{"id":"https://openalex.org/W4200271029","doi":"https://doi.org/10.1142/s0218126622501377","title":"Efficient and Scalable Hardware Implementation of Montgomery Modular Multiplication","display_name":"Efficient and Scalable Hardware Implementation of Montgomery Modular Multiplication","publication_year":2021,"publication_date":"2021-12-14","ids":{"openalex":"https://openalex.org/W4200271029","doi":"https://doi.org/10.1142/s0218126622501377"},"language":"en","primary_location":{"id":"doi:10.1142/s0218126622501377","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218126622501377","pdf_url":null,"source":{"id":"https://openalex.org/S167602672","display_name":"Journal of Circuits Systems and Computers","issn_l":"0218-1266","issn":["0218-1266","1793-6454"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Circuits, Systems and 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/A5007287687","display_name":"M. Issad","orcid":"https://orcid.org/0000-0002-8896-7827"},"institutions":[{"id":"https://openalex.org/I4210102186","display_name":"Centre de D\u00e9veloppement des Technologies Avanc\u00e9es","ror":"https://ror.org/01ay87255","country_code":"DZ","type":"facility","lineage":["https://openalex.org/I4210102186"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"M. Issad","raw_affiliation_strings":["Department of System and Multimedia Architecture, Centre de D\u00e9veloppement des Technologies Avanc\u00e9es, BP. 17 Cit\u00e9 20 Ao\u00fbt 1956, Baba Hassen 16081, Alger, Algeria"],"raw_orcid":"https://orcid.org/0000-0002-8896-7827","affiliations":[{"raw_affiliation_string":"Department of System and Multimedia Architecture, Centre de D\u00e9veloppement des Technologies Avanc\u00e9es, BP. 17 Cit\u00e9 20 Ao\u00fbt 1956, Baba Hassen 16081, Alger, Algeria","institution_ids":["https://openalex.org/I4210102186"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113701843","display_name":"Mohamed Anane","orcid":"https://orcid.org/0009-0000-1502-5524"},"institutions":[{"id":"https://openalex.org/I4210149016","display_name":"\u00c9cole Nationale Sup\u00e9rieure d'Informatique","ror":"https://ror.org/04dj1dn66","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210149016"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"M. Anane","raw_affiliation_strings":["Ecole Sup\u00e9rieure d\u2019Informatique, BP. 68M, Oued Smar, El Harrach 16270, Alger, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole Sup\u00e9rieure d\u2019Informatique, BP. 68M, Oued Smar, El Harrach 16270, Alger, Algeria","institution_ids":["https://openalex.org/I4210149016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039067268","display_name":"Bachir Boudraa","orcid":"https://orcid.org/0000-0003-1213-1545"},"institutions":[{"id":"https://openalex.org/I157169809","display_name":"University of Sciences and Technology Houari Boumediene","ror":"https://ror.org/02kb89c09","country_code":"DZ","type":"education","lineage":["https://openalex.org/I157169809"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"B. Boudraa","raw_affiliation_strings":["Faculty of Electronic and informatics, Universit\u00e9 des Sciences et de la Technologie Houari Boumediene, BP. 32 El Alia, Bab Ezzouar 16111, Alger, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electronic and informatics, Universit\u00e9 des Sciences et de la Technologie Houari Boumediene, BP. 32 El Alia, Bab Ezzouar 16111, Alger, Algeria","institution_ids":["https://openalex.org/I157169809"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074007763","display_name":"Ahmed Mohamed Bellemou","orcid":"https://orcid.org/0000-0002-4144-5204"},"institutions":[{"id":"https://openalex.org/I4210102186","display_name":"Centre de D\u00e9veloppement des Technologies Avanc\u00e9es","ror":"https://ror.org/01ay87255","country_code":"DZ","type":"facility","lineage":["https://openalex.org/I4210102186"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"A. M. Bellemou","raw_affiliation_strings":["Department of System and Multimedia Architecture, Centre de D\u00e9veloppement des Technologies Avanc\u00e9es, BP. 17 Cit\u00e9 20 Ao\u00fbt 1956, Baba Hassen 16081, Alger, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of System and Multimedia Architecture, Centre de D\u00e9veloppement des Technologies Avanc\u00e9es, BP. 17 Cit\u00e9 20 Ao\u00fbt 1956, Baba Hassen 16081, Alger, Algeria","institution_ids":["https://openalex.org/I4210102186"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007287687"],"corresponding_institution_ids":["https://openalex.org/I4210102186"],"apc_list":null,"apc_paid":null,"fwci":1.1087,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.83590213,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"31","issue":"08","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9973999857902527,"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":0.9948999881744385,"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/operand","display_name":"Operand","score":0.8489219546318054},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7928304076194763},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.6804893016815186},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.6709955930709839},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.6435345411300659},