{"id":"https://openalex.org/W3037182681","doi":"https://doi.org/10.1155/2020/4087873","title":"Parallel and Regular Algorithm of Elliptic Curve Scalar Multiplication over Binary Fields","display_name":"Parallel and Regular Algorithm of Elliptic Curve Scalar Multiplication over Binary Fields","publication_year":2020,"publication_date":"2020-06-24","ids":{"openalex":"https://openalex.org/W3037182681","doi":"https://doi.org/10.1155/2020/4087873","mag":"3037182681"},"language":"en","primary_location":{"id":"doi:10.1155/2020/4087873","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/4087873","pdf_url":"https://downloads.hindawi.com/journals/scn/2020/4087873.pdf","source":{"id":"https://openalex.org/S120683614","display_name":"Security and Communication Networks","issn_l":"1939-0114","issn":["1939-0114","1939-0122"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Security and Communication Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/scn/2020/4087873.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101531470","display_name":"Xingran Li","orcid":"https://orcid.org/0000-0002-2057-8737"},"institutions":[{"id":"https://openalex.org/I4210126530","display_name":"Data Assurance and Communication Security","ror":"https://ror.org/02z2gfm30","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210126530","https://openalex.org/I4210156404"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xingran Li","raw_affiliation_strings":["Data Assurances and Communications Security, Institute of Information Engineering, CAS, Beijing 100093, China","School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China","State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China"],"affiliations":[{"raw_affiliation_string":"Data Assurances and Communications Security, Institute of Information Engineering, CAS, Beijing 100093, China","institution_ids":["https://openalex.org/I4210126530","https://openalex.org/I4210156404"]},{"raw_affiliation_string":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China","institution_ids":["https://openalex.org/I4210156404"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035232919","display_name":"Wei Yu","orcid":"https://orcid.org/0000-0002-9015-9351"},"institutions":[{"id":"https://openalex.org/I4210126530","display_name":"Data Assurance and Communication Security","ror":"https://ror.org/02z2gfm30","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210126530","https://openalex.org/I4210156404"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wei Yu","raw_affiliation_strings":["Data Assurances and Communications Security, Institute of Information Engineering, CAS, Beijing 100093, China","State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China"],"affiliations":[{"raw_affiliation_string":"Data Assurances and Communications Security, Institute of Information Engineering, CAS, Beijing 100093, China","institution_ids":["https://openalex.org/I4210126530","https://openalex.org/I4210156404"]},{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China","institution_ids":["https://openalex.org/I4210156404"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101525541","display_name":"Bao Li","orcid":null},"institutions":[{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bao Li","raw_affiliation_strings":["School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China","State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China"],"affiliations":[{"raw_affiliation_string":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China","institution_ids":["https://openalex.org/I4210156404"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035232919"],"corresponding_institution_ids":["https://openalex.org/I4210126530","https://openalex.org/I4210156404"],"apc_list":{"value":2100,"currency":"USD","value_usd":2100},"apc_paid":{"value":2100,"currency":"USD","value_usd":2100},"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.09663114,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998000264167786,"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":0.9998000264167786,"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":0.972100019454956,"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":0.9678999781608582,"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/computer-science","display_name":"Computer science","score":0.7588036060333252},{"id":"https://openalex.org/keywords/scalar-multiplication","display_name":"Scalar multiplication","score":0.7583144903182983},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7311937808990479},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5532962083816528},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.5521140694618225},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4717462956905365},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.43394166231155396},{"id":"https://openalex.org/keywords/side-channel-attack","display_name":"Side channel attack","score":0.4336954653263092},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4217588007450104},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2782941460609436},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21239995956420898},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.20273283123970032},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.12472003698348999},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08258891105651855}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7588036060333252},{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.7583144903182983},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7311937808990479},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5532962083816528},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.5521140694618225},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4717462956905365},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.43394166231155396},{"id":"https://openalex.org/C49289754","wikidata":"https://www.wikidata.org/wiki/Q2267081","display_name":"Side channel attack","level":3,"score":0.4336954653263092},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4217588007450104},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2782941460609436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21239995956420898},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.20273283123970032},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.12472003698348999},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08258891105651855},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2020/4087873","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/4087873","pdf_url":"https://downloads.hindawi.com/journals/scn/2020/4087873.pdf","source":{"id":"https://openalex.org/S120683614","display_name":"Security