{"id":"https://openalex.org/W1550022252","doi":"https://doi.org/10.1007/10722028_24","title":"On Exponential Sums and Group Generators for Elliptic Curves over Finite Fields","display_name":"On Exponential Sums and Group Generators for Elliptic Curves over Finite Fields","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1550022252","doi":"https://doi.org/10.1007/10722028_24","mag":"1550022252"},"language":"en","primary_location":{"id":"doi:10.1007/10722028_24","is_oa":false,"landing_page_url":"https://doi.org/10.1007/10722028_24","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/A5067104694","display_name":"David Kohel","orcid":null},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"David R. Kohel","raw_affiliation_strings":["School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030033231","display_name":"Igor E. Shparlinski","orcid":"https://orcid.org/0000-0002-5246-9391"},"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":"Igor E. Shparlinski","raw_affiliation_strings":["Department of Computing, Macquarie University, NSW 2109, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Computing, Macquarie University, NSW 2109, Australia","institution_ids":["https://openalex.org/I99043593"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5067104694"],"corresponding_institution_ids":["https://openalex.org/I129604602"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":4.1668,"has_fulltext":false,"cited_by_count":69,"citation_normalized_percentile":{"value":0.93850416,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"395","last_page":"404"},"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":0.98089998960495,"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":0.9624999761581421,"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/group","display_name":"Group (periodic table)","score":0.636246919631958},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6353081464767456},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.6333084106445312},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.5771625638008118},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5456053614616394},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5454069972038269},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5370093584060669},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5353608131408691},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.47742757201194763},{"id":"https://openalex.org/keywords/supersingular-elliptic-curve","display_name":"Supersingular elliptic curve","score":0.46329984068870544},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.44725823402404785},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38101375102996826},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33285170793533325},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2588039040565491},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15766781568527222},{"id":"https://openalex.org/keywords/quarter-period","display_name":"Quarter period","score":0.14744305610656738},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06955811381340027}],"concepts":[{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.636246919631958},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6353081464767456},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6333084106445312},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.5771625638008118},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5456053614616394},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5454069972038269},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5370093584060669},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5353608131408691},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.47742757201194763},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.46329984068870544},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.44725823402404785},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38101375102996826},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33285170793533325},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2588039040565491},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15766781568527222},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.14744305610656738},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06955811381340027},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/10722028_24","is_oa":false,"landing_page_url":"https://doi.org/10.1007/10722028_24","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:10.1.1.33.3295","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.3295","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.usyd.edu.au:8000/u/kohel/documents/character.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1486898453","https://openalex.org/W1493424669","https://openalex.org/W1496801598","https://openalex.org/W1507575253","https://openalex.org/W1545473754","https://openalex.org/W1558428627","https://openalex.org/W1561602969","https://openalex.org/W1989233798","https://openalex.org/W2034013822","https://openalex.org/W2075252632","https://openalex.org/W2085595018","https://openalex.org/W2087244305","https://openalex.org/W2111310412","https://openalex.org/W2128718974","https://openalex.org/W2146323046","https://openalex.org/W2168586761","https://openalex.org/W2334612034","https://openalex.org/W2495990585","https://openalex.org/W2501812802","https://openalex.org/W2613956024","https://openalex.org/W4239280186","https://openalex.org/W4247842726","https://openalex.org/W4292027090"],"related_works":["https://openalex.org/W3120152545","https://openalex.org/W74147110","https://openalex.org/W3151023420","https://openalex.org/W3008392579","https://openalex.org/W3128379716","https://openalex.org/W4237299327","https://openalex.org/W3130922687","https://openalex.org/W3103916766","https://openalex.org/W2111109162","https://openalex.org/W2086709251"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}