotechnical University &#x201C;LETI&#x201D;, Saint Petersburg, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automation and Control Processes, Saint Petersburg Electrotechnical University &#x201C;LETI&#x201D;, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I41518628"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054967047","display_name":"Dmitrii Kaplun","orcid":"https://orcid.org/0000-0003-2765-4509"},"institutions":[{"id":"https://openalex.org/I41518628","display_name":"Saint Petersburg State Electrotechnical University","ror":"https://ror.org/023bq8521","country_code":"RU","type":"education","lineage":["https://openalex.org/I41518628"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Dmitrii Kaplun","raw_affiliation_strings":["Department of Automation and Control Processes, Saint Petersburg Electrotechnical University &#x201C;LETI&#x201D;, Saint Petersburg, Russia"],"raw_orcid":"https://orcid.org/0000-0003-2765-4509","affiliations":[{"raw_affiliation_string":"Department of Automation and Control Processes, Saint Petersburg Electrotechnical University &#x201C;LETI&#x201D;, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I41518628"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":9,"corresponding_author_ids":["https://openalex.org/A5026823761"],"corresponding_institution_ids":["https://openalex.org/I24768866","https://openalex.org/I4210105926"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":2.5056,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.91674031,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"8","issue":null,"first_page":"156104","last_page":"156116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998000264167786,"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":0.9998000264167786,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9972000122070312,"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":0.9954000115394592,"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/notation","display_name":"Notation","score":0.6739124059677124},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.641139805316925},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4755406379699707},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43230724334716797},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42914432287216187},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4185643792152405},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3358841836452484},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2027052640914917}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6739124059677124},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.641139805316925},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4755406379699707},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43230724334716797},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42914432287216187},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4185643792152405},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3358841836452484},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2027052640914917},{"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.2020.3019452","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3019452","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:dfdbccb89e474a5484648f02cc9105e5","is_oa":true,"landing_page_url":"https://doaj.org/article/dfdbccb89e474a5484648f02cc9105e5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 8, Pp 156104-156116 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2020.3019452","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3019452","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G8598287168","display_name":null,"funder_award_id":"19-19-00566","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1592261758","https://openalex.org/W1971283446","https://openalex.org/W1976694568","https://openalex.org/W1994831157","https://openalex.org/W2009169197","https://openalex.org/W2086198320","https://openalex.org/W2121176637","https://openalex.org/W2126182229","https://openalex.org/W2469142762","https://openalex.org/W2504999032","https://openalex.org/W2597651559","https://openalex.org/W2599411701","https://openalex.org/W2746392831","https://openalex.org/W2760772103","https://openalex.org/W2768026356","https://openalex.org/W2768236636","https://openalex.org/W2789874832","https://openalex.org/W2901827310","https://openalex.org/W2949897314","https://openalex.org/W2986308587","https://openalex.org/W3010988589","https://openalex.org/W4233185505","https://openalex.org/W4235583970","https://openalex.org/W4244281090"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2504004674","https://openalex.org/W1987679298","https://openalex.org/W2963177394","https://openalex.org/W4313359513","https://openalex.org/W2135584473","https://openalex.org/W2498744856","https://openalex.org/W4390482104","https://openalex.org/W322408318","https://openalex.org/W149041114"],"abstract_inverted_index":{"The":[0],"paper":[1],"presents":[2],"algorithms":[3],"for":[4,29],"the":[5,67,70,79,83,92,104,130,172,209,227],"generation":[6],"of":[7,42,53,59,94,106,132,171,190,211,229,235],"Residue":[8],"Number":[9],"System":[10],"(RNS)":[11],"triples":[12,117,220],"with":[13,22,57,66,75,123,154,203],"<inline-formula":[14,23,136,143,155],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[15,24,137,144,156,196,201],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[16,25,138,145,157],"<tex-math":[17,26,139,146,158],"notation=\"LaTeX\">$SQ=2^{k}-1$":[18],"</tex-math></inline-formula>":[19,28,141,148,160],"and":[20,33,102,120,198,214],"quadruples":[21,34,153,186,232],"notation=\"LaTeX\">$SQ=2^{k}$":[27,159],"some":[30],"k.":[31],"Triples":[32],"allow":[35],"us":[36],"to":[37,142,162,169,222],"design":[38],"efficient":[39],"hardware":[40,107,236],"implementations":[41],"non-modular":[43],"operations":[44],"in":[45,78,88,174],"RNS":[46,116,152,212,218],"such":[47,185],"as":[48,129],"division,":[49],"sign":[50],"detection,":[51],"comparison":[52],"numbers,":[54],"reverse":[55],"conversion":[56],"using":[58],"a":[60,76,175],"diagonal":[61,71],"function":[62],"from":[63,135],"requiring":[64],"division":[65],"remainder":[68,77],"by":[69,233],"module":[72],"SQ.":[73],"Division":[74],"general":[80],"case":[81],"is":[82],"most":[84],"complex":[85],"arithmetic":[86],"operation":[87,101],"computer":[89],"technology.":[90],"However,":[91],"consideration":[93],"special":[95],"cases":[96],"can":[97],"significantly":[98],"simplify":[99],"this":[100,223],"increase":[103],"efficiency":[105],"implementation.":[108,237],"We":[109,207,225],"show":[110],"that":[111,182],"there":[112],"are":[113],"5573":[114],"good":[115],"(2301":[118],"even":[119,205],"2372":[121],"odd)":[122],"elements":[124,173],"less":[125,177],"than":[126,178],"10":[127],"000,":[128],"values":[131,189],"SQ":[133,191],"vary":[134,192],"notation=\"LaTeX\">$2^{5}-1$":[140],"notation=\"LaTeX\">$2^{27}-1$":[147],".":[149],"In":[150],"contrast,":[151],"seem":[161],"be":[163],"quite":[164],"rare.":[165],"Restricting":[166],"our":[167],"search":[168],"sums":[170],"quadruple":[176],"4000":[179],"we":[180],"find":[181,215],"exactly":[183],"31":[184],"exist.":[187],"Their":[188],"between":[193],"2":[194,199],"<sup":[195,200],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">20</sup>":[197],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">30</sup>":[202],"always":[204],"exponent.":[206],"suggest":[208],"measure":[210],"balance":[213],"perfectly":[216],"balanced":[217,231],"among":[219],"according":[221],"measure.":[224],"demonstrate":[226],"advantages":[228],"more":[230],"means":[234]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}