{"id":"https://openalex.org/W2091108121","doi":"https://doi.org/10.1515/jmc-2012-0017","title":"A method for counting the number of polynomial equivalence classes","display_name":"A method for counting the number of polynomial equivalence classes","publication_year":2013,"publication_date":"2013-03-29","ids":{"openalex":"https://openalex.org/W2091108121","doi":"https://doi.org/10.1515/jmc-2012-0017","mag":"2091108121"},"language":"en","primary_location":{"id":"doi:10.1515/jmc-2012-0017","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2012-0017","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2012-0017/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2012-0017/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103281554","display_name":"Tianze Wang","orcid":"https://orcid.org/0000-0003-2717-3596"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tianze Wang","raw_affiliation_strings":["State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100195, P.\u00a0R.\u00a0China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100195, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008820992","display_name":"Dongdai Lin","orcid":"https://orcid.org/0000-0002-3951-7889"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongdai Lin","raw_affiliation_strings":["State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100195, P.\u00a0R.\u00a0China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100195, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103281554"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"],"apc_list":{"value":1000,"currency":"EUR","value_usd":1078},"apc_paid":{"value":1000,"currency":"EUR","value_usd":1078},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13593347,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":"1","first_page":"69","last_page":"95"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.8819000124931335,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.8819000124931335,"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/mathematics","display_name":"Mathematics","score":0.7375945448875427},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.5836891531944275},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5836747884750366},{"id":"https://openalex.org/keywords/cryptosystem","display_name":"Cryptosystem","score":0.5638226866722107},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.5493563413619995},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5236470699310303},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5006835460662842},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.48004114627838135},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.42153042554855347},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3892207145690918},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2659335136413574},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17589735984802246}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7375945448875427},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.5836891531944275},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5836747884750366},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.5638226866722107},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.5493563413619995},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5236470699310303},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5006835460662842},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.48004114627838135},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.42153042554855347},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3892207145690918},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2659335136413574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17589735984802246},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/jmc-2012-0017","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2012-0017","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2012-0017/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:2b6239d5c2b548ba94b3b027e96deca5","is_oa":true,"landing_page_url":"https://doaj.org/article/2b6239d5c2b548ba94b3b027e96deca5","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Mathematical Cryptology, Vol 7, Iss 1, Pp 69-95 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/jmc-2012-0017","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2012-0017","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2012-0017/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4300000071525574,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2091108121.pdf","grobid_xml":"https://content.openalex.org/works/W2091108121.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W206356891","https://openalex.org/W279712484","https://openalex.org/W1492604485","https://openalex.org/W1505418321","https://openalex.org/W1525538022","https://openalex.org/W1539288038","https://openalex.org/W1555224742","https://openalex.org/W1569499052","https://openalex.org/W1584538091","https://openalex.org/W1806793453","https://openalex.org/W1821087317","https://openalex.org/W1823365695","https://openalex.org/W2011039300","https://openalex.org/W2140702311","https://openalex.org/W2150496909","https://openalex.org/W2269124134","https://openalex.org/W2986959318","https://openalex.org/W3029881138","https://openalex.org/W3111297213","https://openalex.org/W6600430606","https://openalex.org/W6639748362"],"related_works":["https://openalex.org/W108845024","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2406961474","https://openalex.org/W2143566611","https://openalex.org/W2013740965","https://openalex.org/W588267724","https://openalex.org/W4297743441","https://openalex.org/W2155753715","https://openalex.org/W1912967923"],"abstract_inverted_index":{"Abstract.":[0],"As":[1],"one":[2],"of":[3,15,33,37,43,54,58,65,83,105,123],"the":[4,23,35,41,52,55,63,81,88,94,102,110,115,120],"most":[5],"fundamental":[6],"problems":[7,48],"in":[8],"multivariate":[9],"public":[10],"key":[11],"cryptosystems":[12],"(MPKC),":[13],"Isomorphism":[14],"Polynomial":[16],"(IP)":[17],"induces":[18],"an":[19,73],"equivalence":[20,38,84,90],"relation":[21,91],"on":[22],"polynomials":[24],"systems.":[25],"The":[26,46],"enumeration":[27],"problem":[28,96],"associated":[29],"to":[30,51,79,87],"IP":[31],"consists":[32],"counting":[34],"number":[36,57,82],"classes":[39,85],"and":[40,62,114],"cardinality":[42],"each":[44],"class.":[45],"two":[47],"correspond":[49],"exactly":[50],"study":[53],"total":[56],"different":[59],"cryptographic":[60],"schemes":[61],"size":[64],"\u201cequivalent":[66],"keys\u201d.":[67],"In":[68],"this":[69,106,124],"paper":[70],"we":[71,118],"give":[72],"algorithm":[74,107,113],"using":[75],"a":[76],"divide-and-conquer":[77],"method":[78],"count":[80],"according":[86],"linear":[89],"induced":[92],"by":[93,100],"IP1S":[95],"when":[97],".":[98],"Then":[99],"giving":[101],"complexity":[103],"gain":[104],"compared":[108],"with":[109],"exhaustive":[111],"search":[112],"experimental":[116],"results,":[117],"show":[119],"high":[121],"efficiency":[122],"new":[125],"algorithm.":[126]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}