{"id":"https://openalex.org/W2037158836","doi":"https://doi.org/10.1007/bf01810847","title":"A short proof for explicit formulas for discrete logarithms in finite fields","display_name":"A short proof for explicit formulas for discrete logarithms in finite fields","publication_year":1990,"publication_date":"1990-03-01","ids":{"openalex":"https://openalex.org/W2037158836","doi":"https://doi.org/10.1007/bf01810847","mag":"2037158836"},"language":"en","primary_location":{"id":"doi:10.1007/bf01810847","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01810847","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"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":"Applicable Algebra in Engineering, Communication and 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/A5086124758","display_name":"Harald Niederreiter","orcid":"https://orcid.org/0000-0001-6224-9969"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"funder","lineage":["https://openalex.org/I138211613"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Harald Niederreiter","raw_affiliation_strings":["Institute for Information Processing, Austrian Academy of Sciences, Dr.-Ignaz-Seipel-Platz 2, A-1010, Vienna, Austria","Institute for Information Processing, Austrian Academy of Sciences, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Institute for Information Processing, Austrian Academy of Sciences, Dr.-Ignaz-Seipel-Platz 2, A-1010, Vienna, Austria","institution_ids":["https://openalex.org/I138211613"]},{"raw_affiliation_string":"Institute for Information Processing, Austrian Academy of Sciences, Vienna, Austria","institution_ids":["https://openalex.org/I138211613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086124758"],"corresponding_institution_ids":["https://openalex.org/I138211613"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.5437,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.90411392,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"1","issue":"1","first_page":"55","last_page":"57"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9980000257492065,"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":0.9977999925613403,"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/discrete-logarithm","display_name":"Discrete logarithm","score":0.6927390098571777},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6822922229766846},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6470567584037781},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5895266532897949},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.42453640699386597},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.41185590624809265},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3245161175727844},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3240421414375305},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2801986336708069},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2795299291610718},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16289669275283813},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.05244135856628418}],"concepts":[{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.6927390098571777},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6822922229766846},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6470567584037781},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5895266532897949},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.42453640699386597},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41185590624809265},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3245161175727844},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3240421414375305},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2801986336708069},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2795299291610718},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16289669275283813},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.05244135856628418},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"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/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01810847","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01810847","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"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":"Applicable Algebra in Engineering, Communication and 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":9,"referenced_works":["https://openalex.org/W587622775","https://openalex.org/W962054662","https://openalex.org/W1490994218","https://openalex.org/W1569612250","https://openalex.org/W2142247058","https://openalex.org/W2164284862","https://openalex.org/W2165638380","https://openalex.org/W2203317094","https://openalex.org/W3151140615"],"related_works":["https://openalex.org/W2893614166","https://openalex.org/W1597678101","https://openalex.org/W1555245969","https://openalex.org/W1490994218","https://openalex.org/W2321282558","https://openalex.org/W2299507895","https://openalex.org/W1900540279","https://openalex.org/W2117672015","https://openalex.org/W2514478013","https://openalex.org/W4300498183"],"abstract_inverted_index":null,"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}