{"id":"https://openalex.org/W4391461981","doi":"https://doi.org/10.13154/tosc.v2019.i1.264-301","title":"General Diffusion Analysis: How to Find Optimal Permutations for Generalized Type-II Feistel Schemes","display_name":"General Diffusion Analysis: How to Find Optimal Permutations for Generalized Type-II Feistel Schemes","publication_year":2019,"publication_date":"2019-03-08","ids":{"openalex":"https://openalex.org/W4391461981","doi":"https://doi.org/10.13154/tosc.v2019.i1.264-301"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-02095007v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02095007","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Transactions on Symmetric Cryptology, 2019, 1, pp.264-301. &#x27E8;10.13154/tosc.v2019.i1.264-301&#x27E9;","raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":["datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doaj.org/article/26e77cc0ac544b9e8bd1e1cac4f13aee","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019977334","display_name":"Victor Cauchois","orcid":null},"institutions":[{"id":"https://openalex.org/I4210161663","display_name":"Institut de recherche math\u00e9matique de Rennes","ror":"https://ror.org/05y76vp22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2800285241","https://openalex.org/I28221208","https://openalex.org/I3124938446","https://openalex.org/I4210117091","https://openalex.org/I4210141950","https://openalex.org/I4210146044","https://openalex.org/I4210161663","https://openalex.org/I4399657933","https://openalex.org/I56067802","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cauchois, Victor","raw_affiliation_strings":["DGA-MI, Bo\u00eete Postale 7, 35998 Rennes Cedex 9; 2 IRMAR, Universit\u00e9 de Rennes 1, Campus de Beaulieu, 35042 Rennes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DGA-MI, Bo\u00eete Postale 7, 35998 Rennes Cedex 9; 2 IRMAR, Universit\u00e9 de Rennes 1, Campus de Beaulieu, 35042 Rennes","institution_ids":["https://openalex.org/I4210161663"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061181916","display_name":"Cl\u00e9ment Gomez","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gomez, Cl\u00e9ment","raw_affiliation_strings":["DGA-MI, Bo\u00eete Postale 7, 35998 Rennes Cedex 9"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DGA-MI, Bo\u00eete Postale 7, 35998 Rennes Cedex 9","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000005233","display_name":"Ga\u00ebl Thomas","orcid":"https://orcid.org/0000-0002-9444-1071"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas, Ga\u00ebl","raw_affiliation_strings":["DGA-MI, Bo\u00eete Postale 7, 35998 Rennes Cedex 9"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DGA-MI, Bo\u00eete Postale 7, 35998 Rennes Cedex 9","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1433,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.60301814,"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":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.7936000227928162,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.7936000227928162,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.7384999990463257,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.7382000088691711,"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/type","display_name":"Type (biology)","score":0.622011661529541},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5552248954772949},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5093554258346558},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.47205454111099243},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.449523389339447},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3377833366394043},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1316213309764862},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.05536738038063049}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.622011661529541},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5552248954772949},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5093554258346558},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.47205454111099243},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.449523389339447},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3377833366394043},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1316213309764862},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.05536738038063049},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:HAL:hal-02095007v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02095007","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Transactions