{"id":"https://openalex.org/W4415821419","doi":"https://doi.org/10.1109/tit.2025.3627983","title":"Revisit the Propagation of States: New Construction Theory and Search Method for Impossible Differentials and Impossible Polytopic Transitions","display_name":"Revisit the Propagation of States: New Construction Theory and Search Method for Impossible Differentials and Impossible Polytopic Transitions","publication_year":2025,"publication_date":"2025-11-03","ids":{"openalex":"https://openalex.org/W4415821419","doi":"https://doi.org/10.1109/tit.2025.3627983"},"language":null,"primary_location":{"id":"doi:10.1109/tit.2025.3627983","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3627983","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Xichao Hu","orcid":"https://orcid.org/0009-0003-1096-3556"},"institutions":[{"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"],"is_corresponding":false,"raw_author_name":"Xichao Hu","raw_affiliation_strings":["State Key Laboratory of Cryptology, Beijing, China"],"raw_orcid":"https://orcid.org/0009-0003-1096-3556","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Cryptology, Beijing, China","institution_ids":["https://openalex.org/I4210132990"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050440253","display_name":"Lin Jiao","orcid":"https://orcid.org/0000-0001-6394-6619"},"institutions":[{"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"],"is_corresponding":false,"raw_author_name":"Lin Jiao","raw_affiliation_strings":["State Key Laboratory of Cryptology, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-6394-6619","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Cryptology, Beijing, China","institution_ids":["https://openalex.org/I4210132990"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100462231","display_name":"Yongqiang Li","orcid":"https://orcid.org/0000-0002-2551-2737"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","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":"Yongqiang Li","raw_affiliation_strings":["State Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China","Institute of Information Engineering, State Key Laboratory of Cyberspace Security Defense, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-2551-2737","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Information Engineering, State Key Laboratory of Cyberspace Security Defense, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071722719","display_name":"Shizhu Tian","orcid":null},"institutions":[{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shizhu Tian","raw_affiliation_strings":["School of Cyber Science and Technology, Hubei University, Wuhan, China"],"raw_orcid":"https://orcid.org/0009-0002-8994-0455","affiliations":[{"raw_affiliation_string":"School of Cyber Science and Technology, Hubei University, Wuhan, China","institution_ids":["https://openalex.org/I75900474"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086547112","display_name":"Zhengbin Liu","orcid":"https://orcid.org/0000-0001-6638-2708"},"institutions":[{"id":"https://openalex.org/I1302611135","display_name":"Ministry of Public Security of the People's Republic of China","ror":"https://ror.org/00bt9we26","country_code":"CN","type":"government","lineage":["https://openalex.org/I1302611135"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengbin Liu","raw_affiliation_strings":["National Key Laboratory of Security Communication, Chengdu, China","National Key Laboratory of Security Communication, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Security Communication, Chengdu, China","institution_ids":["https://openalex.org/I1302611135"]},{"raw_affiliation_string":"National Key Laboratory of Security Communication, China","institution_ids":["https://openalex.org/I1302611135"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108047865","display_name":"Ming\u2010Sheng Wang","orcid":"https://orcid.org/0000-0002-2400-719X"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","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":"Mingsheng Wang","raw_affiliation_strings":["State Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China","Institute of Information Engineering, State Key Laboratory of Cyberspace Security Defense, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Information Engineering, State Key Laboratory of Cyberspace Security Defense, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101790997","display_name":"Dengguo Feng","orcid":"https://orcid.org/0000-0002-8515-7124"},"institutions":[{"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"],"is_corresponding":false,"raw_author_name":"Dengguo Feng","raw_affiliation_strings":["State Key Laboratory of