{"id":"https://openalex.org/W1576903769","doi":"https://doi.org/10.1007/978-3-540-28632-5_6","title":"Efficient Linear Array for Multiplication in GF(2 m ) Using a Normal Basis for Elliptic Curve Cryptography","display_name":"Efficient Linear Array for Multiplication in GF(2 m ) Using a Normal Basis for Elliptic Curve Cryptography","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1576903769","doi":"https://doi.org/10.1007/978-3-540-28632-5_6","mag":"1576903769"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-28632-5_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-28632-5_6","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5089566116","display_name":"Soonhak Kwon","orcid":"https://orcid.org/0000-0002-3336-0817"},"institutions":[{"id":"https://openalex.org/I848706","display_name":"Sungkyunkwan University","ror":"https://ror.org/04q78tk20","country_code":"KR","type":"education","lineage":["https://openalex.org/I848706"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Soonhak Kwon","raw_affiliation_strings":["Inst. of Basic Science and Dept. of Mathematics, Sungkyunkwan University, Suwon, Korea","Sungkyunkwan University"],"affiliations":[{"raw_affiliation_string":"Inst. of Basic Science and Dept. of Mathematics, Sungkyunkwan University, Suwon, Korea","institution_ids":["https://openalex.org/I848706"]},{"raw_affiliation_string":"Sungkyunkwan University","institution_ids":["https://openalex.org/I848706"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004924763","display_name":"Kris Gaj","orcid":"https://orcid.org/0000-0002-5050-8748"},"institutions":[{"id":"https://openalex.org/I162714631","display_name":"George Mason University","ror":"https://ror.org/02jqj7156","country_code":"US","type":"education","lineage":["https://openalex.org/I162714631"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kris Gaj","raw_affiliation_strings":["Dept. of Electrical and Computer Engineering, George Mason University, Fairfax, USA","George Mason University"],"affiliations":[{"raw_affiliation_string":"Dept. of Electrical and Computer Engineering, George Mason University, Fairfax, USA","institution_ids":["https://openalex.org/I162714631"]},{"raw_affiliation_string":"George Mason University","institution_ids":["https://openalex.org/I162714631"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100706567","display_name":"Chang\u2010Hoon Kim","orcid":"https://orcid.org/0009-0005-5328-1883"},"institutions":[{"id":"https://openalex.org/I9323808","display_name":"Daegu University","ror":"https://ror.org/01zqccq48","country_code":"KR","type":"education","lineage":["https://openalex.org/I9323808"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Chang Hoon Kim","raw_affiliation_strings":["Dept. of Computer and Information Engineering, Daegu University, Kyungsan, Korea","Daegu University"],"affiliations":[{"raw_affiliation_string":"Dept. of Computer and Information Engineering, Daegu University, Kyungsan, Korea","institution_ids":["https://openalex.org/I9323808"]},{"raw_affiliation_string":"Daegu University","institution_ids":["https://openalex.org/I9323808"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101159970","display_name":"Chun Pyo Hong","orcid":null},"institutions":[{"id":"https://openalex.org/I9323808","display_name":"Daegu University","ror":"https://ror.org/01zqccq48","country_code":"KR","type":"education","lineage":["https://openalex.org/I9323808"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Chun Pyo Hong","raw_affiliation_strings":["Dept. of Computer and Information Engineering, Daegu University, Kyungsan, Korea","Daegu University"],"affiliations":[{"raw_affiliation_string":"Dept. of Computer and Information Engineering, Daegu University, Kyungsan, Korea","institution_ids":["https://openalex.org/I9323808"]},{"raw_affiliation_string":"Daegu University","institution_ids":["https://openalex.org/I9323808"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5089566116"],"corresponding_institution_ids":["https://openalex.org/I848706"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":3.5704,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.93566558,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"76","last_page":"91"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9991000294685364,"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":0.9926999807357788,"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/gf","display_name":"GF(2)","score":0.8046327829360962},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.7844464778900146},{"id":"https://openalex.org/keywords/normal-basis","display_name":"Normal basis","score":0.7121686339378357},{"id":"https://openalex.org/keywords/polynomial-basis","display_name":"Polynomial basis","score":0.6939337253570557},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.6640685796737671},{"id":"https://openalex.org/keywords/nist","display_name":"NIST","score":0.588425874710083},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5465838313102722},{"id":"https://openalex.org/keywords/critical-path-method","display_name":"Critical path