{"id":"https://openalex.org/W2118210562","doi":"https://doi.org/10.1109/tie.2010.2080653","title":"Modular Multiplication and Exponentiation Architectures for Fast RSA Cryptosystem Based on Digit Serial Computation","display_name":"Modular Multiplication and Exponentiation Architectures for Fast RSA Cryptosystem Based on Digit Serial Computation","publication_year":2010,"publication_date":"2010-09-29","ids":{"openalex":"https://openalex.org/W2118210562","doi":"https://doi.org/10.1109/tie.2010.2080653","mag":"2118210562"},"language":"en","primary_location":{"id":"doi:10.1109/tie.2010.2080653","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2010.2080653","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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 Industrial Electronics","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/A5042034543","display_name":"Gustavo Sutter","orcid":"https://orcid.org/0000-0001-8820-5956"},"institutions":[{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Gustavo D. Sutter","raw_affiliation_strings":["school of Engineering, Universidad Aut\u00f3noma de Madrid, Madrid, Spain","Sch. of Eng., Univ. Autonoma de Madrid, Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"school of Engineering, Universidad Aut\u00f3noma de Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]},{"raw_affiliation_string":"Sch. of Eng., Univ. Autonoma de Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109309081","display_name":"Jean\u2010Pierre Deschamps","orcid":null},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]},{"id":"https://openalex.org/I55952717","display_name":"Universitat Rovira i Virgili","ror":"https://ror.org/00g5sqv46","country_code":"ES","type":"education","lineage":["https://openalex.org/I55952717"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jean-Pierre Deschamps","raw_affiliation_strings":["Faculty of Physics, Complutense University of madrid, Madrid, Spain","Univ. Rovira i Virgili, Tarragona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics, Complutense University of madrid, Madrid, Spain","institution_ids":["https://openalex.org/I121748325"]},{"raw_affiliation_string":"Univ. Rovira i Virgili, Tarragona, Spain","institution_ids":["https://openalex.org/I55952717"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041677215","display_name":"Jos\u00e9 Luis Ima\u00f1a","orcid":"https://orcid.org/0000-0002-4220-4111"},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]},{"id":"https://openalex.org/I55952717","display_name":"Universitat Rovira i Virgili","ror":"https://ror.org/00g5sqv46","country_code":"ES","type":"education","lineage":["https://openalex.org/I55952717"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 Luis Imana","raw_affiliation_strings":["University of Rovira i Virgili, Tarragona, Spain","Fac. of Phys., Complutense Univ. of Madrid, Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Rovira i Virgili, Tarragona, Spain","institution_ids":["https://openalex.org/I55952717"]},{"raw_affiliation_string":"Fac. of Phys., Complutense Univ. of Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I121748325"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":24.7701,"has_fulltext":false,"cited_by_count":77,"citation_normalized_percentile":{"value":0.99309775,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"58","issue":"7","first_page":"3101","last_page":"3109"},"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":0.9987999796867371,"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":0.9977999925613403,"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/modular-exponentiation","display_name":"Modular exponentiation","score":0.9163097143173218},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.7032293081283569},{"id":"https://openalex.org/keywords/cryptosystem","display_name":"Cryptosystem","score":0.6731589436531067},{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.6516177654266357},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6363502740859985},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.6103684306144714},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6091002821922302},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5703584551811218},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.4712291955947876},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.4615471661090851},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.4513801336288452},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.4444524645805359},{"id":"https://openalex.org/keywords/overhead","display_name":"Overhead (engineering)","score":0.4442897439002991},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.44310829043388367},{"id":"https://openalex.org/keywords/adder","display_name":"Adder","score":0.4403463304042816},{"id":"https://openalex.org/keywords/chinese-remainder-theorem","display_name":"Chinese remainder theorem","score":0.4327293038368225},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.4285867214202881},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31579533219337463},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.27723178267478943},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2733036279678345},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.19970625638961792},{"id":"https://openalex.org/keywords/latency","display_name":"Latency (audio)","score":0.1070081889629364}],"concepts":[{"id":"https://openalex.org/C152763109","wikidata":"https://www.wikidata.org/wiki/Q1228841","display_name":"Modular