{"id":"https://openalex.org/W7171392154","doi":"https://doi.org/10.1109/ojcas.2026.3717375","title":"RRNS Arith Lib\u2014Open-Source Redundant Residue Number System Arithmetics for Reliable Circuits","display_name":"RRNS Arith Lib\u2014Open-Source Redundant Residue Number System Arithmetics for Reliable Circuits","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7171392154","doi":"https://doi.org/10.1109/ojcas.2026.3717375"},"language":"en","primary_location":{"id":"doi:10.1109/ojcas.2026.3717375","is_oa":true,"landing_page_url":"https://doi.org/10.1109/ojcas.2026.3717375","pdf_url":null,"source":{"id":"https://openalex.org/S4210192473","display_name":"IEEE Open Journal of Circuits and Systems","issn_l":"2644-1225","issn":["2644-1225"],"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 Open Journal of Circuits and Systems","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/ojcas.2026.3717375","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023447109","display_name":"Tim Oberschulte","orcid":"https://orcid.org/0000-0001-6334-4458"},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tim Oberschulte","raw_affiliation_strings":["Leibniz University Hannover"],"raw_orcid":"https://orcid.org/0000-0001-6334-4458","affiliations":[{"raw_affiliation_string":"Leibniz University Hannover","institution_ids":["https://openalex.org/I114112103"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116425577","display_name":"Enno Sievers","orcid":null},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Enno Sievers","raw_affiliation_strings":["Leibniz University Hannover"],"raw_orcid":"https://orcid.org/0009-0004-9891-7569","affiliations":[{"raw_affiliation_string":"Leibniz University Hannover","institution_ids":["https://openalex.org/I114112103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016532646","display_name":"Holger Blume","orcid":"https://orcid.org/0000-0002-0640-6875"},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Holger Blume","raw_affiliation_strings":["Leibniz University Hannover"],"raw_orcid":"https://orcid.org/0000-0002-0640-6875","affiliations":[{"raw_affiliation_string":"Leibniz University Hannover","institution_ids":["https://openalex.org/I114112103"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I114112103"],"apc_list":{"value":2075,"currency":"USD","value_usd":2075},"apc_paid":{"value":2075,"currency":"USD","value_usd":2075},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.85967489,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":null,"first_page":"434","last_page":"446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9641000032424927,"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":0.9641000032424927,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.01119999960064888,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.00419999985024333,"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":0.607699990272522},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.446399986743927},{"id":"https://openalex.org/keywords/saturation-arithmetic","display_name":"Saturation arithmetic","score":0.41620001196861267},{"id":"https://openalex.org/keywords/residue","display_name":"Residue (chemistry)","score":0.37290000915527344},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.28540000319480896}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.7195000052452087},{"id":"https://openalex.org/C71480937","wikidata":"https://www.wikidata.org/wiki/Q3086516","display_name":"Residue number system","level":2,"score":0.607699990272522},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4970000088214874},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46399998664855957},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4546999931335449},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.446399986743927},{"id":"https://openalex.org/C182775192","wikidata":"https://www.wikidata.org/wiki/Q913725","display_name":"Saturation arithmetic","level":3,"score":0.41620001196861267},{"id":"https://openalex.org/C2781338088","wikidata":"https://www.wikidata.org/wiki/Q903495","display_name":"Residue (chemistry)","level":2,"score":0.37290000915527344},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.28540000319480896},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.2614000141620636}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/ojcas.2026.3717375","is_oa":true,"landing_page_url":"https://doi.org/10.1109/ojcas.2026.3717375","pdf_url":null,"source":{"id":"https://openalex.org/S4210192473","display_name":"IEEE