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5998331308364868},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5807865262031555},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.46086016297340393},{"id":"https://openalex.org/keywords/throughput","display_name":"Throughput","score":0.43866848945617676},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4385170340538025},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.35654622316360474},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22279077768325806},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14134177565574646},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.14082103967666626}],"concepts":[{"id":"https://openalex.org/C55526617","wikidata":"https://www.wikidata.org/wiki/Q719375","display_name":"Operand","level":2,"score":0.8489219546318054},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7928304076194763},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.6804893016815186},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.6709955930709839},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6435345411300659},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5998331308364868},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5807865262031555},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.46086016297340393},{"id":"https://openalex.org/C157764524","wikidata":"https://www.wikidata.org/wiki/Q1383412","display_name":"Throughput","level":3,"score":0.43866848945617676},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4385170340538025},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.35654622316360474},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22279077768325806},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14134177565574646},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.14082103967666626},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218126622501377","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218126622501377","pdf_url":null,"source":{"id":"https://openalex.org/S167602672","display_name":"Journal of Circuits Systems and Computers","issn_l":"0218-1266","issn":["0218-1266","1793-6454"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Circuits, Systems and Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","score":0.5199999809265137,"display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1864311428","https://openalex.org/W2004814164","https://openalex.org/W2018465842","https://openalex.org/W2069719945","https://openalex.org/W2086624215","https://openalex.org/W2107144991","https://openalex.org/W2156186849","https://openalex.org/W2166176217","https://openalex.org/W2539628602","https://openalex.org/W2586653522","https://openalex.org/W2764308837","https://openalex.org/W2782741223","https://openalex.org/W2909218985","https://openalex.org/W2940460717","https://openalex.org/W2942691585","https://openalex.org/W4214660051","https://openalex.org/W4232836212","https://openalex.org/W4241366606"],"related_works":["https://openalex.org/W2320205417","https://openalex.org/W2024456689","https://openalex.org/W2356663714","https://openalex.org/W1528435681","https://openalex.org/W2589564280","https://openalex.org/W75189697","https://openalex.org/W2623582878","https://openalex.org/W122256349","https://openalex.org/W1973319834","https://openalex.org/W2263777287"],"abstract_inverted_index":{"Modular":[0],"multiplication":[1],"(MM)":[2],"is":[3,70,87,115],"an":[4],"important":[5],"arithmetic":[6,123],"operation":[7,34],"in":[8,84,125,159],"public":[9],"key":[10],"cryptography":[11],"(PKC).":[12],"In":[13,45,99,128],"this":[14,33,85],"paper,":[15],"we":[16],"present":[17],"the":[18,22,37,42,49,53,63,72,76,118,121,141,144],"FPGA":[19],"implementation":[20,74,113],"of":[21,32,58,75,120,143],"MM":[23,26],"using":[24],"Montgomery":[25],"(MMM)":[27],"algorithm.":[28],"The":[29,147],"execution":[30,119,145],"performances":[31],"depend":[35],"on":[36,117,150],"radix-[Formula:":[38,50],"see":[39,51,161,163],"text]":[40],"and":[41,109,132,165],"operands":[43,97],"length.":[44,98],"fact,":[46],"when":[47,66],"increasing":[48],"text],":[52],"MMM":[54,77,157],"algorithm":[55],"requires":[56],"multiplications":[57],"digit":[59],"by":[60],"operand.":[61],"On":[62],"other":[64],"hand,":[65],"a":[67,79,90,103,155],"long":[68],"modulus":[69],"used,":[71],"hardware":[73,110],"needs":[78],"large":[80],"area.":[81],"Our":[82],"objective":[83],"work":[86],"to":[88,94,101],"realize":[89],"scalable":[91],"architecture":[92],"able":[93],"support":[95],"any":[96],"order":[100],"achieve":[102],"best":[104],"trade-off":[105],"between":[106],"computation":[107],"throughput":[108],"resources,":[111],"our":[112],"approach":[114],"based":[116],"basic":[122],"operations":[124],"serial":[126],"way.":[127],"addition,":[129],"efficient":[130],"parallel":[131],"pipelined":[133],"strategies":[134],"are":[135],"realized":[136],"at":[137],"low-level":[138],"abstraction":[139],"for":[140],"optimization":[142],"time.":[146],"implementations":[148],"results":[149],"Virtex-7":[151],"circuit":[152],"show":[153],"that":[154],"1024-bit":[156],"runs":[158],"2.09[Formula:":[160],"text][Formula:":[162],"text]s":[164],"consumes":[166],"581":[167],"slices.":[168]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
