{"id":"https://openalex.org/W3190478190","doi":"https://doi.org/10.1587/transinf.2020lop0004","title":"An Algebraic Approach to Verifying Galois-Field Arithmetic Circuits with Multiple-Valued Characteristics","display_name":"An Algebraic Approach to Verifying Galois-Field Arithmetic Circuits with Multiple-Valued Characteristics","publication_year":2021,"publication_date":"2021-07-31","ids":{"openalex":"https://openalex.org/W3190478190","doi":"https://doi.org/10.1587/transinf.2020lop0004","mag":"3190478190"},"language":"en","primary_location":{"id":"doi:10.1587/transinf.2020lop0004","is_oa":true,"landing_page_url":"https://doi.org/10.1587/transinf.2020lop0004","pdf_url":"https://www.jstage.jst.go.jp/article/transinf/E104.D/8/E104.D_2020LOP0004/_pdf","source":{"id":"https://openalex.org/S2486202937","display_name":"IEICE Transactions on Information and Systems","issn_l":"0916-8532","issn":["0916-8532","1745-1361"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Information and Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.jstage.jst.go.jp/article/transinf/E104.D/8/E104.D_2020LOP0004/_pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004043077","display_name":"A. S. Ito","orcid":"https://orcid.org/0000-0002-4602-7570"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Akira ITO","raw_affiliation_strings":["Tohoku University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tohoku University","institution_ids":["https://openalex.org/I201537933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034718952","display_name":"Rei Ueno","orcid":"https://orcid.org/0000-0002-9754-6792"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Rei UENO","raw_affiliation_strings":["Tohoku University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tohoku University","institution_ids":["https://openalex.org/I201537933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069532722","display_name":"Naofumi Homma","orcid":"https://orcid.org/0000-0003-0864-3126"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Naofumi HOMMA","raw_affiliation_strings":["Tohoku University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tohoku University","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I201537933"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11035529,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"E104.D","issue":"8","first_page":"1083","last_page":"1091"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9987000226974487,"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/T10142","display_name":"Formal Methods in Verification","score":0.9983999729156494,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/netlist","display_name":"Netlist","score":0.7867135405540466},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.7286080121994019},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.543509304523468},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5237841010093689},{"id":"https://openalex.org/keywords/arithmetic-circuit-complexity","display_name":"Arithmetic circuit complexity","score":0.4575859606266022},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4554469585418701},{"id":"https://openalex.org/keywords/formal-equivalence-checking","display_name":"Formal equivalence checking","score":0.44875723123550415},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44366490840911865},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.43710723519325256},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4304613471031189},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42685139179229736},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35631781816482544},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34652984142303467},{"id":"https://openalex.org/keywords/formal-verification","display_name":"Formal verification","score":0.34367507696151733},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.3028620481491089},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08888033032417297}],"concepts":[{"id":"https://openalex.org/C177650935","wikidata":"https://www.wikidata.org/wiki/Q1760303","display_name":"Netlist","level":2,"score":0.7867135405540466},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.7286080121994019},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.543509304523468},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5237841010093689},{"id":"https://openalex.org/C155920423","wikidata":"https://www.wikidata.org/wiki/Q4791120","display_name":"Arithmetic circuit complexity","level":3,"score":0.4575859606266022},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4554469585418701},{"id":"https://openalex.org/C96654402","wikidata":"https://www.wikidata.org/wiki/Q5469962","display_name":"Formal equivalence checking","level":3,"score":0.44875723123550415},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44366490840911865},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.43710723519325256},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4304613471031189},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42685139179229736},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35631781816482544},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34652984142303467},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.34367507696151733},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.3028620481491089},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08888033032417297},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1587/transinf.2020lop0004","is_oa":true,"landing_page_url":"https://doi.org/10.1587/transinf.2020lop0004","pdf_url":"https://www.jstage.jst.go.jp/article/transinf/E104.D/8/E104.D_2020LOP0004/_pdf","source":{"id":"https://openalex.org/S2486202937","display_name":"IEICE