exponentiation","level":4,"score":0.9163097143173218},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.7032293081283569},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.6731589436531067},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.6516177654266357},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6363502740859985},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6103684306144714},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6091002821922302},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5703584551811218},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.4712291955947876},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.4615471661090851},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.4513801336288452},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.4444524645805359},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.4442897439002991},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.44310829043388367},{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.4403463304042816},{"id":"https://openalex.org/C151635116","wikidata":"https://www.wikidata.org/wiki/Q193878","display_name":"Chinese remainder theorem","level":2,"score":0.4327293038368225},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.4285867214202881},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31579533219337463},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.27723178267478943},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2733036279678345},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.19970625638961792},{"id":"https://openalex.org/C82876162","wikidata":"https://www.wikidata.org/wiki/Q17096504","display_name":"Latency (audio)","level":2,"score":0.1070081889629364},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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:10.1109/tie.2010.2080653","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2010.2080653","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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 Industrial Electronics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1493873707","https://openalex.org/W1529132699","https://openalex.org/W1538172314","https://openalex.org/W1543517987","https://openalex.org/W1566542142","https://openalex.org/W1928877101","https://openalex.org/W1984943724","https://openalex.org/W1996360405","https://openalex.org/W2004814164","https://openalex.org/W2045682094","https://openalex.org/W2088925378","https://openalex.org/W2098383431","https://openalex.org/W2111139814","https://openalex.org/W2113706793","https://openalex.org/W2125096162","https://openalex.org/W2129788823","https://openalex.org/W2130950843","https://openalex.org/W2156186849","https://openalex.org/W2156460937","https://openalex.org/W2158990735","https://openalex.org/W2161198480","https://openalex.org/W2170940817","https://openalex.org/W2752061190","https://openalex.org/W4214660051","https://openalex.org/W4230453618","https://openalex.org/W4232836212","https://openalex.org/W4237773356","https://openalex.org/W6640212602"],"related_works":["https://openalex.org/W2393695657","https://openalex.org/W1587481360","https://openalex.org/W2787256264","https://openalex.org/W2076621334","https://openalex.org/W2107014706","https://openalex.org/W1983867177","https://openalex.org/W2292159208","https://openalex.org/W1977356083","https://openalex.org/W2137988767","https://openalex.org/W2104685162"],"abstract_inverted_index":{"Modular":[0],"exponentiation":[1,168],"with":[2,111,152,178],"large":[3],"modulus":[4],"and":[5,36,56,66,116,143,169,182],"exponent,":[6],"which":[7],"is":[8,28,34,41],"usually":[9],"accomplished":[10],"by":[11],"repeated":[12],"modular":[13,167],"multiplications,":[14],"has":[15,76],"been":[16],"widely":[17],"used":[18,29],"in":[19,122,125,139,144,185],"public":[20],"key":[21],"cryptosystems.":[22],"Typically,":[23],"the":[24,37,45,53,61,67,77,93,104,119,130,165,173,179],"Montgomery's":[25,54,123],"modular-multiplication":[26,170],"algorithm":[27],"since":[30],"no":[31],"trial":[32],"division":[33],"necessary,":[35],"carry\u2013save":[38],"addition":[39],"(CSA)":[40],"employed":[42],"to":[43,59,107,127],"reduce":[44],"critical":[46,105],"path.":[47],"In":[48,133],"this":[49,134],"paper,":[50,135],"we":[51,136],"optimize":[52],"multiplication":[55,98],"propose":[57],"architectures":[58],"perform":[60],"least":[62],"significant":[63,69],"bit":[64,70],"first":[65,71],"most":[68],"algorithms.":[72],"The":[73],"developed":[74],"architecture":[75],"following":[78],"distinctive":[79],"characteristics:":[80],"1)":[81],"use":[82],"of":[83,92,96,187],"digit":[84],"serial":[85],"approach":[86],"for":[87],"Montgomery":[88],"multiplication.":[89],"2)":[90],"Conversion":[91],"CSA":[94],"representation":[95],"intermediate":[97],"using":[99],"carry\u2013skip":[100],"addition.":[101],"This":[102],"allows":[103],"path":[106],"be":[108],"reduced,":[109],"albeit":[110],"a":[112],"small-area":[113],"speed":[114,128],"penalty;":[115],"3)":[117],"precompute":[118],"quotient":[120],"value":[121],"iteration":[124],"order":[126],"up":[129],"operating":[131],"frequency.":[132],"present":[137],"results":[138,158,162],"Xilinx":[140,155],"Virtex":[141,156],"5":[142],"0.18-$\\mu\\hbox{m}$application-specified":[145],"integrated":[146],"circuit":[147],"technologies.":[148],"For":[149],"fair":[150],"comparison":[151],"previous":[153],"works,":[154],"2":[157],"are":[159],"reported.":[160],"Experimental":[161],"show":[163],"that":[164],"proposed":[166],"design":[171],"obtain":[172],"best":[174],"delay":[175],"performance":[176],"compared":[177],"published":[180],"works":[181],"outperform":[183],"them":[184],"terms":[186],"area\u2013time":[188],"complexity":[189],"as":[190],"well.":[191]},"counts_by_year":[{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":9}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}