{"id":"https://openalex.org/W1979595178","doi":"https://doi.org/10.1007/s00607-009-0032-0","title":"Discrete logarithms for finite groups","display_name":"Discrete logarithms for finite groups","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W1979595178","doi":"https://doi.org/10.1007/s00607-009-0032-0","mag":"1979595178"},"language":"en","primary_location":{"id":"doi:10.1007/s00607-009-0032-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00607-009-0032-0","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing","raw_type":"journal-article"},"type":"article","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/A5066959828","display_name":"Lee Klingler","orcid":null},"institutions":[{"id":"https://openalex.org/I63772739","display_name":"Florida Atlantic University","ror":"https://ror.org/05p8w6387","country_code":"US","type":"education","lineage":["https://openalex.org/I63772739"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Lee C. Klingler","raw_affiliation_strings":["Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL, 33431, USA","Florida Atlantic University, Department of Mathematical Sciences, 777, Glades Road, 33431, Boca Raton, FL, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL, 33431, USA","institution_ids":["https://openalex.org/I63772739"]},{"raw_affiliation_string":"Florida Atlantic University, Department of Mathematical Sciences, 777, Glades Road, 33431, Boca Raton, FL, USA#TAB#","institution_ids":["https://openalex.org/I63772739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044624369","display_name":"Spyros S. Magliveras","orcid":null},"institutions":[{"id":"https://openalex.org/I63772739","display_name":"Florida Atlantic University","ror":"https://ror.org/05p8w6387","country_code":"US","type":"education","lineage":["https://openalex.org/I63772739"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Spyros S. Magliveras","raw_affiliation_strings":["Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL, 33431, USA","Florida Atlantic University, Department of Mathematical Sciences, 777, Glades Road, 33431, Boca Raton, FL, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL, 33431, USA","institution_ids":["https://openalex.org/I63772739"]},{"raw_affiliation_string":"Florida Atlantic University, Department of Mathematical Sciences, 777, Glades Road, 33431, Boca Raton, FL, USA#TAB#","institution_ids":["https://openalex.org/I63772739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019155790","display_name":"Fred Richman","orcid":null},"institutions":[{"id":"https://openalex.org/I63772739","display_name":"Florida Atlantic University","ror":"https://ror.org/05p8w6387","country_code":"US","type":"education","lineage":["https://openalex.org/I63772739"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fred Richman","raw_affiliation_strings":["Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL, 33431, USA","Florida Atlantic University, Department of Mathematical Sciences, 777, Glades Road, 33431, Boca Raton, FL, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL, 33431, USA","institution_ids":["https://openalex.org/I63772739"]},{"raw_affiliation_string":"Florida Atlantic University, Department of Mathematical Sciences, 777, Glades Road, 33431, Boca Raton, FL, USA#TAB#","institution_ids":["https://openalex.org/I63772739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057503833","display_name":"Michal Sramka","orcid":"https://orcid.org/0000-0001-7303-2765"},"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":"Michal Sramka","raw_affiliation_strings":["Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, Canada","University of Calgary, Department of Computer Science, 2500 University Drive NW, T2N 1N4, Calgary, AB, Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, Canada","institution_ids":["https://openalex.org/I168635309"]},{"raw_affiliation_string":"University of Calgary, Department of Computer Science, 2500 University Drive NW, T2N 1N4, Calgary, AB, Canada#TAB#","institution_ids":["https://openalex.org/I168635309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5066959828"],"corresponding_institution_ids":["https://openalex.org/I63772739"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.9059,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79660833,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"85","issue":"1-2","first_page":"3","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9975000023841858,"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/discrete-logarithm","display_name":"Discrete logarithm","score":0.8717561960220337},{"id":"https://openalex.org/keywords/multiset","display_name":"Multiset","score":0.6930440068244934},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6865442991256714},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6778343915939331},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.6693516969680786},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6326266527175903},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5602077841758728},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5517017841339111},{"id":"https://openalex.org/keywords/cryptographic-primitive","display_name":"Cryptographic primitive","score":0.5350260734558105},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5193011164665222},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.4965246319770813},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4801734983921051},{"id":"https://openalex.org/keywords/cryptographic-protocol","display_name":"Cryptographic protocol","score":0.42289188504219055},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4131196439266205},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3292127251625061},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3286800980567932},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3059844374656677},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20731189846992493},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1524914801120758},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.1327570080757141},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.09856373071670532},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07848203182220459}],"concepts":[{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.8717561960220337},{"id":"https://openalex.org/C2779623528","wikidata":"https://www.wikidata.org/wiki/Q864377","display_name":"Multiset","level":2,"score":0.6930440068244934},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6865442991256714},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6778343915939331},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.6693516969680786},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6326266527175903},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5602077841758728},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5517017841339111},{"id":"https://openalex.org/C15927051","wikidata":"https://www.wikidata.org/wiki/Q246593","display_name":"Cryptographic primitive","level":4,"score":0.5350260734558105},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5193011164665222},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.4965246319770813},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4801734983921051},{"id":"https://openalex.org/C33884865","wikidata":"https://www.wikidata.org/wiki/Q1254335","display_name":"Cryptographic protocol","level":3,"score":0.42289188504219055},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4131196439266205},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3292127251625061},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3286800980567932},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3059844374656677},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20731189846992493},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1524914801120758},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.1327570080757141},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.09856373071670532},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07848203182220459},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00607-009-0032-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00607-009-0032-0","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W101851448","https://openalex.org/W153325774","https://openalex.org/W567605243","https://openalex.org/W1015038838","https://openalex.org/W1494492726","https://openalex.org/W1501988436","https://openalex.org/W1548880861","https://openalex.org/W1563048562","https://openalex.org/W1618261469","https://openalex.org/W1650194627","https://openalex.org/W1821434174","https://openalex.org/W1862676808","https://openalex.org/W1976904648","https://openalex.org/W2004328809","https://openalex.org/W2010181278","https://openalex.org/W2023961800","https://openalex.org/W2057494433","https://openalex.org/W2074594718","https://openalex.org/W2080309018","https://openalex.org/W2087377210","https://openalex.org/W2117859227","https://openalex.org/W2128935257","https://openalex.org/W2134403686","https://openalex.org/W2137147061","https://openalex.org/W2146650795","https://openalex.org/W2148003739","https://openalex.org/W2156186849","https://openalex.org/W2166233328","https://openalex.org/W2169753006","https://openalex.org/W2288645285","https://openalex.org/W2495188964","https://openalex.org/W2953094623","https://openalex.org/W3023478445","https://openalex.org/W3114023788","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W7780975","https://openalex.org/W1541224886","https://openalex.org/W4248835387","https://openalex.org/W2231274371","https://openalex.org/W2068167225","https://openalex.org/W1976270018","https://openalex.org/W1979595178","https://openalex.org/W1973527459","https://openalex.org/W2288645285","https://openalex.org/W2395723072"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}