{"id":"https://openalex.org/W2133814675","doi":"https://doi.org/10.1109/tc.2003.1252850","title":"Parallel multipliers based on special irreducible pentanomials","display_name":"Parallel multipliers based on special irreducible pentanomials","publication_year":2003,"publication_date":"2003-12-01","ids":{"openalex":"https://openalex.org/W2133814675","doi":"https://doi.org/10.1109/tc.2003.1252850","mag":"2133814675"},"language":"en","primary_location":{"id":"doi:10.1109/tc.2003.1252850","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2003.1252850","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"],"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":"F. Rodriguez-Henriquez","orcid":null},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"F. Rodriguez-Henriquez","raw_affiliation_strings":["Depto. de Ingenieria Electrica, CINVESTAV-IPN, Mexico City, Mexico"],"affiliations":[{"raw_affiliation_string":"Depto. de Ingenieria Electrica, CINVESTAV-IPN, Mexico City, Mexico","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018100877","display_name":"\u00c7etin Kaya Ko\u00e7","orcid":"https://orcid.org/0000-0002-2572-9565"},"institutions":[{"id":"https://openalex.org/I131249849","display_name":"Oregon State University","ror":"https://ror.org/00ysfqy60","country_code":"US","type":"education","lineage":["https://openalex.org/I131249849"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cetin Kaya Koc","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Oregon State University, Corvallis, OR, USA","Oregon State University>"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Oregon State University, Corvallis, OR, USA","institution_ids":["https://openalex.org/I131249849"]},{"raw_affiliation_string":"Oregon State University>","institution_ids":["https://openalex.org/I131249849"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I68368234"],"apc_list":null,"apc_paid":null,"fwci":16.8107,"has_fulltext":false,"cited_by_count":109,"citation_normalized_percentile":{"value":0.98766156,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"52","issue":"12","first_page":"1535","last_page":"1542"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998000264167786,"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":0.9998000264167786,"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":0.996399998664856,"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/T10237","display_name":"Cryptography and Data Security","score":0.967199981212616,"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/trinomial","display_name":"Trinomial","score":0.9806609153747559},{"id":"https://openalex.org/keywords/irreducible-polynomial","display_name":"Irreducible polynomial","score":0.8740614056587219},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7051955461502075},{"id":"https://openalex.org/keywords/irreducible-element","display_name":"Irreducible element","score":0.5963591933250427},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5950568914413452},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.5936002731323242},{"id":"https://openalex.org/keywords/irreducible-representation","display_name":"Irreducible representation","score":0.5390161275863647},{"id":"https://openalex.org/keywords/polynomial-basis","display_name":"Polynomial basis","score":0.5043200254440308},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49141252040863037},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.42231571674346924},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3501446545124054},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33873218297958374},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32505565881729126},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.10128894448280334},{"id":"https://openalex.org/keywords/fundamental-representation","display_name":"Fundamental representation","score":0.06627067923545837}],"concepts":[{"id":"https://openalex.org/C6791720","wikidata":"https://www.wikidata.org/wiki/Q1670509","display_name":"Trinomial","level":2,"score":0.9806609153747559},{"id":"https://openalex.org/C165030954","wikidata":"https://www.wikidata.org/wiki/Q1476663","display_name":"Irreducible polynomial","level":4,"score":0.8740614056587219},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7051955461502075},{"id":"https://openalex.org/C15376144","wikidata":"https://www.wikidata.org/wiki/Q2989575","display_name":"Irreducible