{"id":"https://openalex.org/W1549217965","doi":"https://doi.org/10.1007/978-3-540-73074-3_6","title":"Efficient Multiplication Using Type 2 Optimal Normal Bases","display_name":"Efficient Multiplication Using Type 2 Optimal Normal Bases","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1549217965","doi":"https://doi.org/10.1007/978-3-540-73074-3_6","mag":"1549217965"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-73074-3_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-73074-3_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":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/112310","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111464444","display_name":"Joachim von zur Gathen","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Joachim von zur Gathen","raw_affiliation_strings":["B-IT, Dahlmannstr. 2, Universit\u00e4t Bonn, 53113 Bonn, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"B-IT, Dahlmannstr. 2, Universit\u00e4t Bonn, 53113 Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058641647","display_name":"Amin Shokrollahi","orcid":"https://orcid.org/0000-0001-7938-7022"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Amin Shokrollahi","raw_affiliation_strings":["ALGO, Station 14, Batiment BC, EPFL, 1015 Lausanne, Switzerland","ALGO, Station 14, Batiment BC, EPFL, 1015 Lausanne, Switzerland#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ALGO, Station 14, Batiment BC, EPFL, 1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"ALGO, Station 14, Batiment BC, EPFL, 1015 Lausanne, Switzerland#TAB#","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060801650","display_name":"Jamshid Shokrollahi","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":"Jamshid Shokrollahi","raw_affiliation_strings":["B-IT, Dahlmannstr. 2, Universit\u00e4t Bonn, 53113 Bonn, Germany, current address: System Security Group, Ruhr-Universit\u00e4t Bochum, D-44780 Bochum, Germany","B-IT, Dahlmannstr. 2, Universit\u00e4t Bonn, 53113 Bonn, Germany, current address: System Security Group, Ruhr-Universit\u00e4t Bochum, D-44780 Bochum, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"B-IT, Dahlmannstr. 2, Universit\u00e4t Bonn, 53113 Bonn, Germany, current address: System Security Group, Ruhr-Universit\u00e4t Bochum, D-44780 Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]},{"raw_affiliation_string":"B-IT, Dahlmannstr. 2, Universit\u00e4t Bonn, 53113 Bonn, Germany, current address: System Security Group, Ruhr-Universit\u00e4t Bochum, D-44780 Bochum, Germany#TAB#","institution_ids":["https://openalex.org/I904495901"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.534,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.82615909,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"55","last_page":"68"},"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":0.9983000159263611,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.6894263029098511},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6463363766670227},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.6310064792633057},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6260517835617065},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5683987140655518},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.5203613638877869},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5002713203430176},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4941141903400421},{"id":"https://openalex.org/keywords/normal-basis","display_name":"Normal basis","score":0.4849093556404114},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4667781889438629},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.46042466163635254},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4566797614097595},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.453829824924469},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43688011169433594},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41501739621162415},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16625472903251648},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07893550395965576}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6894263029098511},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6463363766670227},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.6310064792633057},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6260517835617065},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5683987140655518},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.5203613638877869},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5002713203430176},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4941141903400421},{"id":"https://openalex.org/C205567592","wikidata":"https://www.wikidata.org/wiki/Q3527199","display_name":"Normal basis","level":3,"score":0.4849093556404114},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4667781889438629},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.46042466163635254},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4566797614097595},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.453829824924469},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43688011169433594},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41501739621162415},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16625472903251648},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07893550395965576},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-540-73074-3_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-73074-3_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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.83.6332","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.6332","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://infoscience.epfl.ch/record/112310/files/WaiFi-Final.pdf","raw_type":"text"},{"id":"pmh:oai:infoscience.epfl.ch:112310","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/112310","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5124864","host_organization_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","host_organization_lineage":["https://openalex.org/I5124864"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:112310","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/112310","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5124864","host_organization_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","host_organization_lineage":["https://openalex.org/I5124864"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W162262572","https://openalex.org/W1211536449","https://openalex.org/W1490613968","https://openalex.org/W1511374591","https://openalex.org/W1566706564","https://openalex.org/W1894395730","https://openalex.org/W1950989567","https://openalex.org/W1969341770","https://openalex.org/W1977355730","https://openalex.org/W2041320071","https://openalex.org/W2044416721","https://openalex.org/W2054020579","https://openalex.org/W2096920618","https://openalex.org/W2114353618","https://openalex.org/W2134572726","https://openalex.org/W2150637835","https://openalex.org/W2154419929","https://openalex.org/W2238466295","https://openalex.org/W2397252632","https://openalex.org/W2486224602","https://openalex.org/W2561675875","https://openalex.org/W2802619170","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3099313426","https://openalex.org/W4287593139","https://openalex.org/W2225983048","https://openalex.org/W752783541","https://openalex.org/W1506547947","https://openalex.org/W4206811032","https://openalex.org/W2995605830","https://openalex.org/W4239424132","https://openalex.org/W2596457687","https://openalex.org/W3212757063"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-13T07:04:57.449891","created_date":"2025-10-10T00:00:00"}
