{"id":"https://openalex.org/W2771683899","doi":"https://doi.org/10.1109/tc.2017.2775640","title":"Tight Bounds of Differentially and Linearly Active S-Boxes and Division Property of Lilliput","display_name":"Tight Bounds of Differentially and Linearly Active S-Boxes and Division Property of Lilliput","publication_year":2017,"publication_date":"2017-12-04","ids":{"openalex":"https://openalex.org/W2771683899","doi":"https://doi.org/10.1109/tc.2017.2775640","mag":"2771683899"},"language":"en","primary_location":{"id":"doi:10.1109/tc.2017.2775640","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2017.2775640","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"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 Computers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110692616","display_name":"Yu Sasaki","orcid":null},"institutions":[{"id":"https://openalex.org/I2251713219","display_name":"NTT (Japan)","ror":"https://ror.org/00berct97","country_code":"JP","type":"company","lineage":["https://openalex.org/I2251713219"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yu Sasaki","raw_affiliation_strings":["NTT Secure Platform Laboratories, NTT Corporations, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NTT Secure Platform Laboratories, NTT Corporations, Tokyo, Japan","institution_ids":["https://openalex.org/I2251713219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026273868","display_name":"Yosuke Todo","orcid":"https://orcid.org/0000-0002-6839-4777"},"institutions":[{"id":"https://openalex.org/I2251713219","display_name":"NTT (Japan)","ror":"https://ror.org/00berct97","country_code":"JP","type":"company","lineage":["https://openalex.org/I2251713219"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yosuke Todo","raw_affiliation_strings":["NTT Secure Platform Laboratories, NTT Corporations, Tokyo, Japan"],"raw_orcid":"https://orcid.org/0000-0002-6839-4777","affiliations":[{"raw_affiliation_string":"NTT Secure Platform Laboratories, NTT Corporations, Tokyo, Japan","institution_ids":["https://openalex.org/I2251713219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I2251713219"],"apc_list":null,"apc_paid":null,"fwci":0.5981,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.77298416,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"67","issue":"5","first_page":"717","last_page":"732"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9998000264167786,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9998000264167786,"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":0.9886999726295471,"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/T12122","display_name":"Physical Unclonable Functions (PUFs) and Hardware Security","score":0.9836000204086304,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/division","display_name":"Division (mathematics)","score":0.7090175151824951},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6890850067138672},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5636064410209656},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48379963636398315},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38083720207214355},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3731028437614441},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36777815222740173}],"concepts":[{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.7090175151824951},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6890850067138672},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5636064410209656},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48379963636398315},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38083720207214355},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3731028437614441},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36777815222740173},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.2017.2775640","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2017.2775640","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"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 Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.4699999988079071,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W37385681","https://openalex.org/W45372631","https://openalex.org/W131718440","https://openalex.org/W197228877","https://openalex.org/W380217570","https://openalex.org/W1556212265","https://openalex.org/W1587120902","https://openalex.org/W1590392383","https://openalex.org/W1883151075","https://openalex.org/W1978695162","https://openalex.org/W2002460611","https://openalex.org/W2150381116","https://openalex.org/W2166473670","https://openalex.org/W2344782235","https://openalex.org/W2398210819","https://openalex.org/W2413890865","https://openalex.org/W2513242685","https://openalex.org/W2604948401","https://openalex.org/W2766408490","https://openalex.org/W2912272895","https://openalex.org/W3028985826","https://openalex.org/W3196193057","https://openalex.org/W6605393820","https://openalex.org/W6613066373","https://openalex.org/W6635228357","https://openalex.org/W6639475506","https://openalex.org/W6682611894","https://openalex.org/W6705065176","https://openalex.org/W6778756263"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W3086542228","https://openalex.org/W2017331178","https://openalex.org/W2976797620","https://openalex.org/W2031510948","https://openalex.org/W2949149100","https://openalex.org/W2140068691","https://openalex.org/W4236696036","https://openalex.org/W2506252583","https://openalex.org/W4200435726"],"abstract_inverted_index":{"This":[0],"paper":[1],"provides":[2],"security":[3,53,130,152,157],"analysis":[4],"of":[5,32,45,63,66,110,127],"a":[6,43,91,107,171,189],"lightweight":[7],"block":[8],"cipher":[9],"called":[10],"LILLIPUT,":[11],"which":[12,50],"was":[13],"proposed":[14],"in":[15,20],"IEEE":[16],"Transactions":[17],"on":[18,176,195],"Computers":[19],"2015.":[21],"LILLIPUT":[22],"adopts":[23],"an":[24],"extended":[25,187],"generalized":[26],"Feistel":[27],"network":[28],"(EGFN).":[29],"EGFN":[30,148],"consists":[31],"non-linear,":[33],"linear,":[34],"and":[35,38,133],"permutation":[36],"layers,":[37],"the":[39,46,60,64,72,77,124,141,163,177,196],"linear":[40,86,119,134],"layer":[41],"updates":[42],"part":[44],"state":[47],"only":[48],"linearly,":[49],"causes":[51],"several":[52],"concerns.":[54],"Our":[55],"first":[56],"discovery":[57],"is":[58,115,136,140,158,185],"that":[59,100,174,193],"lower":[61],"bounds":[62,79,104],"number":[65,109],"differentially":[67],"active":[68],"S-boxes":[69],"provided":[70],"by":[71,82,96,180,200],"designers":[73,146,164],"are":[74,80],"incorrect.":[75],"Thus":[76],"new":[78],"derived":[81],"using":[83],"mixed":[84],"integer":[85],"programming":[87],"(MILP).":[88],"We":[89],"apply":[90],"two-stage":[92],"search":[93,113],"procedure":[94],"introduced":[95],"Sun":[97],"et":[98],"al.":[99],"leads":[101],"to":[102,149,188],"tight":[103],"even":[105],"for":[106,118],"large":[108],"rounds.":[111,182,202],"The":[112,145,183],"tool":[114],"then":[116],"converted":[117],"cryptanalysis.":[120,144,155],"With":[121],"those":[122],"updates,":[123],"challenging":[125],"problem":[126],"evaluating":[128],"LILLIPUT's":[129],"against":[131,153],"differential":[132],"cryptanalysis":[135],"closed.":[137],"Another":[138],"contribution":[139],"best":[142,198],"third-party":[143],"expected":[147],"efficiently":[150],"enhance":[151],"integral":[154],"However,":[156],"not":[159],"as":[160,162],"enhanced":[161],"expected.":[165],"In":[166],"fact,":[167],"division":[168],"property":[169],"finds":[170],"13-round":[172],"distinguisher":[173,179,184],"improves":[175,194],"previous":[178,197],"4":[181],"further":[186],"17-round":[190],"key":[191],"recovery":[192],"attack":[199],"3":[201]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}