element","level":5,"score":0.5963591933250427},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5950568914413452},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.5936002731323242},{"id":"https://openalex.org/C142292226","wikidata":"https://www.wikidata.org/wiki/Q13690522","display_name":"Irreducible representation","level":2,"score":0.5390161275863647},{"id":"https://openalex.org/C2778406171","wikidata":"https://www.wikidata.org/wiki/Q6901742","display_name":"Polynomial basis","level":2,"score":0.5043200254440308},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49141252040863037},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.42231571674346924},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3501446545124054},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33873218297958374},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32505565881729126},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.10128894448280334},{"id":"https://openalex.org/C5106717","wikidata":"https://www.wikidata.org/wiki/Q3427416","display_name":"Fundamental representation","level":4,"score":0.06627067923545837},{"id":"https://openalex.org/C183877218","wikidata":"https://www.wikidata.org/wiki/Q7979858","display_name":"Weight","level":3,"score":0.0},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.2003.1252850","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2003.1252850","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311401","display_name":"Oregon State University","ror":"https://ror.org/00ysfqy60"},{"id":"https://openalex.org/F4320323147","display_name":"Istituto Nazionale di Astrofisica","ror":"https://ror.org/02gh4kt33"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W56645331","https://openalex.org/W1512914916","https://openalex.org/W1515926918","https://openalex.org/W1541795511","https://openalex.org/W1587576127","https://openalex.org/W1995214476","https://openalex.org/W2050685430","https://openalex.org/W2078420256","https://openalex.org/W2091899615","https://openalex.org/W2096013791","https://openalex.org/W2128903967","https://openalex.org/W2138169871","https://openalex.org/W2144129711","https://openalex.org/W2145254449","https://openalex.org/W2171653730","https://openalex.org/W2231511903","https://openalex.org/W7018817413","https://openalex.org/W7053059753"],"related_works":["https://openalex.org/W2122699041","https://openalex.org/W277036587","https://openalex.org/W2951514803","https://openalex.org/W2133814675","https://openalex.org/W2039888964","https://openalex.org/W173333345","https://openalex.org/W2785547368","https://openalex.org/W901371731","https://openalex.org/W1549048277","https://openalex.org/W2048290165"],"abstract_inverted_index":{"The":[0],"state-of-the-art":[1],"Galois":[2],"field":[3,15],"GF(2/sup":[4],"m/)":[5],"multipliers":[6],"offer":[7],"advantageous":[8],"space":[9,157],"and":[10,69,115,140,151,158],"time":[11,159],"complexities":[12],"when":[13,32],"the":[14,25,33,55,62,103,127],"is":[16,36,75],"generated":[17],"by":[18],"so":[19],"special":[20,131,148],"irreducible":[21,34,52,82,96,100,106,134,149],"polynomial.":[22],"To":[23],"date,":[24],"best":[26],"complexity":[27],"results":[28],"have":[29],"been":[30,109],"obtained":[31],"polynomial":[35,44],"either":[37],"a":[38,50,122],"trinomial":[39,83,97],"or":[40],"an":[41,81,95,99],"equally":[42],"spaced":[43],"(ESP).":[45],"Unfortunately,":[46],"there":[47,116],"exist":[48],"only":[49],"few":[51],"ESPs":[53],"in":[54,87],"range":[56],"of":[57,61,84,105,129,133,155],"interest":[58],"for":[59,121],"most":[60],"applications,":[63],"e.g.,":[64],"error-correcting":[65],"codes,":[66],"computer":[67],"algebra,":[68],"elliptic":[70],"curve":[71],"cryptography.":[72],"Furthermore,":[73],"it":[74],"not":[76],"always":[77],"possible":[78],"to":[79],"find":[80],"degree":[85],"m":[86],"this":[88],"range.":[89],"For":[90],"those":[91],"cases":[92],"where":[93],"neither":[94],"nor":[98],"ESP":[101],"exists,":[102],"use":[104,128],"pentanomials":[107,112,150],"has":[108],"suggested.":[110],"Irreducible":[111],"are":[113,117],"abundant,":[114],"several":[118],"eligible":[119],"candidates":[120],"given":[123],"m.":[124],"We":[125,136],"promote":[126],"two":[130],"types":[132],"pentanomials.":[135],"propose":[137],"new":[138],"Mastrovito":[139],"dual":[141],"basis":[142],"multiplier":[143],"architectures":[144],"based":[145],"on":[146],"these":[147],"give":[152],"rigorous":[153],"analyses":[154],"their":[156],"complexity.":[160]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2016-06-24T00:00:00"}
