{"id":"https://openalex.org/W2044843614","doi":"https://doi.org/10.1109/tit.2012.2214203","title":"On the Influence of the Algebraic Degree of $F^{-1}$ on the Algebraic Degree of $G \\circ F$","display_name":"On the Influence of the Algebraic Degree of $F^{-1}$ on the Algebraic Degree of $G \\circ F$","publication_year":2012,"publication_date":"2012-09-15","ids":{"openalex":"https://openalex.org/W2044843614","doi":"https://doi.org/10.1109/tit.2012.2214203","mag":"2044843614"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2214203","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2214203","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00738398","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089459456","display_name":"Christina Boura","orcid":"https://orcid.org/0000-0001-6796-8874"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I204657281","display_name":"Gemalto (Israel)","ror":"https://ror.org/0134cjh35","country_code":"IL","type":"company","lineage":["https://openalex.org/I204657281","https://openalex.org/I4210087377","https://openalex.org/I4210140930"]},{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]}],"countries":["CN","FR","IL"],"is_corresponding":false,"raw_author_name":"Christina Boura","raw_affiliation_strings":["SECRET Project-Team, INRIA Paris-Rocquencourt, Le Chesnay, France","Security, Cryptology and Transmissions","Gemalto [Meudon]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SECRET Project-Team, INRIA Paris-Rocquencourt, Le Chesnay, France","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"Security, Cryptology and Transmissions","institution_ids":["https://openalex.org/I4210132990"]},{"raw_affiliation_string":"Gemalto [Meudon]","institution_ids":["https://openalex.org/I204657281"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050062480","display_name":"Anne Canteaut","orcid":"https://orcid.org/0000-0002-6292-8336"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]}],"countries":["CN","FR"],"is_corresponding":false,"raw_author_name":"Anne Canteaut","raw_affiliation_strings":["SECRET Project-Team, INRIA Paris-Rocquencourt, Le Chesnay, France","Security, Cryptology and Transmissions"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SECRET Project-Team, INRIA Paris-Rocquencourt, Le Chesnay, France","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"Security, Cryptology and Transmissions","institution_ids":["https://openalex.org/I4210132990"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.7497,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.95864374,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"59","issue":"1","first_page":"691","last_page":"702"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9987000226974487,"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/degree","display_name":"Degree (music)","score":0.8326666951179504},{"id":"https://openalex.org/keywords/block-cipher","display_name":"Block cipher","score":0.6623858213424683},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6559625864028931},{"id":"https://openalex.org/keywords/stream-cipher","display_name":"Stream cipher","score":0.5909924507141113},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5811563730239868},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.560693621635437},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5240086317062378},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4963100552558899},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4797859787940979},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.46315446496009827},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1910320222377777}],"concepts":[{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.8326666951179504},{"id":"https://openalex.org/C106544461","wikidata":"https://www.wikidata.org/wiki/Q543151","display_name":"Block cipher","level":3,"score":0.6623858213424683},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6559625864028931},{"id":"https://openalex.org/C92950451","wikidata":"https://www.wikidata.org/wiki/Q864718","display_name":"Stream cipher","level":3,"score":0.5909924507141113},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5811563730239868},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.560693621635437},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5240086317062378},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4963100552558899},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4797859787940979},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.46315446496009827},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1910320222377777},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2012.2214203","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2214203","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00738398v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00738398","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 2013, 59 (1), pp.691-702. &#x27E8;10.1109/TIT.2012.2214203&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00738398v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00738398","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 2013, 59 (1), pp.691-702. &#x27E8;10.1109/TIT.2012.2214203&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1699105","https://openalex.org/W37385681","https://openalex.org/W97949831","https://openalex.org/W107680689","https://openalex.org/W125031485","https://openalex.org/W178840540","https://openalex.org/W198545191","https://openalex.org/W1528065150","https://openalex.org/W1542020576","https://openalex.org/W1559083062","https://openalex.org/W1565237252","https://openalex.org/W1576368798","https://openalex.org/W1582925429","https://openalex.org/W1587687098","https://openalex.org/W1599220669","https://openalex.org/W1601159549","https://openalex.org/W1627303988","https://openalex.org/W1654806544","https://openalex.org/W1758759527","https://openalex.org/W1886859749","https://openalex.org/W1948713329","https://openalex.org/W1984093600","https://openalex.org/W1993791430","https://openalex.org/W2009454758","https://openalex.org/W2027325533","https://openalex.org/W2058946938","https://openalex.org/W2101800793","https://openalex.org/W2136370860","https://openalex.org/W2146453677","https://openalex.org/W2159665206","https://openalex.org/W2160494425","https://openalex.org/W2234576048","https://openalex.org/W2403571297","https://openalex.org/W2913594971","https://openalex.org/W2964102210","https://openalex.org/W4236509984","https://openalex.org/W4242423410","https://openalex.org/W4250295045","https://openalex.org/W6603952376","https://openalex.org/W6604385719","https://openalex.org/W6632521940","https://openalex.org/W6636787054","https://openalex.org/W6636945652","https://openalex.org/W6648553136","https://openalex.org/W6683655721","https://openalex.org/W6689615373","https://openalex.org/W6818108484"],"related_works":["https://openalex.org/W2381843700","https://openalex.org/W2393423895","https://openalex.org/W2133254303","https://openalex.org/W2550683610","https://openalex.org/W2615869418","https://openalex.org/W2379367584","https://openalex.org/W2163846246","https://openalex.org/W2903451324","https://openalex.org/W24612159","https://openalex.org/W2893407266"],"abstract_inverted_index":{"We":[0],"present":[1,95],"a":[2,58,76,103],"study":[3],"on":[4,23],"the":[5,24,28,31,47,51,55,61,108,116,122,126],"algebraic":[6,25,78,91],"degree":[7,21,26,53,105],"of":[8,27,30,54,57,98,107,125],"iterated":[9],"permutations":[10,124],"seen":[11],"as":[12],"multivariate":[13],"polynomials.":[14],"The":[15],"main":[16],"result":[17,37],"shows":[18],"that":[19],"this":[20,99],"depends":[22],"inverse":[29,56],"permutation":[32,59],"which":[33],"is":[34,38,50],"iterated.":[35],"This":[36,63],"also":[39],"extended":[40],"to":[41,102,115,121],"noninjective":[42],"balanced":[43],"vectorial":[44],"functions":[45,128],"where":[46],"relevant":[48],"quantity":[49],"minimal":[52],"expanding":[60],"function.":[62],"property":[64],"has":[65],"consequences":[66],"in":[67],"symmetric":[68],"cryptography":[69],"since":[70],"several":[71],"attacks":[72],"or":[73,90],"distinguishers":[74],"exploit":[75],"low":[77],"degree,":[79],"like":[80],"higher":[81,104],"order":[82],"differential":[83],"attacks,":[84,86],"cube":[85,88],"and":[87,120,130],"testers,":[89],"attacks.":[92],"Here,":[93],"we":[94],"some":[96],"applications":[97],"improved":[100],"bound":[101],"variant":[106],"block":[109,117],"cipher":[110,118],"<i":[111],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[112],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">KN</i>":[113],",":[114],"Rijndael-256":[119],"inner":[123],"hash":[127],"ECHO":[129],"JH.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
