{"id":"https://openalex.org/W2586653522","doi":"https://doi.org/10.1109/tvlsi.2017.2652979","title":"A General Digit-Serial Architecture for Montgomery Modular Multiplication","display_name":"A General Digit-Serial Architecture for Montgomery Modular Multiplication","publication_year":2017,"publication_date":"2017-02-07","ids":{"openalex":"https://openalex.org/W2586653522","doi":"https://doi.org/10.1109/tvlsi.2017.2652979","mag":"2586653522"},"language":"en","primary_location":{"id":"doi:10.1109/tvlsi.2017.2652979","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvlsi.2017.2652979","pdf_url":null,"source":{"id":"https://openalex.org/S37538908","display_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","issn_l":"1063-8210","issn":["1063-8210","1557-9999"],"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 Very Large Scale Integration (VLSI) Systems","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/A5084241552","display_name":"Serdar S\u00fcer Erdem","orcid":"https://orcid.org/0000-0002-9637-583X"},"institutions":[{"id":"https://openalex.org/I109297418","display_name":"Gebze Technical University","ror":"https://ror.org/01sdnnq10","country_code":"TR","type":"education","lineage":["https://openalex.org/I109297418"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Serdar Suer Erdem","raw_affiliation_strings":["Department of Electronics Engineering, Gebze Technical University, Gebze, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Electronics Engineering, Gebze Technical University, Gebze, Turkey","institution_ids":["https://openalex.org/I109297418"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002484167","display_name":"Tu\u011frul Yan\u0131k","orcid":null},"institutions":[{"id":"https://openalex.org/I16748637","display_name":"Manisa Celal Bayar University","ror":"https://ror.org/053f2w588","country_code":"TR","type":"education","lineage":["https://openalex.org/I16748637"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Tugrul Yanik","raw_affiliation_strings":["Department of Computer Engineering, Celal Bayar University, Muradiye, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering, Celal Bayar University, Muradiye, Turkey","institution_ids":["https://openalex.org/I16748637"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039720236","display_name":"An\u0131l \u00c7elebi","orcid":"https://orcid.org/0000-0002-0921-3040"},"institutions":[{"id":"https://openalex.org/I51826884","display_name":"Kocaeli \u00dcniversitesi","ror":"https://ror.org/0411seq30","country_code":"TR","type":"education","lineage":["https://openalex.org/I51826884"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Anil Celebi","raw_affiliation_strings":["Department of Electronics and Communication Engineering, Kocaeli University, \u0130zmit, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Electronics and Communication Engineering, Kocaeli University, \u0130zmit, Turkey","institution_ids":["https://openalex.org/I51826884"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084241552"],"corresponding_institution_ids":["https://openalex.org/I109297418"],"apc_list":null,"apc_paid":null,"fwci":4.8362,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.95377948,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"25","issue":"5","first_page":"1658","last_page":"1668"},"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":0.9976999759674072,"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":0.9950000047683716,"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-arithmetic","display_name":"Modular arithmetic","score":0.7418135404586792},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6740716695785522},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.6342683434486389},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5865697860717773},{"id":"https://openalex.org/keywords/adder","display_name":"Adder","score":0.5743656158447266},{"id":"https://openalex.org/keywords/carry","display_name":"Carry (investment)","score":0.5276759266853333},{"id":"https://openalex.org/keywords/precomputation","display_name":"Precomputation","score":0.5011603832244873},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.48500367999076843},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.4630899727344513},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4481359124183655},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.4182886779308319},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32158130407333374},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.3209439218044281},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2924976348876953},{"id":"https://openalex.org/keywords/latency","display_name":"Latency (audio)","score":0.22431603074073792},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08700624108314514}],"concepts":[{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.7418135404586792},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6740716695785522},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6342683434486389},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5865697860717773},{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.5743656158447266},{"id":"https://openalex.org/C2776299755","wikidata":"https://www.wikidata.org/wiki/Q432449","display_name":"Carry (investment)","level":2,"score":0.5276759266853333},{"id":"https://openalex.org/C159379195","wikidata":"https://www.wikidata.org/wiki/Q7239568","display_name":"Precomputation","level":3,"score":0.5011603832244873},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.48500367999076843},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.4630899727344513},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4481359124183655},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.4182886779308319},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32158130407333374},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3209439218044281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2924976348876953},{"id":"https://openalex.org/C82876162","wikidata":"https://www.wikidata.org/wiki/Q17096504","display_name":"Latency (audio)","level":2,"score":0.22431603074073792},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08700624108314514},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/tvlsi.2017.2652979","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvlsi.2017.2652979","pdf_url":null,"source":{"id":"https://openalex.org/S37538908","display_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","issn_l":"1063-8210","issn":["1063-8210","1557-9999"],"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 Very Large Scale Integration (VLSI) Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","score":0.4699999988079071,"id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1550170577","https://openalex.org/W1965994627","https://openalex.org/W1996360405","https://openalex.org/W2003736153","https://openalex.org/W2004814164","https://openalex.org/W2018747984","https://openalex.org/W2036378739","https://openalex.org/W2043950313","https://openalex.org/W2045682094","https://openalex.org/W2049347491","https://openalex.org/W2069719945","https://openalex.org/W2088925378","https://openalex.org/W2098383431","https://openalex.org/W2107953479","https://openalex.org/W2108686456","https://openalex.org/W2110122313","https://openalex.org/W2118738175","https://openalex.org/W2130112858","https://openalex.org/W2133708535","https://openalex.org/W2136870067","https://openalex.org/W2138917317","https://openalex.org/W2140850958","https://openalex.org/W4232836212","https://openalex.org/W4237773356"],"related_works":["https://openalex.org/W2101177093","https://openalex.org/W1513163841","https://openalex.org/W3187512444","https://openalex.org/W2189114920","https://openalex.org/W2028996897","https://openalex.org/W1650124897","https://openalex.org/W1530970176","https://openalex.org/W2026418103","https://openalex.org/W2107078627","https://openalex.org/W2091557303"],"abstract_inverted_index":{"The":[0,104],"Montgomery":[1,22,55,142],"algorithm":[2,23,143],"is":[3,30,37,63,68,102,158],"a":[4,33],"fast":[5],"modular":[6,56,90],"multiplication":[7],"method":[8],"frequently":[9],"used":[10,78,139],"in":[11,140],"cryptographic":[12],"applications.":[13],"This":[14,118],"paper":[15,119],"investigates":[16],"the":[17,21,40,45,89,94,125,128,141,151],"digit-serial":[18,46,54],"implementations":[19],"of":[20,127,150],"for":[24,39,110,124,144],"large":[25],"integers.":[26],"A":[27],"detailed":[28],"analysis":[29],"given":[31],"and":[32,65,92,115],"tight":[34],"upper":[35],"bound":[36],"presented":[38],"intermediate":[41],"results":[42],"obtained":[43],"during":[44],"computation.":[47],"Based":[48],"on":[49,154],"this":[50,71,97],"analysis,":[51],"an":[52],"efficient":[53],"multiplier":[57],"architecture":[58,106,153],"using":[59],"carry":[60,74,85],"save":[61,86],"adders":[62,76],"proposed":[64,105,152],"its":[66],"complexity":[67],"presented.":[69,159],"In":[70],"architecture,":[72],"pipelined":[73],"select":[75],"are":[77],"to":[79],"perform":[80],"two":[81],"final":[82],"tasks:":[83],"adding":[84],"vectors":[87],"representing":[88],"product":[91],"subtracting":[93],"modulus":[95,116],"from":[96],"addition,":[98],"if":[99],"further":[100],"reduction":[101],"needed.":[103],"can":[107],"be":[108],"designed":[109],"any":[111],"digit":[112],"size":[113],"\u03b4":[114,145],"\u03b8.":[117],"also":[120],"presents":[121],"logic":[122],"formulas":[123],"bits":[126],"precomputation":[129],"-\u03b8":[130],"<sup":[131,136],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[132,137],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-1</sup>":[133],"mod":[134],"2":[135],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b4</sup>":[138],"\u2264":[146],"8.":[147],"Finally,":[148],"evaluation":[149],"Virtex":[155],"7":[156],"FPGAs":[157]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}