{"id":"https://openalex.org/W4408241262","doi":"https://doi.org/10.46586/tosc.v2025.i1.542-591","title":"Exact Formula for RX-Differential Probability Through Modular Addition for All Rotations","display_name":"Exact Formula for RX-Differential Probability Through Modular Addition for All Rotations","publication_year":2025,"publication_date":"2025-03-07","ids":{"openalex":"https://openalex.org/W4408241262","doi":"https://doi.org/10.46586/tosc.v2025.i1.542-591"},"language":"en","primary_location":{"id":"doi:10.46586/tosc.v2025.i1.542-591","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2025.i1.542-591","pdf_url":"https://tosc.iacr.org/index.php/ToSC/article/download/12087/11927","source":{"id":"https://openalex.org/S4210236173","display_name":"IACR Transactions on Symmetric Cryptology","issn_l":"2519-173X","issn":["2519-173X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Symmetric Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://tosc.iacr.org/index.php/ToSC/article/download/12087/11927","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072754929","display_name":"Alex Biryukov","orcid":"https://orcid.org/0000-0003-1404-6686"},"institutions":[{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]}],"countries":["LU"],"is_corresponding":true,"raw_author_name":"Alex Biryukov","raw_affiliation_strings":["DCS, University of Luxembourg, Esch-sur-Alzette, Luxembourg; SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg","DCS, University of Luxembourg, Esch-sur-Alzette, Luxembourg","SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg"],"affiliations":[{"raw_affiliation_string":"DCS, University of Luxembourg, Esch-sur-Alzette, Luxembourg; SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg","institution_ids":["https://openalex.org/I186903577"]},{"raw_affiliation_string":"DCS, University of Luxembourg, Esch-sur-Alzette, Luxembourg","institution_ids":["https://openalex.org/I186903577"]},{"raw_affiliation_string":"SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070936023","display_name":"Baptiste Lambin","orcid":"https://orcid.org/0000-0002-3040-4503"},"institutions":[{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]}],"countries":["LU"],"is_corresponding":false,"raw_author_name":"Baptiste Lambin","raw_affiliation_strings":["SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg"],"affiliations":[{"raw_affiliation_string":"SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022255409","display_name":"Aleksei Udovenko","orcid":"https://orcid.org/0000-0001-8318-6274"},"institutions":[{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]}],"countries":["LU"],"is_corresponding":false,"raw_author_name":"Aleksei Udovenko","raw_affiliation_strings":["SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg"],"affiliations":[{"raw_affiliation_string":"SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072754929"],"corresponding_institution_ids":["https://openalex.org/I186903577"],"apc_list":null,"apc_paid":null,"fwci":1.4083,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.79686572,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"2025","issue":"1","first_page":"542","last_page":"591"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.8809000253677368,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.8809000253677368,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.8359000086784363,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.8184000253677368,"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/modular-design","display_name":"Modular design","score":0.7464300990104675},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5865753293037415},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4306579828262329},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35360804200172424},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1425265073776245},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09631776809692383},{"id":"https://openalex.org/keywords/aerospace-engineering","display_name":"Aerospace