Transactions on Information and Systems","issn_l":"0916-8532","issn":["0916-8532","1745-1361"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Information and Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1587/transinf.2020lop0004","is_oa":true,"landing_page_url":"https://doi.org/10.1587/transinf.2020lop0004","pdf_url":"https://www.jstage.jst.go.jp/article/transinf/E104.D/8/E104.D_2020LOP0004/_pdf","source":{"id":"https://openalex.org/S2486202937","display_name":"IEICE Transactions on Information and Systems","issn_l":"0916-8532","issn":["0916-8532","1745-1361"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Information and Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4920161775","display_name":"\u30c8\u30ed\u30a4\u30d5\u30ea\u30fc\u6697\u53f7\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u306e\u9ad8\u6c34\u6e96\u8a2d\u8a08\u30fb\u691c\u8a3c\u624b\u6cd5\u306e\u958b\u62d3","funder_award_id":"20J12887","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6385471558","display_name":"Development of highly secure and reliable authentication system based on physically unclonable hardware identifier","funder_award_id":"20K19765","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G648744600","display_name":"Formal design and analysis of security hardare: evolution and beyond","funder_award_id":"21H04867","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320322525","display_name":"Secom Science and Technology Foundation","ror":"https://ror.org/05ggzej07"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3190478190.pdf","grobid_xml":"https://content.openalex.org/works/W3190478190.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W32438244","https://openalex.org/W34381828","https://openalex.org/W1488416029","https://openalex.org/W1545320146","https://openalex.org/W1595607623","https://openalex.org/W1610688607","https://openalex.org/W1975335740","https://openalex.org/W1975344255","https://openalex.org/W2014239329","https://openalex.org/W2032767749","https://openalex.org/W2037107113","https://openalex.org/W2054115926","https://openalex.org/W2057382040","https://openalex.org/W2075743607","https://openalex.org/W2078214592","https://openalex.org/W2098529560","https://openalex.org/W2114296878","https://openalex.org/W2117635926","https://openalex.org/W2127271657","https://openalex.org/W2142233933","https://openalex.org/W2171279237","https://openalex.org/W2344855325","https://openalex.org/W2508860103","https://openalex.org/W2740157106","https://openalex.org/W2793599397","https://openalex.org/W2891942978","https://openalex.org/W2962698160","https://openalex.org/W3119223494","https://openalex.org/W3129276718"],"related_works":["https://openalex.org/W21388859","https://openalex.org/W3046927439","https://openalex.org/W2360029815","https://openalex.org/W4295791056","https://openalex.org/W2895905110","https://openalex.org/W2171786655","https://openalex.org/W2788911029","https://openalex.org/W2131861297","https://openalex.org/W2153025757","https://openalex.org/W2122796136"],"abstract_inverted_index":{"This":[0],"study":[1],"presents":[2],"a":[3,42,45,50,61,105],"formal":[4],"verification":[5,160],"method":[6,22,65,98,135],"for":[7],"Galois-field":[8],"(GF)":[9],"arithmetic":[10,72,141],"circuits":[11],"with":[12],"the":[13,25,31,39,78,87,94,101,117,124,133,153,170],"characteristics":[14],"of":[15,27,116],"more":[16],"than":[17,83,169],"two":[18],"values.":[19],"The":[20],"proposed":[21,134],"formally":[23],"verifies":[24],"correctness":[26],"circuit":[28,107],"functionality":[29],"(i.e.,":[30],"input-output":[32],"relations":[33],"given":[34],"as":[35],"GF-polynomials)":[36],"by":[37],"checking":[38],"equivalence":[40],"between":[41],"specification":[43],"and":[44,56],"gate-level":[46],"netlist.":[47],"We":[48],"represent":[49],"netlist":[51],"using":[52,86],"simultaneous":[53],"algebraic":[54],"equations":[55],"solve":[57],"them":[58],"based":[59],"on":[60],"novel":[62],"polynomial":[63,125,155],"reduction":[64,156],"that":[66,132,152,161],"can":[67,99,136,158],"be":[68],"efficiently":[69,137],"applied":[70],"to":[71,92,122,164],"over":[73],"extension":[74,115],"fields":[75],"$\\mathbb{F}_{p^m}$,":[76],"where":[77],"characteristic":[79],"p":[80],"is":[81,162],"larger":[82],"two.":[84],"By":[85],"reverse":[88],"topological":[89],"term":[90],"order":[91],"derive":[93],"Gr\u00f6bner":[95],"basis,":[96],"our":[97],"complete":[100],"verification,":[102],"even":[103],"when":[104],"target":[106],"includes":[108],"bugs.":[109],"In":[110],"addition,":[111],"we":[112,150],"introduce":[113],"an":[114],"Galois-Field":[118],"binary":[119],"moment":[120],"diagrams":[121],"perform":[123],"reductions":[126],"faster.":[127],"Our":[128],"experimental":[129],"results":[130],"show":[131],"verify":[138],"practical":[139],"$\\mathbb{F}_{p^m}$":[140],"circuits,":[142],"including":[143],"those":[144],"used":[145],"in":[146],"modern":[147],"cryptography.":[148],"Moreover,":[149],"demonstrate":[151],"extended":[154],"technique":[157],"enable":[159],"up":[163],"approximately":[165],"five":[166],"times":[167],"faster":[168],"original":[171],"one.":[172]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