method","score":0.5427188873291016},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5388171076774597},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5148517489433289},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.490956574678421},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.48876500129699707},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4672638773918152},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.46265465021133423},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4573577642440796},{"id":"https://openalex.org/keywords/elliptic-curve-point-multiplication","display_name":"Elliptic curve point multiplication","score":0.4147588014602661},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3876749575138092},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3866584897041321},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34030449390411377},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.22687864303588867},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20775195956230164},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.17960461974143982},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14682528376579285},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13562703132629395},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.10755154490470886},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09503769874572754},{"id":"https://openalex.org/keywords/speech-recognition","display_name":"Speech recognition","score":0.08309116959571838}],"concepts":[{"id":"https://openalex.org/C156350748","wikidata":"https://www.wikidata.org/wiki/Q5513324","display_name":"GF(2)","level":3,"score":0.8046327829360962},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.7844464778900146},{"id":"https://openalex.org/C205567592","wikidata":"https://www.wikidata.org/wiki/Q3527199","display_name":"Normal basis","level":3,"score":0.7121686339378357},{"id":"https://openalex.org/C2778406171","wikidata":"https://www.wikidata.org/wiki/Q6901742","display_name":"Polynomial basis","level":2,"score":0.6939337253570557},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.6640685796737671},{"id":"https://openalex.org/C111219384","wikidata":"https://www.wikidata.org/wiki/Q6954384","display_name":"NIST","level":2,"score":0.588425874710083},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5465838313102722},{"id":"https://openalex.org/C115874739","wikidata":"https://www.wikidata.org/wiki/Q825377","display_name":"Critical path method","level":2,"score":0.5427188873291016},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5388171076774597},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5148517489433289},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.490956574678421},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.48876500129699707},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4672638773918152},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.46265465021133423},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4573577642440796},{"id":"https://openalex.org/C117121985","wikidata":"https://www.wikidata.org/wiki/Q78380999","display_name":"Elliptic curve point multiplication","level":3,"score":0.4147588014602661},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3876749575138092},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3866584897041321},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34030449390411377},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.22687864303588867},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20775195956230164},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.17960461974143982},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14682528376579285},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13562703132629395},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.10755154490470886},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09503769874572754},{"id":"https://openalex.org/C28490314","wikidata":"https://www.wikidata.org/wiki/Q189436","display_name":"Speech recognition","level":1,"score":0.08309116959571838},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C201995342","wikidata":"https://www.wikidata.org/wiki/Q682496","display_name":"Systems engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-28632-5_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-28632-5_6","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1515926918","https://openalex.org/W1527059802","https://openalex.org/W1574338402","https://openalex.org/W1894395730","https://openalex.org/W1978030427","https://openalex.org/W1978404551","https://openalex.org/W2049990610","https://openalex.org/W2050533226","https://openalex.org/W2056371549","https://openalex.org/W2084897040","https://openalex.org/W2091899615","https://openalex.org/W2096920618","https://openalex.org/W2114353618","https://openalex.org/W2149916978","https://openalex.org/W2164336166","https://openalex.org/W2167456209","https://openalex.org/W2499339068","https://openalex.org/W2499710379","https://openalex.org/W2914712547","https://openalex.org/W4213415225","https://openalex.org/W4256247563"],"related_works":["https://openalex.org/W4231082137","https://openalex.org/W2002742877","https://openalex.org/W2182826407","https://openalex.org/W3149313810","https://openalex.org/W2587136861","https://openalex.org/W1492702491","https://openalex.org/W1576903769","https://openalex.org/W2363425320","https://openalex.org/W2378104619","https://openalex.org/W2261276023"],"abstract_inverted_index":null,"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