Cryptology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Cryptology, Beijing, China","institution_ids":["https://openalex.org/I4210132990"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1514599,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"1","first_page":"742","last_page":"764"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9807999730110168,"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":0.9807999730110168,"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":0.008299999870359898,"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"}},{"id":"https://openalex.org/T11424","display_name":"Security and Verification in Computing","score":0.004699999932199717,"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/block-cipher","display_name":"Block cipher","score":0.7389000058174133},{"id":"https://openalex.org/keywords/differential-cryptanalysis","display_name":"Differential cryptanalysis","score":0.632099986076355},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.6098999977111816},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4966000020503998},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.49070000648498535},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4603999853134155},{"id":"https://openalex.org/keywords/linear-cryptanalysis","display_name":"Linear cryptanalysis","score":0.4578000009059906},{"id":"https://openalex.org/keywords/contrast","display_name":"Contrast (vision)","score":0.4129999876022339}],"concepts":[{"id":"https://openalex.org/C106544461","wikidata":"https://www.wikidata.org/wiki/Q543151","display_name":"Block cipher","level":3,"score":0.7389000058174133},{"id":"https://openalex.org/C36123800","wikidata":"https://www.wikidata.org/wiki/Q1224471","display_name":"Differential cryptanalysis","level":4,"score":0.632099986076355},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.6098999977111816},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4966000020503998},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.49070000648498535},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4603999853134155},{"id":"https://openalex.org/C82424418","wikidata":"https://www.wikidata.org/wiki/Q1826463","display_name":"Linear cryptanalysis","level":4,"score":0.4578000009059906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43849998712539673},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42089998722076416},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.4129999876022339},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4104999899864197},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.40880000591278076},{"id":"https://openalex.org/C181149355","wikidata":"https://www.wikidata.org/wiki/Q897511","display_name":"Cryptanalysis","level":3,"score":0.37540000677108765},{"id":"https://openalex.org/C41431624","wikidata":"https://www.wikidata.org/wiki/Q1053357","display_name":"Block size","level":3,"score":0.34610000252723694},{"id":"https://openalex.org/C112145980","wikidata":"https://www.wikidata.org/wiki/Q2569509","display_name":"Key schedule","level":5,"score":0.3418000042438507},{"id":"https://openalex.org/C2780221543","wikidata":"https://www.wikidata.org/wiki/Q4681865","display_name":"Cipher","level":3,"score":0.34040001034736633},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C120488936","wikidata":"https://www.wikidata.org/wiki/Q3005748","display_name":"Impossible differential cryptanalysis","level":5,"score":0.32670000195503235},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32510000467300415},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.303600013256073},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.2759000062942505}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2025.3627983","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3627983","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7538674750","display_name":null,"funder_award_id":"XDB0690200","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8484331881","display_name":null,"funder_award_id":"12371525","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W148161500","https://openalex.org/W149885373","https://openalex.org/W158618165","https://openalex.org/W1500356409","https://openalex.org/W1503864966","https://openalex.org/W1539178658","https://openalex.org/W1540875416","https://openalex.org/W1541703086","https://openalex.org/W1565705707","https://openalex.org/W1572300106","https://openalex.org/W1598147411","https://openalex.org/W1599175145","https://openalex.org/W1629301835","https://openalex.org/W1791039952","https://openalex.org/W1853704432","https://openalex.org/W1894646615","https://openalex.org/W1964723977","https://openalex.org/W2027325533","https://openalex.