{"id":"https://openalex.org/W2790012533","doi":"https://doi.org/10.1504/ijes.2018.10011708","title":"Fast elliptic curve algorithm using deformed Fibonacci-type series","display_name":"Fast elliptic curve algorithm using deformed Fibonacci-type series","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2790012533","doi":"https://doi.org/10.1504/ijes.2018.10011708","mag":"2790012533"},"language":"en","primary_location":{"id":"doi:10.1504/ijes.2018.10011708","is_oa":false,"landing_page_url":"https://doi.org/10.1504/ijes.2018.10011708","pdf_url":null,"source":{"id":"https://openalex.org/S204369148","display_name":"International Journal of Embedded Systems","issn_l":"1741-1068","issn":["1741-1068","1741-1076"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310317825","host_organization_name":"Inderscience Publishers","host_organization_lineage":["https://openalex.org/P4310317825"],"host_organization_lineage_names":["Inderscience Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Embedded 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/A5049151787","display_name":"Xu An Wang","orcid":"https://orcid.org/0000-0003-2070-4913"},"institutions":[{"id":"https://openalex.org/I4210136859","display_name":"Xi\u2019an University of Posts and Telecommunications","ror":"https://ror.org/04jn0td46","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210136859"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu An Wang","raw_affiliation_strings":["School of Telecommunication and Information Engineering, Xi'an University of Post Telecommunications, Xi'an 710121, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Telecommunication and Information Engineering, Xi'an University of Post Telecommunications, Xi'an 710121, China","institution_ids":["https://openalex.org/I4210136859"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015145199","display_name":"Shuanggen Liu","orcid":"https://orcid.org/0000-0002-8188-2820"},"institutions":[{"id":"https://openalex.org/I4210136859","display_name":"Xi\u2019an University of Posts and Telecommunications","ror":"https://ror.org/04jn0td46","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210136859"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuanggen Liu","raw_affiliation_strings":["Xi'an University of Post Telecommunications, Xi'an 710121, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Xi'an University of Post Telecommunications, Xi'an 710121, China","institution_ids":["https://openalex.org/I4210136859"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102299566","display_name":"Guanglu Qi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210134428","display_name":"Chinese People's Armed Police Force Engineering University","ror":"https://ror.org/031jzbb03","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210134428"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guanglu Qi","raw_affiliation_strings":["Electronics Department, Engineering University of the Armed Police Force, Xi'an 710086, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electronics Department, Engineering University of the Armed Police Force, Xi'an 710086, China","institution_ids":["https://openalex.org/I4210134428"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01851475,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"2","first_page":"104","last_page":"104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9983999729156494,"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":0.9983999729156494,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9406999945640564,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9261999726295471,"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/fibonacci-number","display_name":"Fibonacci number","score":0.8788696527481079},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6328099370002747},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5249954462051392},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5105463266372681},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.508983850479126},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3603123128414154},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2101919949054718},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.08574286103248596}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.8788696527481079},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6328099370002747},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5249954462051392},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5105463266372681},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.508983850479126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3603123128414154},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2101919949054718},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.08574286103248596},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1504/ijes.2018.10011708","is_oa":false,"landing_page_url":"https://doi.org/10.1504/ijes.2018.10011708","pdf_url":null,"source":{"id":"https://openalex.org/S204369148","display_name":"International Journal of Embedded Systems","issn_l":"1741-1068","issn":["1741-1068","1741-1076"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310317825","host_organization_name":"Inderscience Publishers","host_organization_lineage":["https://openalex.org/P4310317825"],"host_organization_lineage_names":["Inderscience Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Embedded Systems","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":0,"referenced_works":[],"related_works":["https://openalex.org/W2920386017","https://openalex.org/W2795454383","https://openalex.org/W4317662907","https://openalex.org/W2557230772","https://openalex.org/W2054041134","https://openalex.org/W3131374234","https://openalex.org/W1965364641","https://openalex.org/W2896847511","https://openalex.org/W2313406248","https://openalex.org/W2357589199"],"abstract_inverted_index":{"The":[0,38],"efficient":[1],"and":[2,14,50,69],"secure":[3],"scalar":[4,82],"multiplication":[5,83],"can":[6],"be":[7,88],"constructed":[8],"by":[9,47,108],"combining":[10],"the":[11,35,76,79,92,97,100,103,110,116,119,125],"addition":[12,31,53,139],"chain":[13,32,54,104,117,127,140],"elliptic":[15,80],"curve.":[16],"In":[17,56],"this":[18,61],"paper,":[19],"we":[20],"propose":[21],"an":[22],"explicit":[23],"algorithm":[24],"which":[25],"is":[26,45,63,105],"a":[27,70],"kind":[28],"of":[29,41,60,78,102,118],"'double-addition'":[30,39,77],"based":[33,74],"on":[34,75],"Fibonacci-type":[36],"sequence.":[37],"sequence":[40],"arbitrary":[42],"integer":[43],"k":[44],"calculated":[46],"using":[48,109],"Fibonacci":[49],"golden":[51],"ratio":[52],"method.":[55],"addition,":[57],"each":[58],"cycle":[59],"method":[62],"fixed":[64],"to":[65,87,90,132,136],"perform":[66],"double":[67,111],"point":[68,71,112],"add":[72],"operations":[73],"curve":[81],"algorithm,":[84],"so":[85],"as":[86],"able":[89],"resist":[91],"simple":[93],"power":[94],"attack.":[95],"At":[96],"same":[98],"time,":[99],"length":[101,128],"greatly":[106],"shortened":[107],"operation":[113],"compared":[114,135],"with":[115],"Fibonacci.":[120],"Experimental":[121],"results":[122],"showed":[123],"that":[124],"average":[126],"has":[129],"attained":[130],"38%":[131],"55%":[133],"reduction":[134],"other":[137],"doubling-free":[138],"methods.":[141]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