on Symmetric Cryptology, 2019, 1, pp.264-301. &#x27E8;10.13154/tosc.v2019.i1.264-301&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:26e77cc0ac544b9e8bd1e1cac4f13aee","is_oa":true,"landing_page_url":"https://doaj.org/article/26e77cc0ac544b9e8bd1e1cac4f13aee","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Transactions on Symmetric Cryptology, Vol 2019, Iss 1 (2019)","raw_type":"article"},{"id":"doi:10.13154/tosc.v2019.i1.264-301","is_oa":true,"landing_page_url":"https://doi.org/10.13154/tosc.v2019.i1.264-301","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:doaj.org/article:26e77cc0ac544b9e8bd1e1cac4f13aee","is_oa":true,"landing_page_url":"https://doaj.org/article/26e77cc0ac544b9e8bd1e1cac4f13aee","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Transactions on Symmetric Cryptology, Vol 2019, Iss 1 (2019)","raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Type-II":[0],"Generalized":[1,12],"Feistel":[2,13,23],"Schemes":[3],"are":[4,47,99,146,279,290],"one":[5],"of":[6,11,28,57,108,119,143,159,201],"the":[7,35,66,88,104,117,157,199,270],"most":[8],"popular":[9],"versions":[10],"Schemes.":[14],"Their":[15],"round":[16],"function":[17],"consists":[18],"in":[19],"applying":[20],"a":[21,50,70,165,249],"classical":[22],"transformation":[24],"to":[25,84,167,192,208,219,245,252],"p":[26],"sub-blocks":[27],"two":[29,97],"consecutive":[30],"words":[31,39],"and":[32,127,228,236,281],"then":[33],"shifting":[34],"k":[36,180,193,225,233,237,264,284],"=":[37,226,234,238,285],"2p":[38],"cyclically.":[40],"The":[41],"low":[42,51],"implementation":[43,76],"costs":[44],"it":[45],"offers":[46],"balanced":[48],"by":[49,64],"diffusion,":[52],"limiting":[53],"its":[54],"efficiency.":[55],"Diffusion":[56],"such":[58],"structures":[59],"may":[60],"however":[61],"be":[62],"improved":[63],"replacing":[65],"cyclic":[67],"shift":[68],"with":[69,87,164,211],"different":[71],"permutation":[72,223],"without":[73],"any":[74],"additional":[75],"cost.":[77],"In":[78],"this":[79,202],"paper,":[80],"we":[81,102,115,130,204,241,256],"study":[82,103],"ways":[83],"determine":[85],"permutations":[86,109,120,139,189,210,277,289],"fastest":[89],"diffusion":[90,214],"called":[91],"optimal":[92,221,276,288],"permutations.":[93,247,292],"To":[94],"do":[95],"so,":[96],"ideas":[98],"used.":[100],"First,":[101],"natural":[105],"equivalence":[106,161,254],"classes":[107,162,261],"that":[110,136,278],"preserve":[111],"cryptographic":[112],"properties;":[113],"second,":[114],"use":[116,205],"representation":[118],"as":[121],"coloured":[122],"trees.":[123],"For":[124,196],"both":[125],"heuristic":[126,217],"historical":[128],"reasons,":[129],"focus":[131],"first":[132],"on":[133,156,171,187,260],"even-odd":[134,222,280,291],"permutations,":[135],"is,":[137],"those":[138,175],"for":[140,178,224,231,262,283],"which":[141],"images":[142],"even":[144],"numbers":[145],"odd.":[147],"We":[148,173],"derive":[149],"from":[150],"their":[151,160],"structure":[152],"an":[153,220],"upper":[154],"bound":[155],"number":[158],"together":[163],"strategy":[166,251],"perform":[168,257],"exhaustive":[169,176,185,258],"searches":[170,177,186,259],"classes.":[172],"performed":[174],"sizes":[179,197,232,263],"\u2264":[181,194,265],"24,":[182],"while":[183],"previous":[184],"all":[188,246,287],"were":[190],"limited":[191],"16.":[195],"beyond":[198],"reach":[200],"method,":[203],"tree":[206],"representations":[207],"find":[209],"good":[212],"intermediate":[213],"properties.":[215],"This":[216],"leads":[218],"26":[227],"best-known":[229],"results":[230,268],"64":[235],"128.":[239],"Finally,":[240],"transpose":[242],"these":[243],"methods":[244],"Using":[248],"new":[250],"exhaust":[253],"classes,":[255],"20":[266],"whose":[267],"confirmed":[269],"initial":[271],"heuristic:":[272],"there":[273],"always":[274],"exist":[275],"furthermore":[282],"18":[286]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
