{"id":"https://openalex.org/W2136830460","doi":"https://doi.org/10.1007/11535218_5","title":"On the Discrete Logarithm Problem on Algebraic Tori","display_name":"On the Discrete Logarithm Problem on Algebraic Tori","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2136830460","doi":"https://doi.org/10.1007/11535218_5","mag":"2136830460"},"language":"en","primary_location":{"id":"doi:10.1007/11535218_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/11535218_5","pdf_url":"https://link.springer.com/content/pdf/10.1007/11535218_5.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/10.1007/11535218_5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081064506","display_name":"Robert Granger","orcid":null},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"R. Granger","raw_affiliation_strings":["Department of Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, United Kingdom","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032574536","display_name":"Fr\u00e9derik Vercauteren","orcid":"https://orcid.org/0000-0002-7208-9599"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"F. Vercauteren","raw_affiliation_strings":["Department of Electrical Engineering, University of Leuven, Kasteelpark Arenberg 10, B-3001, Leuven-Heverlee, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Leuven, Kasteelpark Arenberg 10, B-3001, Leuven-Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081064506"],"corresponding_institution_ids":["https://openalex.org/I36234482"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":4.4469,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.95534542,"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":"66","last_page":"85"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9995999932289124,"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":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.9019721746444702},{"id":"https://openalex.org/keywords/cryptosystem","display_name":"Cryptosystem","score":0.6819820404052734},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.640186071395874},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6239386796951294},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6208642721176147},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6188564300537109},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4925537705421448},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.4818759858608246},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4527058005332947},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38344132900238037},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2916816473007202},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23890912532806396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22345203161239624},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1649336814880371},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.15699973702430725},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.06672567129135132},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0623852014541626}],"concepts":[{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.9019721746444702},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.6819820404052734},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.640186071395874},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6239386796951294},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6208642721176147},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6188564300537109},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4925537705421448},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.4818759858608246},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4527058005332947},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38344132900238037},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2916816473007202},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23890912532806396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22345203161239624},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1649336814880371},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.15699973702430725},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.06672567129135132},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0623852014541626},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":10,"locations":[{"id":"doi:10.1007/11535218_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/11535218_5","pdf_url":"https://link.springer.com/content/pdf/10.1007/11535218_5.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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.133.4546","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.133.4546","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://homes.esat.kuleuven.be/~fvercaut/papers/crypto2005.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.416.6248","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.416.6248","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.iacr.org/cryptodb/archive/2005/CRYPTO/1374/1374.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.88.3334","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.88.3334","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://homes.esat.kuleuven.be/~fvercaut/dlog/crypto2005.pdf","raw_type":"text"},{"id":"pmh:oai:epubs.surrey.ac.uk:850410","is_oa":false,"landing_page_url":"http://epubs.surrey.ac.uk/850410/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400680","display_name":"Surrey Research Insight Open Access (The University of Surrey)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28290843","host_organization_name":"University of Surrey","host_organization_lineage":["https://openalex.org/I28290843"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Item"},{"id":"pmh:oai:infoscience.epfl.ch:215173","is_oa":false,"landing_page_url":"http://infoscience.epfl.ch/record/215173","pdf_url":null,"source":{"id":"https://openalex.org/S4306400488","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},{"id":"pmh:oai:infoscience.tind.io:215130","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/215130","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":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"conference proceedings"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/70726","is_oa":false,"landing_page_url":"https://lirias.kuleuven.be/bitstream/123456789/70726/1/article-625.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Lecture Notes in Computer Science, vol. 3621, (66-85)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/78f6f058-522f-43c2-a5ea-092b86850415","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/78f6f058-522f-43c2-a5ea-092b86850415","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Granger, R & Vercauteren, F R G 2005, On the Discrete Logarithm Problem on Algebraic Tori. in Advances in Cryptology - CRYPTO 2005. vol. 3621, Lecture Notes in Computer Science, Springer Berlin Heidelberg, pp. 66 - 85. < http://www.cs.bris.ac.uk/Publications/pub_info.jsp?id=2000247 >","raw_type":"contributionToPeriodical"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/78f6f058-522f-43c2-a5ea-092b86850415","is_oa":false,"landing_page_url":"https://research-information.bristol.ac.uk/en/publications/on-the-discrete-logarithm-problem-on-algebraic-tori(78f6f058-522f-43c2-a5ea-092b86850415).html","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Granger, R & Vercauteren, F R G 2005, On the Discrete Logarithm Problem on Algebraic Tori. in Advances in Cryptology - CRYPTO 2005. vol. 3621, Lecture Notes in Computer Science, Springer Berlin Heidelberg, pp. 66 - 85. < http://www.cs.bris.ac.uk/Publications/pub_info.jsp?id=2000247 >","raw_type":"contributionToPeriodical"}],"best_oa_location":{"id":"doi:10.1007/11535218_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/11535218_5","pdf_url":"https://link.springer.com/content/pdf/10.1007/11535218_5.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/W2136830460.pdf","grobid_xml":"https://content.openalex.org/works/W2136830460.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W254314359","https://openalex.org/W1490994218","https://openalex.org/W1502078890","https://openalex.org/W1507575253","https://openalex.org/W1511374591","https://openalex.org/W1527059802","https://openalex.org/W1532875186","https://openalex.org/W1534388293","https://openalex.org/W1534901184","https://openalex.org/W1544893529","https://openalex.org/W1548095416","https://openalex.org/W1571393139","https://openalex.org/W1575538702","https://openalex.org/W1583105647","https://openalex.org/W1597678101","https://openalex.org/W1597998262","https://openalex.org/W1660562555","https://openalex.org/W1887700307","https://openalex.org/W1917151705","https://openalex.org/W1921672120","https://openalex.org/W1977069128","https://openalex.org/W2018615018","https://openalex.org/W2038345254","https://openalex.org/W2055909024","https://openalex.org/W2095708839","https://openalex.org/W2105154875","https://openalex.org/W2108834246","https://openalex.org/W2128687423","https://openalex.org/W2144048023","https://openalex.org/W2156186849","https://openalex.org/W2160886236","https://openalex.org/W2162593813","https://openalex.org/W2477011922","https://openalex.org/W2480001466","https://openalex.org/W2480510614","https://openalex.org/W2484860292","https://openalex.org/W2486408843","https://openalex.org/W2490262601","https://openalex.org/W2624923838","https://openalex.org/W3035112273","https://openalex.org/W4285719527","https://openalex.org/W4289127653"],"related_works":["https://openalex.org/W1555245969","https://openalex.org/W27999159","https://openalex.org/W2321282558","https://openalex.org/W1999127230","https://openalex.org/W2299507895","https://openalex.org/W1900540279","https://openalex.org/W2944491272","https://openalex.org/W18328579","https://openalex.org/W2018555057","https://openalex.org/W2154571469"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}