{"id":"https://openalex.org/W4210564231","doi":"https://doi.org/10.3390/e24020242","title":"An Efficient Parallel Reverse Conversion of Residue Code to Mixed-Radix Representation Based on the Chinese Remainder Theorem","display_name":"An Efficient Parallel Reverse Conversion of Residue Code to Mixed-Radix Representation Based on the Chinese Remainder Theorem","publication_year":2022,"publication_date":"2022-02-05","ids":{"openalex":"https://openalex.org/W4210564231","doi":"https://doi.org/10.3390/e24020242","pmid":"https://pubmed.ncbi.nlm.nih.gov/35205536"},"language":"en","primary_location":{"id":"doi:10.3390/e24020242","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020242","pdf_url":"https://www.mdpi.com/1099-4300/24/2/242/pdf?version=1644805332","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/2/242/pdf?version=1644805332","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052304724","display_name":"Mikhail Selianinau","orcid":"https://orcid.org/0000-0001-5669-701X"},"institutions":[{"id":"https://openalex.org/I126406834","display_name":"Jan D\u0142ugosz University","ror":"https://ror.org/0566yhn94","country_code":"PL","type":"education","lineage":["https://openalex.org/I126406834"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Mikhail Selianinau","raw_affiliation_strings":["Department of Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13/15, 42-200 Czestochowa, Poland"],"raw_orcid":"https://orcid.org/0000-0001-5669-701X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13/15, 42-200 Czestochowa, Poland","institution_ids":["https://openalex.org/I126406834"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090626156","display_name":"Yuriy Povstenko","orcid":"https://orcid.org/0000-0002-7492-5394"},"institutions":[{"id":"https://openalex.org/I126406834","display_name":"Jan D\u0142ugosz University","ror":"https://ror.org/0566yhn94","country_code":"PL","type":"education","lineage":["https://openalex.org/I126406834"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Yuriy Povstenko","raw_affiliation_strings":["Department of Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13/15, 42-200 Czestochowa, Poland"],"raw_orcid":"https://orcid.org/0000-0002-7492-5394","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13/15, 42-200 Czestochowa, Poland","institution_ids":["https://openalex.org/I126406834"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090626156"],"corresponding_institution_ids":["https://openalex.org/I126406834"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.2743,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.83233442,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"24","issue":"2","first_page":"242","last_page":"242"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9825999736785889,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9812999963760376,"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/chinese-remainder-theorem","display_name":"Chinese remainder theorem","score":0.8115188479423523},{"id":"https://openalex.org/keywords/residue-number-system","display_name":"Residue number system","score":0.7591910362243652},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.6766543388366699},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.5871866941452026},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5480074286460876},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5475987195968628},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.526066243648529},{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.452802449464798},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4390202760696411},{"id":"https://openalex.org/keywords/radix","display_name":"Radix (gastropod)","score":0.42077067494392395},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4157508313655853},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.360621839761734}],"concepts":[{"id":"https://openalex.org/C151635116","wikidata":"https://www.wikidata.org/wiki/Q193878","display_name":"Chinese remainder theorem","level":2,"score":0.8115188479423523},{"id":"https://openalex.org/C71480937","wikidata":"https://www.wikidata.org/wiki/Q3086516","display_name":"Residue number system","level":2,"score":0.7591910362243652},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.6766543388366699},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.5871866941452026},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5480074286460876},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5475987195968628},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.526066243648529},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.452802449464798},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4390202760696411},{"id":"https://openalex.org/C2779091547","wikidata":"https://www.wikidata.org/wiki/Q287565","display_name":"Radix (gastropod)","level":2,"score":0.42077067494392395},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4157508313655853},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.360621839761734},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e24020242","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020242","pdf_url":"https://www.mdpi.com/1099-4300/24/2/242/pdf?version=1644805332","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:35205536","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35205536","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:1f31c8c774294ac7906a77e48e2a2ddf","is_oa":true,"landing_page_url":"https://doaj.org/article/1f31c8c774294ac7906a77e48e2a2ddf","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":"Entropy, Vol 24, Iss 2, p 242 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/2/242/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24020242","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 24; Issue 2; Pages: 242","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8871111","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8871111","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e24020242","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020242","pdf_url":"https://www.mdpi.com/1099-4300/24/2/242/pdf?version=1644805332","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4210564231.pdf"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1925248","https://openalex.org/W933374218","https://openalex.org/W1828880226","https://openalex.org/W1964539827","https://openalex.org/W1985654253","https://openalex.org/W2001108804","https://openalex.org/W2011654054","https://openalex.org/W2038318831","https://openalex.org/W2082000319","https://openalex.org/W2082154304","https://openalex.org/W2086198320","https://openalex.org/W2104635580","https://openalex.org/W2127072298","https://openalex.org/W2129587464","https://openalex.org/W2138957340","https://openalex.org/W2153430250","https://openalex.org/W2172127662","https://openalex.org/W2462789209","https://openalex.org/W2469142762","https://openalex.org/W2602038345","https://openalex.org/W2981330313","https://openalex.org/W2985535052","https://openalex.org/W3009399224","https://openalex.org/W3114197135","https://openalex.org/W3129049429","https://openalex.org/W3155146901","https://openalex.org/W3165361020","https://openalex.org/W4235583970","https://openalex.org/W4255598772","https://openalex.org/W4299827018","https://openalex.org/W4300041665","https://openalex.org/W4388288416","https://openalex.org/W6679404585","https://openalex.org/W6791187952","https://openalex.org/W6983655718","https://openalex.org/W7071160428"],"related_works":["https://openalex.org/W1608773862","https://openalex.org/W2295223161","https://openalex.org/W2535688509","https://openalex.org/W2963480066","https://openalex.org/W2999343070","https://openalex.org/W2985535052","https://openalex.org/W2055981901","https://openalex.org/W2155005491","https://openalex.org/W2258400458","https://openalex.org/W2768026356"],"abstract_inverted_index":{"In":[0,68,135],"this":[1],"paper,":[2],"we":[3],"deal":[4],"with":[5],"the":[6,50,55,64,72,83,88,94,102,122,138,142],"critical":[7],"problems":[8],"in":[9,63,87,149],"residue":[10,56],"arithmetic.":[11],"The":[12,98,127],"reverse":[13,52,147],"conversion":[14,53,148],"from":[15,54],"a":[16,25,32,46,59,79],"Residue":[17],"Number":[18],"System":[19,66],"(RNS)":[20],"to":[21,39,49,78,93],"positional":[22],"notation":[23],"is":[24,115,130,145],"main":[26],"non-modular":[27,36],"operation,":[28],"and":[29,111],"it":[30],"constitutes":[31],"basis":[33],"of":[34,74,82,101,124,141],"other":[35],"procedures":[37],"used":[38,125],"implement":[40],"various":[41],"computational":[42,99],"algorithms.":[43],"We":[44],"present":[45],"novel":[47],"approach":[48],"parallel":[51,80],"code":[57],"into":[58],"weighted":[60],"number":[61,123],"representation":[62],"Mixed-Radix":[65],"(MRS).":[67],"our":[69],"proposed":[70,143],"method,":[71],"calculation":[73],"mixed-radix":[75],"digits":[76],"reduces":[77],"summation":[81],"small":[84],"word-length":[85],"residues":[86],"independent":[89],"modular":[90,108,132,151],"channels":[91],"corresponding":[92],"primary":[95],"RNS":[96],"moduli.":[97,126],"complexity":[100,129],"developed":[103],"method":[104],"concerning":[105],"both":[106],"required":[107],"addition":[109],"operations":[110],"one-input":[112],"lookup":[113],"tables":[114],"estimated":[116],"as":[117],"Ok2/2,":[118],"where":[119],"k":[120],"equals":[121],"time":[128],"Olog2k":[131],"clock":[133,152],"cycles.":[134],"pipeline":[136],"mode,":[137],"throughput":[139],"rate":[140],"algorithm":[144],"one":[146,150],"cycle.":[153]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
