{"id":"https://openalex.org/W2529865900","doi":"https://doi.org/10.1080/00207160.2016.1247439","title":"Residue-to-binary conversion for general moduli sets based on approximate Chinese remainder theorem","display_name":"Residue-to-binary conversion for general moduli sets based on approximate Chinese remainder theorem","publication_year":2016,"publication_date":"2016-10-15","ids":{"openalex":"https://openalex.org/W2529865900","doi":"https://doi.org/10.1080/00207160.2016.1247439","mag":"2529865900"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2016.1247439","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2016.1247439","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"N.I. Chervyakov","orcid":"https://orcid.org/0000-0002-4355-085X"},"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":"N.I. Chervyakov","raw_affiliation_strings":["Department of Applied Mathematics and Mathematical Modelling, North-Caucasian Federal University, Stavropol, Russian Federation"],"raw_orcid":"https://orcid.org/0000-0002-4355-085X","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Mathematical Modelling, North-Caucasian Federal University, Stavropol, Russian Federation","institution_ids":["https://openalex.org/I210043505"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056136163","display_name":"Amir Sabbagh Molahosseini","orcid":"https://orcid.org/0000-0003-3603-9401"},"institutions":[{"id":"https://openalex.org/I4210152146","display_name":"Islamic Azad University Kerman","ror":"https://ror.org/04ywz9252","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210152146"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"A. S. Molahosseini","raw_affiliation_strings":["Department of Computer Engineering, Kerman Branch, Islamic Azad University, Kerman, Iran"],"raw_orcid":"https://orcid.org/0000-0003-3603-9401","affiliations":[{"raw_affiliation_string":"Department of Computer Engineering, Kerman Branch, Islamic Azad University, Kerman, Iran","institution_ids":["https://openalex.org/I4210152146"]}]},{"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"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"P. A. Lyakhov","raw_affiliation_strings":["Department of Applied Mathematics and Mathematical Modelling, North-Caucasian Federal University, Stavropol, Russian Federation"],"raw_orcid":"https://orcid.org/0000-0003-0487-4779","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Mathematical Modelling, North-Caucasian Federal University, Stavropol, Russian Federation","institution_ids":["https://openalex.org/I210043505"]}]},{"author_position":"middle","author":{"id":null,"display_name":"M. G. Babenko","orcid":"https://orcid.org/0000-0002-1892-8232"},"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":"M. G. Babenko","raw_affiliation_strings":["Department of Applied Mathematics and Mathematical Modelling, North-Caucasian Federal University, Stavropol, Russian Federation"],"raw_orcid":"https://orcid.org/0000-0002-1892-8232","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Mathematical Modelling, North-Caucasian Federal University, Stavropol, Russian Federation","institution_ids":["https://openalex.org/I210043505"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030124351","display_name":"Maxim Deryabin","orcid":"https://orcid.org/0000-0002-6761-3667"},"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":"M. A. Deryabin","raw_affiliation_strings":["Department of Applied Mathematics and Mathematical Modelling, North-Caucasian Federal University, Stavropol, Russian Federation"],"raw_orcid":"https://orcid.org/0000-0002-6761-3667","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Mathematical Modelling, North-Caucasian Federal University, Stavropol, Russian Federation","institution_ids":["https://openalex.org/I210043505"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056136163"],"corresponding_institution_ids":["https://openalex.org/I4210152146"],"apc_list":null,"apc_paid":null,"fwci":11.5027,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.98330597,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"94","issue":"9","first_page":"1833","last_page":"1849"},"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":0.9961000084877014,"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":0.9926999807357788,"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":0.9443337917327881},{"id":"https://openalex.org/keywords/chinese-remainder-theorem","display_name":"Chinese remainder theorem","score":0.9344558715820312},{"id":"https://openalex.org/keywords/moduli","display_name":"Moduli","score":0.708504319190979},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.7006702423095703},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6575658917427063},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6116423010826111},{"id":"https://openalex.org/keywords/residue","display_name":"Residue (chemistry)","score":0.5110222101211548},{"id":"https://openalex.org/keywords/converters","display_name":"Converters","score":0.4567412734031677},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4484829008579254},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.4243495464324951},{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.4135705828666687},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39154067635536194},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25586646795272827},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.1321377456188202}],"concepts":[{"id":"https://openalex.org/C71480937","wikidata":"https://www.wikidata.org/wiki/Q3086516","display_name":"Residue number system","level":2,"score":0.9443337917327881},{"id":"https://openalex.org/C151635116","wikidata":"https://www.wikidata.org/wiki/Q193878","display_name":"Chinese remainder theorem","level":2,"score":0.9344558715820312},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.708504319190979},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.7006702423095703},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6575658917427063},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6116423010826111},{"id":"https://openalex.org/C2781338088","wikidata":"https://www.wikidata.org/wiki/Q903495","display_name":"Residue (chemistry)","level":2,"score":0.5110222101211548},{"id":"https://openalex.org/C2778422915","wikidata":"https://www.wikidata.org/wiki/Q10302051","display_name":"Converters","level":3,"score":0.4567412734031677},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4484829008579254},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.4243495464324951},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.4135705828666687},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39154067635536194},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25586646795272827},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.1321377456188202},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2016.1247439","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2016.1247439","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1539786092","https://openalex.org/W1587217691","https://openalex.org/W1601793793","https://openalex.org/W1931129436","https://openalex.org/W1964539827","https://openalex.org/W1965469050","https://openalex.org/W1967061303","https://openalex.org/W1971283446","https://openalex.org/W2003078948","https://openalex.org/W2016066384","https://openalex.org/W2022989647","https://openalex.org/W2027305836","https://openalex.org/W2038879815","https://openalex.org/W2043204218","https://openalex.org/W2069045670","https://openalex.org/W2087096176","https://openalex.org/W2087114937","https://openalex.org/W2089034133","https://openalex.org/W2093926087","https://openalex.org/W2097158081","https://openalex.org/W2097883101","https://openalex.org/W2098282500","https://openalex.org/W2100264217","https://openalex.org/W2100677916","https://openalex.org/W2105709059","https://openalex.org/W2112570083","https://openalex.org/W2112998193","https://openalex.org/W2115245846","https://openalex.org/W2117651800","https://openalex.org/W2126182229","https://openalex.org/W2126360616","https://openalex.org/W2147756065","https://openalex.org/W2155095649","https://openalex.org/W2164556899","https://openalex.org/W2469142762","https://openalex.org/W2491528583","https://openalex.org/W4210673018","https://openalex.org/W4229484196","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1608773862","https://openalex.org/W2105248505","https://openalex.org/W1852876249","https://openalex.org/W2169683161","https://openalex.org/W2099981328","https://openalex.org/W1562996865","https://openalex.org/W2096224473","https://openalex.org/W2751010637","https://openalex.org/W2923392082","https://openalex.org/W2100848782"],"abstract_inverted_index":{"The":[0,107],"residue":[1,130],"number":[2,8,27,75,131],"system":[3,9],"(RNS)":[4],"is":[5,83,88],"an":[6,49],"unconventional":[7],"which":[10],"can":[11,140],"lead":[12],"to":[13,90,101],"parallel":[14],"and":[15,35,113,136],"fault-tolerant":[16],"arithmetic":[17],"operations.":[18],"However,":[19],"the":[20,31,57,73],"complexity":[21],"of":[22,28,59,76],"residue-to-binary":[23,62,81,115],"conversion":[24,63,82,125],"for":[25,39,64,79,117,134],"large":[26],"moduli":[29,67,120],"reduces":[30],"overall":[32],"RNS":[33,66,119],"performance,":[34],"makes":[36],"it":[37],"inefficient":[38],"nowadays":[40],"high-performance":[41],"computation":[42],"systems.":[43],"In":[44],"this":[45,71,124],"paper,":[46],"we":[47],"present":[48],"improved":[50],"approximate":[51],"Chinese":[52],"remainder":[53],"theorem":[54],"(CRT)":[55],"with":[56,123],"aim":[58],"performing":[60],"efficient":[61],"general":[65,118],"sets.":[68,121],"To":[69],"achieve":[70],"aim,":[72],"required":[74],"fraction":[77],"bits":[78],"accurate":[80],"derived.":[84],"Besides,":[85],"a":[86,103],"method":[87],"proposed":[89,108],"substitute":[91],"fractional":[92],"calculations":[93],"by":[94],"similar":[95],"computations":[96],"based":[97],"on":[98],"integer":[99],"numbers":[100],"have":[102],"hardware":[104],"amenable":[105],"algorithm.":[106],"approach":[109],"results":[110],"in":[111],"high-speed":[112],"low-area":[114],"converters":[116],"Therefore,":[122],"method,":[126],"high":[127],"dynamic":[128],"range":[129],"systems":[132],"suitable":[133],"cryptography":[135],"digital":[137],"signal":[138],"processing":[139],"be":[141],"designed.":[142]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}