{"id":"https://openalex.org/W1993934432","doi":"https://doi.org/10.3390/s130709483","title":"Fixed-Base Comb with Window-Non-Adjacent Form (NAF) Method for Scalar Multiplication","display_name":"Fixed-Base Comb with Window-Non-Adjacent Form (NAF) Method for Scalar Multiplication","publication_year":2013,"publication_date":"2013-07-23","ids":{"openalex":"https://openalex.org/W1993934432","doi":"https://doi.org/10.3390/s130709483","mag":"1993934432","pmid":"https://pubmed.ncbi.nlm.nih.gov/23881143"},"language":"en","primary_location":{"id":"doi:10.3390/s130709483","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s130709483","pdf_url":null,"source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/s130709483","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085541661","display_name":"Hwajeong Seo","orcid":"https://orcid.org/0000-0003-0069-9061"},"institutions":[{"id":"https://openalex.org/I4921948","display_name":"Pusan National University","ror":"https://ror.org/01an57a31","country_code":"KR","type":"education","lineage":["https://openalex.org/I4921948"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Hwajeong Seo","raw_affiliation_strings":["Computer engineering, Pusan National University, Pusan 609-735, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer engineering, Pusan National University, Pusan 609-735, Korea","institution_ids":["https://openalex.org/I4921948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100359572","display_name":"Hyunjin Kim","orcid":"https://orcid.org/0000-0003-2461-9935"},"institutions":[{"id":"https://openalex.org/I4921948","display_name":"Pusan National University","ror":"https://ror.org/01an57a31","country_code":"KR","type":"education","lineage":["https://openalex.org/I4921948"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Hyunjin Kim","raw_affiliation_strings":["Computer engineering, Pusan National University, Pusan 609-735, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer engineering, Pusan National University, Pusan 609-735, Korea","institution_ids":["https://openalex.org/I4921948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103166926","display_name":"Taehwan Park","orcid":"https://orcid.org/0000-0002-9982-5859"},"institutions":[{"id":"https://openalex.org/I4921948","display_name":"Pusan National University","ror":"https://ror.org/01an57a31","country_code":"KR","type":"education","lineage":["https://openalex.org/I4921948"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Taehwan Park","raw_affiliation_strings":["Computer engineering, Pusan National University, Pusan 609-735, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer engineering, Pusan National University, Pusan 609-735, Korea","institution_ids":["https://openalex.org/I4921948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037945080","display_name":"Yeoncheol Lee","orcid":null},"institutions":[{"id":"https://openalex.org/I4921948","display_name":"Pusan National University","ror":"https://ror.org/01an57a31","country_code":"KR","type":"education","lineage":["https://openalex.org/I4921948"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Yeoncheol Lee","raw_affiliation_strings":["Computer engineering, Pusan National University, Pusan 609-735, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer engineering, Pusan National University, Pusan 609-735, Korea","institution_ids":["https://openalex.org/I4921948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100462347","display_name":"Zhe Liu","orcid":"https://orcid.org/0000-0001-8578-2635"},"institutions":[{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]}],"countries":["LU"],"is_corresponding":false,"raw_author_name":"Zhe Liu","raw_affiliation_strings":["Laboratory of Algorithmics, Cryptology and Security, University of Luxembourg, 6, Rue Richard Coudenhove-Kalergi, Luxembourg L\u20131359, Luxembourg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Algorithmics, Cryptology and Security, University of Luxembourg, 6, Rue Richard Coudenhove-Kalergi, Luxembourg L\u20131359, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101975138","display_name":"Howon Kim","orcid":"https://orcid.org/0000-0001-8475-7294"},"institutions":[{"id":"https://openalex.org/I4921948","display_name":"Pusan National University","ror":"https://ror.org/01an57a31","country_code":"KR","type":"education","lineage":["https://openalex.org/I4921948"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Howon Kim","raw_affiliation_strings":["Computer engineering, Pusan National University, Pusan 609-735, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer engineering, Pusan National University, Pusan 609-735, Korea","institution_ids":["https://openalex.org/I4921948"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101975138"],"corresponding_institution_ids":["https://openalex.org/I4921948"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2673},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2673},"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.16140899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"13","issue":"7","first_page":"9483","last_page":"9512"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9969000220298767,"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/T11130","display_name":"Coding theory and cryptography","score":0.9962000250816345,"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/scalar-multiplication","display_name":"Scalar multiplication","score":0.8672788739204407},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6739186644554138},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6561179161071777},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.6549326181411743},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.5397177338600159},{"id":"https://openalex.org/keywords/table","display_name":"Table (database)","score":0.47765982151031494},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.44668588042259216},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.43812939524650574},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.4229370355606079},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4124568700790405},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3474847674369812},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3407692313194275},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.31936657428741455},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2929033637046814},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.15374013781547546},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.08868685364723206},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.0766342282295227}],"concepts":[{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.8672788739204407},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6739186644554138},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6561179161071777},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6549326181411743},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.5397177338600159},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.47765982151031494},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.44668588042259216},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.43812939524650574},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.4229370355606079},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4124568700790405},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3474847674369812},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3407692313194275},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.31936657428741455},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2929033637046814},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.15374013781547546},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.08868685364723206},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0766342282295227},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3390/s130709483","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s130709483","pdf_url":null,"source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},{"id":"pmid:23881143","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/23881143","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:ceb922b754ea490c8405e4a84658ea9d","is_oa":true,"landing_page_url":"https://doaj.org/article/ceb922b754ea490c8405e4a84658ea9d","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors, Vol 13, Iss 7, Pp 9483-9512 (2013)","raw_type":"article"},{"id":"pmh:oai:europepmc.org:2755187","is_oa":true,"landing_page_url":"http://europepmc.org/articles/PMC3758659","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:mdpi.com:/1424-8220/13/7/9483/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/s130709483","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors; Volume 13; Issue 7; Pages: 9483-9512","raw_type":"Text"},{"id":"pmh:oai:orbilu.uni.lu:10993/12937","is_oa":true,"landing_page_url":"https://orbilu.uni.lu/handle/10993/12937","pdf_url":null,"source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors. (2013).","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pubmedcentral.nih.gov:3758659","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3758659","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/s130709483","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s130709483","pdf_url":null,"source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W113723871","https://openalex.org/W120075083","https://openalex.org/W195801986","https://openalex.org/W1486898453","https://openalex.org/W1517725369","https://openalex.org/W1575893707","https://openalex.org/W1592482282","https://openalex.org/W1880212920","https://openalex.org/W2003736153","https://openalex.org/W2025361551","https://openalex.org/W2036378739","https://openalex.org/W6604576735"],"related_works":["https://openalex.org/W2946358183","https://openalex.org/W118355721","https://openalex.org/W2070976279","https://openalex.org/W3203056599","https://openalex.org/W1993936776","https://openalex.org/W2343736460","https://openalex.org/W2351744923","https://openalex.org/W2152593841","https://openalex.org/W3201415091","https://openalex.org/W2163763568"],"abstract_inverted_index":{"Elliptic":[0],"curve":[1],"cryptography":[2],"(ECC)":[3],"is":[4,53],"one":[5],"of":[6,14,30,62],"the":[7,28,54,132,159],"most":[8,55],"promising":[9],"public-key":[10],"techniques":[11],"in":[12,58,101,110],"terms":[13],"short":[15],"key":[16],"size":[17,153],"and":[18,67,77,87,151],"various":[19],"crypto":[20],"protocols.":[21],"For":[22],"this":[23,44,93],"reason,":[24],"many":[25],"studies":[26,63],"on":[27,32,49],"implementation":[29],"ECC":[31],"resource-constrained":[33],"devices":[34],"within":[35],"a":[36,72,83,88,97,144,170],"practical":[37,138],"execution":[38],"time":[39],"have":[40,64,81],"been":[41],"conducted.":[42],"To":[43],"end,":[45],"we":[46,95,130,156,167],"must":[47],"focus":[48],"scalar":[50,69,121],"multiplication,":[51,122],"which":[52,102],"expensive":[56],"operation":[57],"ECC.":[59],"A":[60],"number":[61],"proposed":[65],"pre-computation":[66,90,99,127,160],"advanced":[68],"multiplication":[70],"using":[71],"non-adjacent":[73],"form":[74],"(NAF)":[75],"representation,":[76],"more":[78,107],"sophisticated":[79],"approaches":[80],"employed":[82],"width-w":[84],"NAF":[85],"representation":[86],"modified":[89],"table.":[91],"In":[92],"paper,":[94],"propose":[96],"new":[98,145],"method":[100,114,134],"zero":[103],"occurrences":[104],"are":[105],"much":[106],"frequent":[108],"than":[109],"previous":[111,133],"methods.":[112],"This":[113,140],"can":[115,157,168],"be":[116],"applied":[117],"to":[118],"ordinary":[119],"group":[120],"but":[123],"it":[124],"requires":[125],"large":[126],"table,":[128],"so":[129,155],"combined":[131],"with":[135],"ours":[136],"for":[137,162,174],"purposes.":[139,165],"novel":[141],"structure":[142],"establishes":[143],"feature":[146],"that":[147],"adjusts":[148],"speed":[149],"performance":[150],"table":[152,161,173],"finely,":[154],"customize":[158],"our":[163],"own":[164],"Finally,":[166],"establish":[169],"customized":[171],"look-up":[172],"embedded":[175],"microprocessors.":[176]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