Open Journal of Circuits and Systems","issn_l":"2644-1225","issn":["2644-1225"],"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 Open Journal of Circuits and Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:7214e56e8e5d4901b1df1819e21533a9","is_oa":false,"landing_page_url":"https://doaj.org/article/7214e56e8e5d4901b1df1819e21533a9","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Open Journal of Circuits and Systems, Vol 7, Pp 434-446 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/ojcas.2026.3717375","is_oa":true,"landing_page_url":"https://doi.org/10.1109/ojcas.2026.3717375","pdf_url":null,"source":{"id":"https://openalex.org/S4210192473","display_name":"IEEE Open Journal of Circuits and Systems","issn_l":"2644-1225","issn":["2644-1225"],"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 Open Journal of Circuits and Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1601793793","https://openalex.org/W1608773862","https://openalex.org/W1895520214","https://openalex.org/W1900037105","https://openalex.org/W1912864429","https://openalex.org/W1970134997","https://openalex.org/W1993260327","https://openalex.org/W2080580079","https://openalex.org/W2105709059","https://openalex.org/W2112998193","https://openalex.org/W2129306436","https://openalex.org/W2131483653","https://openalex.org/W2145800822","https://openalex.org/W2157999631","https://openalex.org/W2170278114","https://openalex.org/W2546162547","https://openalex.org/W2553980449","https://openalex.org/W2773750423","https://openalex.org/W2799995256","https://openalex.org/W2801001989","https://openalex.org/W3023192521","https://openalex.org/W3215469679","https://openalex.org/W4243810185","https://openalex.org/W4244281090","https://openalex.org/W4252220425","https://openalex.org/W4391408072"],"related_works":[],"abstract_inverted_index":{"A":[0],"Residue":[1,54],"Number":[2,55],"System":[3,56],"(RNS)":[4],"represents":[5],"integers":[6],"through":[7,149],"a":[8,17,150],"set":[9,19],"of":[10,20,64,74,83,101,132,146,175,181,185],"residues":[11],"obtained":[12],"by":[13],"integer":[14],"division":[15],"using":[16],"predefined":[18],"pairwise":[21],"coprime":[22],"moduli.":[23],"RNS":[24],"is":[25,122,126],"well-known":[26],"for":[27,80,130],"enabling":[28],"efficient":[29],"carry-free":[30],"arithmetic":[31,85,114],"and":[32,97,128,197],"representing":[33],"large":[34],"numbers":[35,131],"with":[36],"multiple":[37],"shorter":[38],"numerical":[39],"values.":[40],"By":[41],"incorporating":[42],"additional":[43],"moduli,":[44],"the":[45,62,72,81,94,99,102,142,147,160,165,179,209],"system":[46],"can":[47],"be":[48],"extended":[49],"into":[50,86,159],"an":[51,75,106,117,182],"overdetermined":[52],"Redundant":[53],"(RRNS),":[57],"introducing":[58],"redundancy":[59],"that":[60,124],"facilitates":[61],"detection":[63,144,173],"bit":[65,136],"errors.":[66],"In":[67,189],"this":[68],"paper,":[69],"we":[70,140],"present":[71],"development":[73],"open-source":[76],"VHDL":[77],"library":[78,104],"designed":[79],"integration":[82],"RRNS":[84,103,125,148,193],"ASIC":[87,191],"or":[88],"FPGA":[89,153],"architectures.":[90],"The":[91,168],"paper":[92],"details":[93],"design":[95],"considerations":[96],"evaluates":[98],"performance":[100,174],"on":[105],"FPGA,":[107],"comparing":[108],"it":[109,121],"to":[110,163,201],"conventional":[111],"redundant":[112],"binary":[113,205],"implementations.":[115],"For":[116],"exemplary":[118],"matrix":[119],"multiplication,":[120],"shown":[123],"smaller":[127,195],"faster":[129],"more":[133],"than":[134,204],"42":[135],"dynamic":[137],"range.":[138],"Furthermore,":[139],"demonstrate":[141],"error":[143,172],"capabilities":[145],"realistic":[151],"real-world":[152],"application,":[154],"wherein":[155],"faults":[156],"are":[157],"injected":[158],"configuration":[161],"memory":[162],"validate":[164],"system\u2019s":[166],"robustness.":[167],"results":[169],"show":[170],"better-than-DMR":[171],"99.9":[176],"%":[177],"at":[178],"cost":[180],"area":[183,196],"overhead":[184],"about":[186],"18":[187],"%.":[188],"pre-layout":[190],"designs,":[192],"shows":[194],"power":[198],"consumption":[199],"(up":[200],"\u221260":[202],"%)":[203],"DMR":[206],"while":[207],"maintaining":[208],"same":[210],"clock":[211],"frequency.":[212]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2026-07-28T00:00:00"}
