{"id":"https://openalex.org/W1889596231","doi":"https://doi.org/10.1109/tc.1985.1676616","title":"VLSI Architectures for Computing Multiplications and Inverses in GF(2<sup>m</sup>)","display_name":"VLSI Architectures for Computing Multiplications and Inverses in GF(2<sup>m</sup>)","publication_year":1985,"publication_date":"1985-08-01","ids":{"openalex":"https://openalex.org/W1889596231","doi":"https://doi.org/10.1109/tc.1985.1676616","mag":"1889596231","pmid":"https://pubmed.ncbi.nlm.nih.gov/11539660"},"language":"en","primary_location":{"id":"doi:10.1109/tc.1985.1676616","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1985.1676616","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5106222652","display_name":"Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I1334627681","display_name":"Jet Propulsion Laboratory","ror":"https://ror.org/027k65916","country_code":"US","type":"facility","lineage":["https://openalex.org/I122411786","https://openalex.org/I1334627681","https://openalex.org/I4210124779"]},{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wang","raw_affiliation_strings":["Communications Systems Research, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA","Communications Systems Research, Jet Propulsion Laboratory, California Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Communications Systems Research, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I1334627681"]},{"raw_affiliation_string":"Communications Systems Research, Jet Propulsion Laboratory, California Institute of Technology","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106043281","display_name":"Troung","orcid":null},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Troung","raw_affiliation_strings":["California Institute of Technology, Pasadena\u00a7"],"affiliations":[{"raw_affiliation_string":"California Institute of Technology, Pasadena\u00a7","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036583552","display_name":"Shao","orcid":null},"institutions":[{"id":"https://openalex.org/I1334627681","display_name":"Jet Propulsion Laboratory","ror":"https://ror.org/027k65916","country_code":"US","type":"facility","lineage":["https://openalex.org/I122411786","https://openalex.org/I1334627681","https://openalex.org/I4210124779"]},{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shao","raw_affiliation_strings":["Communications Systems Research, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA","California Institute of Technology, Pasadena\u00a7"],"affiliations":[{"raw_affiliation_string":"Communications Systems Research, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I1334627681"]},{"raw_affiliation_string":"California Institute of Technology, Pasadena\u00a7","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5096105037","display_name":"Deutsch","orcid":null},"institutions":[{"id":"https://openalex.org/I1334627681","display_name":"Jet Propulsion Laboratory","ror":"https://ror.org/027k65916","country_code":"US","type":"facility","lineage":["https://openalex.org/I122411786","https://openalex.org/I1334627681","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Deutsch","raw_affiliation_strings":["Communications Systems Research, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA"],"affiliations":[{"raw_affiliation_string":"Communications Systems Research, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I1334627681"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106139963","display_name":"Omura","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Omura","raw_affiliation_strings":["Department of Electrical Engineering, School of Engineering and Applied Sciences, University of California, Los Angeles, CA, USA","University of California\u2013Los Angeles"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, School of Engineering and Applied Sciences, University of California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"University of California\u2013Los Angeles","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110756947","display_name":"R Reed","orcid":null},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Reed","raw_affiliation_strings":["Department of Electrical Engineering, School of Engineering, University of Southern California, Los Angeles, CA, USA","University of Southern California , Los Angeles#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, School of Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"University of Southern California , Los Angeles#TAB#","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5106222652"],"corresponding_institution_ids":["https://openalex.org/I122411786","https://openalex.org/I1334627681"],"apc_list":null,"apc_paid":null,"fwci":8.3991,"has_fulltext":false,"cited_by_count":320,"citation_normalized_percentile":{"value":0.97326903,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"C-34","issue":"8","first_page":"709","last_page":"717"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9991000294685364,"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/T11130","display_name":"Coding theory and cryptography","score":0.9991000294685364,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9983000159263611,"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":0.9541000127792358,"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/finite-field","display_name":"Finite field","score":0.7717887163162231},{"id":"https://openalex.org/keywords/very-large-scale-integration","display_name":"Very-large-scale integration","score":0.7187923789024353},{"id":"https://openalex.org/keywords/normal-basis","display_name":"Normal