org/W2072787545","https://openalex.org/W2087928947","https://openalex.org/W2400958143","https://openalex.org/W2538419163","https://openalex.org/W2604948401","https://openalex.org/W2730078344","https://openalex.org/W2741840250","https://openalex.org/W2755060642","https://openalex.org/W2888915893","https://openalex.org/W2912250127","https://openalex.org/W3090879314","https://openalex.org/W3097161896","https://openalex.org/W3097858784","https://openalex.org/W4255288622","https://openalex.org/W4383112429","https://openalex.org/W4392387567","https://openalex.org/W4399805183","https://openalex.org/W4402380724","https://openalex.org/W4403183071"],"related_works":[],"abstract_inverted_index":{"Impossible":[0],"differential":[1,209],"cryptanalysis":[2,6],"and":[3,29,97,130,157,169,194,208,242,255,277,293,302,317,352],"impossible":[4,30,67,95,98,128,131,167,170,192,195,235,250,261,310,339],"polytopic":[5,31],"are":[7,45,76],"among":[8,330],"the":[9,15,35,38,87,115,153,206,225,269,285,298,328,356,360],"most":[10],"effective":[11],"techniques":[12],"for":[13,25,34,64,188,237,252,281,323,359],"evaluating":[14],"security":[16,270,299],"of":[17,37,66,72,89,127,141,191,211,249,271,284,300],"block":[18,48,74,212,286],"ciphers.":[19,287],"However,":[20],"previous":[21,81],"automatic":[22,154],"search":[23,63,155,181],"methods":[24,82],"their":[26],"distinguishers\u2014dimpossible":[27],"differentials":[28,68,96,129,168,193,236,251,311],"transitions\u2014neither":[32],"account":[33],"influence":[36],"key":[39],"schedule":[40],"in":[41,118,336],"single-key":[42],"settings":[43],"nor":[44],"applicable":[46,217],"to":[47,62,80,113,139,162,218,267,296,348],"ciphers":[49,213],"featuring":[50],"large":[51,221],"S-boxes,":[52],"variable":[53],"rotations,":[54],"or":[55,91],"key-dependent":[56],"permutations.":[57],"Furthermore,":[58],"existing":[59],"approaches":[60],"fail":[61],"clusters":[65,190,248],"when":[69,326],"all":[70,282],"details":[71,207,283],"a":[73,185,230],"cipher":[75],"considered.":[77],"In":[78,257],"contrast":[79],"that":[83,124,307],"focus":[84],"solely":[85],"on":[86,106],"propagation":[88],"differences":[90],"s-difference,":[92],"we":[93,122,151,183,232,263,289,305,344],"redefine":[94],"(<italic":[99,132,171,196,340],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[100,133,172,197,341],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">s</i>":[101,134,173],"+":[102,135,174],"1)-polytopic":[103,136,175],"transitions":[104,137],"based":[105],"state":[107],"propagation.":[108],"This":[109,200],"redefinition":[110],"enables":[111],"us":[112],"overcome":[114],"limitations":[116],"inherent":[117],"earlier":[119],"methodologies.":[120],"Theoretically,":[121],"demonstrate":[123],"traditional":[125],"definitions":[126],"correspond":[138],"subsets":[140],"our":[142,165,265,346],"redefined":[143,166],"concepts,":[144],"which":[145],"offer":[146],"broader":[147],"analytical":[148],"perspectives.":[149],"Technically,":[150],"reformulate":[152],"model":[156],"develop":[158],"an":[159],"SAT-based":[160],"tool":[161],"efficiently":[163],"evaluate":[164,268,297],"transitions.":[176,199],"Building":[177],"upon":[178],"this":[179],"foundational":[180],"method,":[182],"construct":[184],"comprehensive":[186],"framework":[187,201],"detecting":[189],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">s</i>+1)-polytopic":[198,342],"not":[202],"only":[203],"fully":[204],"incorporates":[205],"properties":[210],"but":[214],"is":[215],"also":[216],"those":[219],"employing":[220],"S-boxes":[222],"while":[223,279],"considering":[224,327],"full":[226],"linear":[227],"layer.":[228],"As":[229],"result,":[231],"derive":[233],"new":[234,247,338],"GIFT64,":[238,272,350],"PRINTcipher48/96,":[239,273],"MISTY1,":[240,274],"RC5-32/64/128":[241],"SPECK,":[243,253,275],"as":[244,246],"well":[245],"DES":[254,278],"ARIA.":[256],"assessing":[258],"resistance":[259],"against":[260],"differentials,":[262],"apply":[264,294,345],"method":[266],"SIMON,":[276],"accounting":[280],"Moreover,":[288],"propose":[290],"acceleration":[291],"strategies":[292],"them":[295],"MISTY1":[301],"AES-128.":[303],"Notably,":[304],"prove":[306],"no":[308],"5-round":[309],"with":[312],"one":[313,318],"active":[314,319],"input":[315],"byte":[316,321],"output":[320],"exist":[322],"AES-128,":[324],"even":[325],"dependencies":[329],"three":[331],"consecutive":[332],"round":[333],"keys.":[334],"Finally,":[335],"exploring":[337],"transition,":[343],"approach":[347],"PRINTcipher48,":[349],"RC5-32/64":[351],"SIMON32-64,":[353],"successfully":[354],"yielding":[355],"corresponding":[357],"distinguishers":[358],"first":[361],"time.":[362]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-11-03T00:00:00"}