{"id":"https://openalex.org/W2102308384","doi":"https://doi.org/10.1007/11935230_9","title":"Extending Scalar Multiplication Using Double Bases","display_name":"Extending Scalar Multiplication Using Double Bases","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2102308384","doi":"https://doi.org/10.1007/11935230_9","mag":"2102308384"},"language":"en","primary_location":{"id":"doi:10.1007/11935230_9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/11935230_9","pdf_url":"https://link.springer.com/content/pdf/10.1007/11935230_9.pdf","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":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/11935230_9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111606942","display_name":"Roberto Avanzi","orcid":null},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Roberto Avanzi","raw_affiliation_strings":["Faculty of Mathematics and Horst G\u00f6rtz Institute for IT Security, Ruhr-University Bochum, Germany","Faculty of Mathematics and Horst G\u00f6rtz Institute for IT Security, Ruhr-University, Bochum, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Horst G\u00f6rtz Institute for IT Security, Ruhr-University Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]},{"raw_affiliation_string":"Faculty of Mathematics and Horst G\u00f6rtz Institute for IT Security, Ruhr-University, Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037298442","display_name":"Vassil S. Dimitrov","orcid":null},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Vassil Dimitrov","raw_affiliation_strings":["Advanced Technology Information Processing Systems laboratory, Centre for Informations Security and Cryptography, University of Calgary, Canada","Advanced Technology Information Processing Systems laboratory, Centre for Informations Security and Cryptography, University of Calgary, Canada#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Advanced Technology Information Processing Systems laboratory, Centre for Informations Security and Cryptography, University of Calgary, Canada","institution_ids":["https://openalex.org/I168635309"]},{"raw_affiliation_string":"Advanced Technology Information Processing Systems laboratory, Centre for Informations Security and Cryptography, University of Calgary, Canada#TAB#","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008443234","display_name":"Christophe Doche","orcid":null},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Christophe Doche","raw_affiliation_strings":["Department of Computing, Macquarie University, North Ryde, NSW 2109, Australia","Dept. of Computing, Macquarie University, North Ryde, Australia#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing, Macquarie University, North Ryde, NSW 2109, Australia","institution_ids":["https://openalex.org/I99043593"]},{"raw_affiliation_string":"Dept. of Computing, Macquarie University, North Ryde, Australia#TAB#","institution_ids":["https://openalex.org/I99043593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065948382","display_name":"Francesco Sica","orcid":"https://orcid.org/0000-0002-6027-2548"},"institutions":[{"id":"https://openalex.org/I163902620","display_name":"Mount Allison University","ror":"https://ror.org/03grc6f14","country_code":"CA","type":"education","lineage":["https://openalex.org/I163902620"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Francesco Sica","raw_affiliation_strings":["Department of Mathematics and Computer Science \u2013 Acecrypt, Mount Allison University, Sackville, Canada","Department of Mathematics and Computer Science \u2013 Acecrypt, Mount Allison University, Sackville, Canada#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science \u2013 Acecrypt, Mount Allison University, Sackville, Canada","institution_ids":["https://openalex.org/I163902620"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science \u2013 Acecrypt, Mount Allison University, Sackville, Canada#TAB#","institution_ids":["https://openalex.org/I163902620"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":6.5927,"has_fulltext":true,"cited_by_count":45,"citation_normalized_percentile":{"value":0.97539543,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"130","last_page":"144"},"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":0.986299991607666,"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":0.9661999940872192,"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":0.9397907257080078},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.6722016334533691},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.6472328901290894},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.547601580619812},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5414519309997559},{"id":"https://openalex.org/keywords/supersingular-elliptic-curve","display_name":"Supersingular elliptic curve","score":0.5199404954910278},{"id":"https://openalex.org/keywords/elliptic-curve-point-multiplication","display_name":"Elliptic curve point multiplication","score":0.5054464340209961},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.4998469352722168},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4715835154056549},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47011199593544006},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.46253421902656555},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.424618661403656},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28335264325141907},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21795719861984253},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14030343294143677},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13913661241531372},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.11779654026031494},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.05935928225517273}],"concepts":[{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.9397907257080078},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6722016334533691},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6472328901290894},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.547601580619812},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5414519309997559},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.5199404954910278},{"id":"https://openalex.org/C117121985","wikidata":"https://www.wikidata.org/wiki/Q78380999","display_name":"Elliptic curve point multiplication","level":3,"score":0.5054464340209961},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.4998469352722168},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4715835154056549},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47011199593544006},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.46253421902656555},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.424618661403656},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28335264325141907},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21795719861984253},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14030343294143677},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13913661241531372},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.11779654026031494},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.05935928225517273},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/11935230_9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/11935230_9","pdf_url":"https://link.springer.com/content/pdf/10.1007/11935230_9.pdf","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":{"id":"doi:10.1007/11935230_9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/11935230_9","pdf_url":"https://link.springer.com/content/pdf/10.1007/11935230_9.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2102308384.pdf","grobid_xml":"https://content.openalex.org/works/W2102308384.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1211098324","https://openalex.org/W1487297807","https://openalex.org/W1487915764","https://openalex.org/W1500494440","https://openalex.org/W1507106163","https://openalex.org/W1564047975","https://openalex.org/W1572782736","https://openalex.org/W1579743517","https://openalex.org/W1587889588","https://openalex.org/W1592482282","https://openalex.org/W1632631493","https://openalex.org/W1637905077","https://openalex.org/W1808634574","https://openalex.org/W1872826169","https://openalex.org/W1957825227","https://openalex.org/W2042037294","https://openalex.org/W2098240387","https://openalex.org/W2115190247","https://openalex.org/W2121371977","https://openalex.org/W2128718974","https://openalex.org/W2161531038","https://openalex.org/W2162316726","https://openalex.org/W2394496775","https://openalex.org/W2402957761","https://openalex.org/W4230265636","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3203056599","https://openalex.org/W3201415091","https://openalex.org/W2946358183","https://openalex.org/W2356198393","https://openalex.org/W2416836265","https://openalex.org/W2099732842","https://openalex.org/W2388837654","https://openalex.org/W1521649858","https://openalex.org/W2182900437","https://openalex.org/W2951901236"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