basis","score":0.695411205291748},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.6664499044418335},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5536794662475586},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5439486503601074},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4953705072402954},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4901650846004486},{"id":"https://openalex.org/keywords/pipeline","display_name":"Pipeline (software)","score":0.4863446354866028},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4794011116027832},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4314047694206238},{"id":"https://openalex.org/keywords/gf","display_name":"GF(2)","score":0.42942774295806885},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.3946387767791748},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3710211217403412},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.3492758274078369},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32228851318359375},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.228945791721344},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.09371572732925415},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0630171000957489}],"concepts":[{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7717887163162231},{"id":"https://openalex.org/C14580979","wikidata":"https://www.wikidata.org/wiki/Q876049","display_name":"Very-large-scale integration","level":2,"score":0.7187923789024353},{"id":"https://openalex.org/C205567592","wikidata":"https://www.wikidata.org/wiki/Q3527199","display_name":"Normal basis","level":3,"score":0.695411205291748},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.6664499044418335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5536794662475586},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5439486503601074},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4953705072402954},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4901650846004486},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.4863446354866028},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4794011116027832},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4314047694206238},{"id":"https://openalex.org/C156350748","wikidata":"https://www.wikidata.org/wiki/Q5513324","display_name":"GF(2)","level":3,"score":0.42942774295806885},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.3946387767791748},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3710211217403412},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3492758274078369},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32228851318359375},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.228945791721344},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.09371572732925415},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0630171000957489},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003199","descriptor_name":"Computer Systems","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003199","descriptor_name":"Computer Systems","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003199","descriptor_name":"Computer Systems","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1109/tc.1985.1676616","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1985.1676616","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"},{"id":"pmid:11539660","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/11539660","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":"IEEE transactions on computers. Institute of Electrical and Electronics Engineers","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1606480398","https://openalex.org/W1894395730","https://openalex.org/W1967575124","https://openalex.org/W1989008275","https://openalex.org/W2017369466","https://openalex.org/W2042559745","https://openalex.org/W2051495459","https://openalex.org/W2081934516","https://openalex.org/W2088225293","https://openalex.org/W2182112064"],"related_works":["https://openalex.org/W2587136861","https://openalex.org/W2395601077","https://openalex.org/W4231082137","https://openalex.org/W2002742877","https://openalex.org/W2098343516","https://openalex.org/W2142116768","https://openalex.org/W3128023985","https://openalex.org/W1528972180","https://openalex.org/W172172592","https://openalex.org/W4248505260"],"abstract_inverted_index":{"Finite":[0],"field":[1,69],"arithmetic":[2],"logic":[3],"is":[4,18,59,89],"central":[5],"in":[6,13,66,95],"the":[7,63,67,72,77,101,105],"implementation":[8],"of":[9,76,107],"Reed-Solomon":[10],"coders":[11],"and":[12,24,36,104,114],"some":[14],"cryptographic":[15],"algorithms.":[16],"There":[17],"a":[19,40,49,56,86],"need":[20],"for":[21,44,91,100,118],"good":[22],"multiplication":[23,42],"inversion":[25],"algorithms":[26],"that":[27],"can":[28],"be":[29],"easily":[30],"realized":[31],"on":[32,48],"VLSI":[33,119],"chips.":[34],"Massey":[35],"Omura":[37],"recently":[38],"developed":[39,60,90,99],"new":[41],"algorithm":[43],"Galois":[45],"fields":[46],"based":[47],"normal":[50,78],"basis":[51,79],"representation.":[52],"In":[53],"this":[54,84],"paper,":[55],"pipeline":[57,87],"structure":[58],"to":[61],"realize":[62],"Massey-Omura":[64,102],"multiplier":[65,103],"finite":[68],"GF(2m).":[70,96],"With":[71],"simple":[73],"squaring":[74],"property":[75],"representation":[80],"used":[81],"together":[82],"with":[83],"multiplier,":[85],"architecture":[88],"computing":[92],"inverse":[93,108],"elements":[94,109],"The":[97],"designs":[98],"computation":[106],"are":[110],"regular,":[111],"simple,":[112],"expandable,":[113],"therefore,":[115],"naturally":[116],"suitable":[117],"implementation.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":11}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}