{"id":"https://openalex.org/W2108989775","doi":"https://doi.org/10.1109/tassp.1985.1164761","title":"The VLSI design of a single chip for the multiplication of integers modulo a Fermat number","display_name":"The VLSI design of a single chip for the multiplication of integers modulo a Fermat number","publication_year":1985,"publication_date":"1985-12-01","ids":{"openalex":"https://openalex.org/W2108989775","doi":"https://doi.org/10.1109/tassp.1985.1164761","mag":"2108989775"},"language":"en","primary_location":{"id":"doi:10.1109/tassp.1985.1164761","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tassp.1985.1164761","pdf_url":null,"source":{"id":"https://openalex.org/S98930721","display_name":"IEEE Transactions on Acoustics Speech and Signal Processing","issn_l":"0096-3518","issn":["0096-3518"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Acoustics, Speech, and Signal Processing","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/A5073227331","display_name":"J. J. Chang","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":true,"raw_author_name":"Jaw Chang","raw_affiliation_strings":["Jet Propulsion Laboratory, Pasadena, CA, USA","Jet, Propulsion Laboratory (Pasadena, CA)"],"affiliations":[{"raw_affiliation_string":"Jet Propulsion Laboratory, Pasadena, CA, USA","institution_ids":["https://openalex.org/I1334627681"]},{"raw_affiliation_string":"Jet, Propulsion Laboratory (Pasadena, CA)","institution_ids":["https://openalex.org/I1334627681"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108811088","display_name":"T. K. Truong","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":"T. Truong","raw_affiliation_strings":["Jet Propulsion Laboratory, Pasadena, CA, USA","Jet Propulsion laboratory, Pasadena, CA, USA"],"affiliations":[{"raw_affiliation_string":"Jet Propulsion Laboratory, Pasadena, CA, USA","institution_ids":["https://openalex.org/I1334627681"]},{"raw_affiliation_string":"Jet Propulsion laboratory, Pasadena, CA, USA","institution_ids":["https://openalex.org/I1334627681"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029592502","display_name":"H. Shao","orcid":"https://orcid.org/0000-0003-4038-3512"},"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":"H. Shao","raw_affiliation_strings":["Jet Propulsion Laboratory, Pasadena, CA, USA","Jet Propulsion laboratory, Pasadena, CA, USA"],"affiliations":[{"raw_affiliation_string":"Jet Propulsion Laboratory, Pasadena, CA, USA","institution_ids":["https://openalex.org/I1334627681"]},{"raw_affiliation_string":"Jet Propulsion laboratory, Pasadena, CA, USA","institution_ids":["https://openalex.org/I1334627681"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111556135","display_name":"I.S. 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":"I. Reed","raw_affiliation_strings":["Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","Department of Electrical Engineering , University of Southern California , Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Department of Electrical Engineering , University of Southern California , Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045362414","display_name":"I. S. Hsu","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":"In-Shek Hsu","raw_affiliation_strings":["Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","Department of Electrical Engineering , University of Southern California , Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Department of Electrical Engineering , University of Southern California , Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5073227331"],"corresponding_institution_ids":["https://openalex.org/I1334627681"],"apc_list":null,"apc_paid":null,"fwci":6.6725,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.97028395,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"6","first_page":"1599","last_page":"1602"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9980000257492065,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.7314830422401428},{"id":"https://openalex.org/keywords/fermat-number","display_name":"Fermat number","score":0.677375853061676},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6683870553970337},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.6677037477493286},{"id":"https://openalex.org/keywords/very-large-scale-integration","display_name":"Very-large-scale integration","score":0.6591317653656006},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5991933941841125},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.5503902435302734},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5282299518585205},{"id":"https://openalex.org/keywords/chip","display_name":"Chip","score":0.49055975675582886},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42945462465286255},{"id":"https://openalex.org/keywords/residue-number-system","display_name":"Residue