{"id":"https://openalex.org/W166560619","doi":"https://doi.org/10.1007/978-3-540-76900-2_26","title":"Black-Box Extension Fields and the Inexistence of Field-Homomorphic One-Way Permutations","display_name":"Black-Box Extension Fields and the Inexistence of Field-Homomorphic One-Way Permutations","publication_year":2007,"publication_date":"2007-11-04","ids":{"openalex":"https://openalex.org/W166560619","doi":"https://doi.org/10.1007/978-3-540-76900-2_26","mag":"166560619"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-76900-2_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-76900-2_26","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-76900-2_26.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/10.1007/978-3-540-76900-2_26.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064085132","display_name":"Ueli Maurer","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Ueli Maurer","raw_affiliation_strings":["ETH Zurich, Department of Computer Science, CH-8092 Zurich, Switzerland","ETH Zurich, Department of Computer Science, Zurich, Switzerland;"],"affiliations":[{"raw_affiliation_string":"ETH Zurich, Department of Computer Science, CH-8092 Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"ETH Zurich, Department of Computer Science, Zurich, Switzerland;","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058570984","display_name":"Dominik Raub","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Dominik Raub","raw_affiliation_strings":["ETH Zurich, Department of Computer Science, CH-8092 Zurich, Switzerland","ETH Zurich, Department of Computer Science, Zurich, Switzerland;"],"affiliations":[{"raw_affiliation_string":"ETH Zurich, Department of Computer Science, CH-8092 Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"ETH Zurich, Department of Computer Science, Zurich, Switzerland;","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064085132"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.374,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.8207577,"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":"427","last_page":"443"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9987999796867371,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.637509822845459},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5683853626251221},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5665813684463501},{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.5248510837554932},{"id":"https://openalex.org/keywords/black-box","display_name":"Black box","score":0.5191799402236938},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.48027896881103516},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.46691420674324036},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.45678433775901794},{"id":"https://openalex.org/keywords/algebraically-closed-field","display_name":"Algebraically closed field","score":0.45090004801750183},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43644797801971436},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.42479225993156433},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4144347608089447},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39597007632255554},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3305826485157013},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2509627938270569},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1973111927509308},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.17174819111824036},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.11824741959571838},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09796783328056335}],"concepts":[{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.637509822845459},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5683853626251221},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5665813684463501},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.5248510837554932},{"id":"https://openalex.org/C94966114","wikidata":"https://www.wikidata.org/wiki/Q29256","display_name":"Black box","level":2,"score":0.5191799402236938},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.48027896881103516},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.46691420674324036},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.45678433775901794},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.45090004801750183},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43644797801971436},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.42479225993156433},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4144347608089447},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39597007632255554},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3305826485157013},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2509627938270569},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1973111927509308},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.17174819111824036},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.11824741959571838},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09796783328056335},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-76900-2_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-76900-2_26","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-76900-2_26.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:10.1007/978-3-540-76900-2_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-76900-2_26","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-76900-2_26.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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W166560619.pdf","grobid_xml":"https://content.openalex.org/works/W166560619.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W171553832","https://openalex.org/W1490394993","https://openalex.org/W1491251281","https://openalex.org/W1497795032","https://openalex.org/W1507575253","https://openalex.org/W1793111075","https://openalex.org/W1963716248","https://openalex.org/W1978872857","https://openalex.org/W1980351200","https://openalex.org/W1983236952","https://openalex.org/W2000103501","https://openalex.org/W2051803699","https://openalex.org/W2117060314","https://openalex.org/W2137180374","https://openalex.org/W2156186849","https://openalex.org/W2164988972","https://openalex.org/W2612543848","https://openalex.org/W2613956024","https://openalex.org/W4206441762","https://openalex.org/W4214951289"],"related_works":["https://openalex.org/W2990042598","https://openalex.org/W3191608549","https://openalex.org/W2074052495","https://openalex.org/W2376336218","https://openalex.org/W2539930818","https://openalex.org/W2361715264","https://openalex.org/W2003007890","https://openalex.org/W4380343522","https://openalex.org/W4393118461","https://openalex.org/W2951293591"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