engineering","score":0.08023011684417725}],"concepts":[{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.7464300990104675},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5865753293037415},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4306579828262329},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35360804200172424},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1425265073776245},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09631776809692383},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.08023011684417725}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.46586/tosc.v2025.i1.542-591","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2025.i1.542-591","pdf_url":"https://tosc.iacr.org/index.php/ToSC/article/download/12087/11927","source":{"id":"https://openalex.org/S4210236173","display_name":"IACR Transactions on Symmetric Cryptology","issn_l":"2519-173X","issn":["2519-173X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Symmetric Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:orbilu.uni.lu:10993/64546","is_oa":true,"landing_page_url":"https://orbilu.uni.lu/handle/10993/64546","pdf_url":null,"source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"IACR Transactions on Symmetric Cryptology, 2025 (1), 542-591 (2025-03-07); FSE2025 - 31st Fast Software Encryption Conference, Rome, Italy [IT], March 17-21, 2025","raw_type":"peer reviewed"},{"id":"pmh:oai:doaj.org/article:20c7343b56de401ca4be0a64f14dff48","is_oa":true,"landing_page_url":"https://doaj.org/article/20c7343b56de401ca4be0a64f14dff48","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Transactions on Symmetric Cryptology, Vol 2025, Iss 1 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46586/tosc.v2025.i1.542-591","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2025.i1.542-591","pdf_url":"https://tosc.iacr.org/index.php/ToSC/article/download/12087/11927","source":{"id":"https://openalex.org/S4210236173","display_name":"IACR Transactions on Symmetric Cryptology","issn_l":"2519-173X","issn":["2519-173X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Symmetric Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4408241262.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"This":[0],"work":[1,49],"presents":[2],"an":[3],"exact":[4,134],"and":[5,36,70,147,153],"compact":[6],"formula":[7,30,43,54,72,93,98],"for":[8,18,55,73,99,127],"the":[9,67,74,89,171,174],"probability":[10],"of":[11,66,91,151,160,173],"rotation-xor":[12],"differentials":[13],"(RX-differentials)":[14],"through":[15],"modular":[16],"addition,":[17],"arbitrary":[19,100],"rotation":[20,56,75],"amounts,":[21],"which":[22,189],"has":[23,190],"been":[24],"a":[25,33,47,53,105,148,181,191],"long-standing":[26],"open":[27],"problem.":[28],"The":[29],"comes":[31],"with":[32,185],"rigorous":[34],"proof":[35],"is":[37],"also":[38,63,178],"verified":[39],"by":[40],"extensive":[41],"experiments.Our":[42],"uncovers":[44,85],"error":[45],"in":[46],"recent":[48],"from":[50],"2022":[51],"proposing":[52],"amounts":[57],"bigger":[58],"than":[59],"1.":[60],"Surprisingly,":[61],"it":[62,84],"affects":[64],"correctness":[65],"more":[68],"studied":[69],"used":[71],"amount":[76],"equal":[77],"to":[78,140,169],"1":[79],"(from":[80],"TOSC":[81],"2016).":[82],"Specifically,":[83],"rare":[86],"cases":[87],"where":[88,109],"assumptions":[90],"this":[92],"do":[94],"not":[95],"hold.":[96],"Correct":[97],"rotations":[101],"now":[102],"opens":[103],"up":[104],"larger":[106],"search":[107],"space":[108],"one":[110],"can":[111],"often":[112],"find":[113],"better":[114],"trails.For":[115],"applications,":[116],"we":[117,177],"propose":[118],"automated":[119],"mixed":[120],"integer":[121],"linear":[122],"programming":[123],"(MILP)":[124],"modeling":[125],"techniques":[126],"searching":[128],"optimal":[129,165],"RX-trails":[130],"based":[131,162],"on":[132,163],"our":[133],"formula.":[135],"They":[136],"are":[137],"consequently":[138],"applied":[139],"several":[141],"ARX":[142],"designs,":[143],"including":[144],"Salsa,":[145],"Alzette":[146],"small-key":[149],"variant":[150],"Speck,":[152],"yield":[154],"many":[155],"new":[156],"RX-differential":[157,175,193],"distinguishers,":[158],"some":[159],"them":[161],"provably":[164],"trails.":[166],"In":[167],"order":[168],"showcase":[170],"relevance":[172],"analysis,":[176],"design":[179],"Malzette,":[180],"12-round":[182],"Alzette-based":[183],"permutation":[184],"maliciously":[186],"chosen":[187],"constants,":[188],"practical":[192],"distinguisher,":[194],"while":[195],"standard":[196],"differential/linear":[197],"security":[198],"arguments":[199],"suggest":[200],"sufficient":[201],"security.":[202]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-02-27T16:54:17.756197","created_date":"2025-10-10T00:00:00"}