number system","score":0.42929667234420776},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39807939529418945},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.3707532286643982},{"id":"https://openalex.org/keywords/fermats-last-theorem","display_name":"Fermat's Last Theorem","score":0.3701084554195404},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.24023771286010742},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11687430739402771},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.11169832944869995},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.08746081590652466}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.7314830422401428},{"id":"https://openalex.org/C171223647","wikidata":"https://www.wikidata.org/wiki/Q207264","display_name":"Fermat number","level":3,"score":0.677375853061676},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6683870553970337},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.6677037477493286},{"id":"https://openalex.org/C14580979","wikidata":"https://www.wikidata.org/wiki/Q876049","display_name":"Very-large-scale integration","level":2,"score":0.6591317653656006},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5991933941841125},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.5503902435302734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5282299518585205},{"id":"https://openalex.org/C165005293","wikidata":"https://www.wikidata.org/wiki/Q1074500","display_name":"Chip","level":2,"score":0.49055975675582886},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42945462465286255},{"id":"https://openalex.org/C71480937","wikidata":"https://www.wikidata.org/wiki/Q3086516","display_name":"Residue number system","level":2,"score":0.42929667234420776},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39807939529418945},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3707532286643982},{"id":"https://openalex.org/C87670640","wikidata":"https://www.wikidata.org/wiki/Q132469","display_name":"Fermat's Last Theorem","level":2,"score":0.3701084554195404},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.24023771286010742},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11687430739402771},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.11169832944869995},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.08746081590652466},{"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tassp.1985.1164761","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tassp.1985.1164761","pdf_url":null,"source":{"id":"https://openalex.org/S98930721","display_name":"IEEE Transactions on Acoustics Speech and Signal Processing","issn_l":"0096-3518","issn":["0096-3518"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Acoustics, Speech, and Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1982022511","https://openalex.org/W2034833016","https://openalex.org/W2054674262","https://openalex.org/W2113994308","https://openalex.org/W2793366120"],"related_works":["https://openalex.org/W2991280424","https://openalex.org/W2943053837","https://openalex.org/W4379791326","https://openalex.org/W3110331480","https://openalex.org/W2792684808","https://openalex.org/W2952739523","https://openalex.org/W2054853546","https://openalex.org/W2545076974","https://openalex.org/W2734922190","https://openalex.org/W3209967888"],"abstract_inverted_index":{"Multiplication":[0],"is":[1,17,40,63,74,78,85,97,120],"central":[2],"in":[3,45,87,99],"the":[4,36,46,70],"implementation":[5],"of":[6,48,56,72,109],"Fermat":[7,52],"number":[8,14],"transforms":[9],"(FNT)":[10],"and":[11,112,124],"other":[12],"residue":[13],"algorithms.":[15],"There":[16],"need":[18],"for":[19,116,127],"a":[20,30,51,107],"good":[21],"multiplication":[22,44,73],"algorithm":[23,59,62,66,104],"which":[24],"can":[25],"be":[26],"realized":[27],"easily":[28],"on":[29],"VLSI":[31,128],"chip.":[32],"In":[33,80],"this":[34,57,81,100,103,117],"paper,":[35],"Leibowitz":[37],"multiplier":[38,119],"[1]":[39],"modified":[41],"to":[42],"realize":[43],"ring":[47],"integers":[49],"modulo":[50,68,84],"number.":[53],"The":[54,114],"advantage":[55],"new":[58,82,118],"over":[60],"Leibowitz's":[61,65],"that":[64],"takes":[67],"after":[69],"product":[71],"obtained.":[75],"Hence":[76],"time":[77,96],"wasted.":[79],"algorithm,":[83],"taken":[86],"every":[88],"bit":[89],"operation":[90],"when":[91],"performing":[92],"multiplication.":[93],"Therefore":[94],"no":[95],"wasted":[98],"respect.":[101],"Furthermore,":[102],"requires":[105],"only":[106],"sequence":[108],"cyclic":[110],"shifts":[111],"additions.":[113],"design":[115],"regular,":[121],"simple,":[122],"expandable,":[123],"therefore,":[125],"suitable":[126],"implementation.":[129]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
