{"id":"https://openalex.org/W2148682337","doi":"https://doi.org/10.1109/tc.1980.1675473","title":"Implementation of Multiplication, Modulo a Prime Number, with Applications to Number Theoretic Transforms","display_name":"Implementation of Multiplication, Modulo a Prime Number, with Applications to Number Theoretic Transforms","publication_year":1980,"publication_date":"1980-10-01","ids":{"openalex":"https://openalex.org/W2148682337","doi":"https://doi.org/10.1109/tc.1980.1675473","mag":"2148682337"},"language":"en","primary_location":{"id":"doi:10.1109/tc.1980.1675473","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1980.1675473","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","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":"https://openalex.org/A5058394082","display_name":"Jullien","orcid":null},"institutions":[{"id":"https://openalex.org/I74413500","display_name":"University of Windsor","ror":"https://ror.org/01gw3d370","country_code":"CA","type":"education","lineage":["https://openalex.org/I74413500"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Jullien","raw_affiliation_strings":["Department of Electrical Engineering, University of Windsor, Windsor, ONT, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Windsor, Windsor, ONT, Canada","institution_ids":["https://openalex.org/I74413500"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058394082"],"corresponding_institution_ids":["https://openalex.org/I74413500"],"apc_list":null,"apc_paid":null,"fwci":3.4022,"has_fulltext":false,"cited_by_count":90,"citation_normalized_percentile":{"value":0.91791045,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"C-29","issue":"10","first_page":"899","last_page":"905"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9987999796867371,"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":0.9925000071525574,"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/modulo","display_name":"Modulo","score":0.7423538565635681},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.6074128150939941},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.6073582172393799},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5994148254394531},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5896785259246826},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5023193359375},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4822171926498413},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.47364842891693115},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.42713046073913574},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34404969215393066},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3440369963645935},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23833581805229187},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17325225472450256},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09307271242141724}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.7423538565635681},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.6074128150939941},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6073582172393799},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5994148254394531},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5896785259246826},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5023193359375},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4822171926498413},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.47364842891693115},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.42713046073913574},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34404969215393066},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3440369963645935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23833581805229187},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17325225472450256},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09307271242141724}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.1980.1675473","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1980.1675473","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","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":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1489433220","https://openalex.org/W1819199145","https://openalex.org/W1992283714","https://openalex.org/W2059569686","https://openalex.org/W2069448237","https://openalex.org/W2093794779","https://openalex.org/W2113994308","https://openalex.org/W2120062331","https://openalex.org/W2154123414","https://openalex.org/W2801179766","https://openalex.org/W2986057930","https://openalex.org/W4212899991","https://openalex.org/W6775794996"],"related_works":["https://openalex.org/W2770581008","https://openalex.org/W2151719298","https://openalex.org/W248825282","https://openalex.org/W3087194925","https://openalex.org/W280421009","https://openalex.org/W1997999036","https://openalex.org/W4288118777","https://openalex.org/W2783678733","https://openalex.org/W2962773893","https://openalex.org/W2165647384"],"abstract_inverted_index":{"This":[0],"paper":[1],"discusses":[2],"a":[3,9,31,37],"technique":[4],"for":[5],"multiplying":[6],"numbers,":[7],"modulo":[8],"prime":[10],"number,":[11],"using":[12],"look-up":[13],"tables":[14],"stored":[15],"in":[16,22,30,48],"read-only":[17],"memories.":[18],"The":[19],"application":[20],"is":[21,34],"the":[23],"computation":[24],"of":[25,40],"number":[26],"theoretic":[27],"transforms":[28],"implemented":[29],"ring":[32],"which":[33],"isomorphic":[35],"to":[36],"direct":[38],"sum":[39],"several":[41],"Galois":[42],"fields,":[43],"parallel":[44],"computations":[45],"being":[46],"performed":[47],"each":[49],"field.":[50]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}