and Communication Networks","issn_l":"1939-0114","issn":["1939-0114","1939-0122"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Security and Communication Networks","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:dc1a3774468d43b8b7bc51fb41093c97","is_oa":true,"landing_page_url":"https://doaj.org/article/dc1a3774468d43b8b7bc51fb41093c97","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Security and Communication Networks, Vol 2020 (2020)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2020/4087873","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/4087873","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"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":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2020/4087873","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/4087873","pdf_url":"https://downloads.hindawi.com/journals/scn/2020/4087873.pdf","source":{"id":"https://openalex.org/S120683614","display_name":"Security and Communication Networks","issn_l":"1939-0114","issn":["1939-0114","1939-0122"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Security and Communication Networks","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1149538870","display_name":null,"funder_award_id":"U1936209","funder_id":"https://openalex.org/F4320325902","funder_display_name":"Beijing Municipal Science and Technology Commission"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3493642570","display_name":null,"funder_award_id":"61772515","funder_id":"https://openalex.org/F4320325902","funder_display_name":"Beijing Municipal Science and Technology Commission"},{"id":"https://openalex.org/G3678364691","display_name":null,"funder_award_id":"Z191100007119006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3863659765","display_name":null,"funder_award_id":"U1936209","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4057760331","display_name":null,"funder_award_id":"MMJJ20180216","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4696242431","display_name":null,"funder_award_id":"61502487","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4735193301","display_name":null,"funder_award_id":"Z191100007119006","funder_id":"https://openalex.org/F4320325902","funder_display_name":"Beijing Municipal Science and Technology Commission"},{"id":"https://openalex.org/G5166565193","display_name":null,"funder_award_id":"61872442","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5199858852","display_name":null,"funder_award_id":"61502487","funder_id":"https://openalex.org/F4320325902","funder_display_name":"Beijing Municipal Science and Technology Commission"},{"id":"https://openalex.org/G5731743211","display_name":null,"funder_award_id":"61872442","funder_id":"https://openalex.org/F4320325902","funder_display_name":"Beijing Municipal Science and Technology Commission"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6643576938","display_name":null,"funder_award_id":"MMJJ20180216","funder_id":"https://openalex.org/F4320325902","funder_display_name":"Beijing Municipal Science and Technology Commission"},{"id":"https://openalex.org/G7935533444","display_name":null,"funder_award_id":"201802","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8752556728","display_name":null,"funder_award_id":"61772515","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320325902","display_name":"Beijing Municipal Science and Technology Commission","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3037182681.pdf","grobid_xml":"https://content.openalex.org/works/W3037182681.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1964311183","https://openalex.org/W1971605365","https://openalex.org/W1998588091","https://openalex.org/W1999613060","https://openalex.org/W2036378739","https://openalex.org/W2055403242","https://openalex.org/W2085997550","https://openalex.org/W2095423754","https://openalex.org/W2121371977","https://openalex.org/W2144952508"],"related_works":["https://openalex.org/W2946358183","https://openalex.org/W2070976279","https://openalex.org/W2188111145","https://openalex.org/W3203056599","https://openalex.org/W2952185445","https://openalex.org/W2343736460","https://openalex.org/W1993936776","https://openalex.org/W3000187300","https://openalex.org/W2351744923","https://openalex.org/W2102786134"],"abstract_inverted_index":{"Accelerating":[0],"scalar":[1,65],"multiplication":[2],"has":[3],"always":[4],"been":[5,20],"a":[6,56,70,107],"significant":[7],"topic":[8],"when":[9],"people":[10],"talk":[11],"about":[12],"the":[13,99,120],"elliptic":[14],"curve":[15],"cryptosystem.":[16],"Many":[17],"approaches":[18],"have":[19,36],"come":[21],"up":[22,64],"with":[23],"to":[24,43,62,105],"achieve":[25],"this":[26,52],"aim.":[27],"An":[28],"interesting":[29],"perspective":[30],"is":[31,76,126],"that":[32],"computers":[33],"nowadays":[34],"usually":[35],"multicore":[37],"processors":[38],"which":[39,75,112],"could":[40],"be":[41],"used":[42],"do":[44],"cryptographic":[45],"computations":[46],"in":[47],"parallel":[48,58,110],"style.":[49],"Inspired":[50],"by":[51,79],"idea,":[53],"we":[54,68,87,97],"present":[55],"new":[57,71,108],"and":[59,94,102],"efficient":[60,78],"algorithm":[61,111,125],"speed":[63],"multiplication.":[66],"First,":[67],"introduce":[69],"regular":[72,127],"halve-and-add":[73,103],"method":[74],"very":[77],"utilizing":[80],"<mml:math":[81,115],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[82,116],"id=\"M1\"><mml:mi>\u03bb</mml:mi></mml:math>":[83],"projective":[84],"coordinate.":[85],"Then,":[86],"compare":[88],"many":[89],"different":[90],"algorithms":[91],"calculating":[92],"double-and-add":[93,101],"halve-and-add.":[95],"Finally,":[96],"combine":[98],"best":[100],"methods":[104],"get":[106],"faster":[109],"costs":[113],"around":[114],"id=\"M2\"><mml:mn>12.0</mml:mn><mml:mo>%</mml:mo></mml:math>":[117],"less":[118],"than":[119],"previous":[121],"best.":[122],"Furthermore,":[123],"our":[124],"without":[128],"any":[129],"dummy":[130],"operations,":[131],"so":[132],"it":[133],"naturally":[134],"provides":[135],"protection":[136],"against":[137],"simple":[138],"side-channel":[139],"attacks.":[140]},"counts_by_year":[{"year":2024,"cited_by_count":3}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}