{"id":"https://openalex.org/W3167606741","doi":"https://doi.org/10.46586/tosc.v2021.i2.292-313","title":"Maximums of the Additive Differential Probability of Exclusive-Or","display_name":"Maximums of the Additive Differential Probability of Exclusive-Or","publication_year":2021,"publication_date":"2021-06-11","ids":{"openalex":"https://openalex.org/W3167606741","doi":"https://doi.org/10.46586/tosc.v2021.i2.292-313","mag":"3167606741"},"language":"en","primary_location":{"id":"doi:10.46586/tosc.v2021.i2.292-313","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2021.i2.292-313","pdf_url":"https://tosc.iacr.org/index.php/ToSC/article/download/8912/8488","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/8912/8488","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036504001","display_name":"Nicky Mouha","orcid":"https://orcid.org/0000-0001-8861-782X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nicky Mouha","raw_affiliation_strings":["Strativia, Largo, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Strativia, Largo, MD, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077673696","display_name":"N. A. Kolomeec","orcid":"https://orcid.org/0000-0003-4367-3507"},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Nikolay Kolomeec","raw_affiliation_strings":["Sobolev Institute of Mathematics, Novosibirsk, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia","institution_ids":["https://openalex.org/I4210096862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036629613","display_name":"Danil Akhtiamov","orcid":"https://orcid.org/0000-0002-9238-9636"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Danil Akhtiamov","raw_affiliation_strings":["The Hebrew University of Jerusalem, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002548872","display_name":"Ivan Sutormin","orcid":null},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Ivan Sutormin","raw_affiliation_strings":["Sobolev Institute of Mathematics, Novosibirsk, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia","institution_ids":["https://openalex.org/I4210096862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004839032","display_name":"Matvey Panferov","orcid":null},"institutions":[{"id":"https://openalex.org/I188973947","display_name":"Novosibirsk State University","ror":"https://ror.org/04t2ss102","country_code":"RU","type":"education","lineage":["https://openalex.org/I188973947"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Matvey Panferov","raw_affiliation_strings":["Novosibirsk State University, Novosibirsk, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Novosibirsk State University, Novosibirsk, Russia","institution_ids":["https://openalex.org/I188973947"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006713613","display_name":"Kseniya V. Titova","orcid":null},"institutions":[{"id":"https://openalex.org/I188973947","display_name":"Novosibirsk State University","ror":"https://ror.org/04t2ss102","country_code":"RU","type":"education","lineage":["https://openalex.org/I188973947"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Kseniya Titova","raw_affiliation_strings":["Novosibirsk State University, Novosibirsk, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Novosibirsk State University, Novosibirsk, Russia","institution_ids":["https://openalex.org/I188973947"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063815799","display_name":"Tatiana Bonich","orcid":null},"institutions":[{"id":"https://openalex.org/I188973947","display_name":"Novosibirsk State University","ror":"https://ror.org/04t2ss102","country_code":"RU","type":"education","lineage":["https://openalex.org/I188973947"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Tatiana Bonich","raw_affiliation_strings":["Novosibirsk State University, Novosibirsk, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Novosibirsk State University, Novosibirsk, Russia","institution_ids":["https://openalex.org/I188973947"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086097612","display_name":"Evgeniya Ishchukova","orcid":"https://orcid.org/0000-0002-6818-1608"},"institutions":[{"id":"https://openalex.org/I137534880","display_name":"Southern Federal University","ror":"https://ror.org/01tv9ph92","country_code":"RU","type":"education","lineage":["https://openalex.org/I137534880"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Evgeniya Ishchukova","raw_affiliation_strings":["Southern Federal University, Taganrog, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Southern Federal University, Taganrog, Russia","institution_ids":["https://openalex.org/I137534880"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066542850","display_name":"Natalia Tokareva","orcid":"https://orcid.org/0000-0002-4343-7048"},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Natalia Tokareva","raw_affiliation_strings":["Sobolev Institute of Mathematics, Novosibirsk, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics, Novosibirsk, Russia","institution_ids":["https://openalex.org/I4210096862"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088575562","display_name":"Bulat Zhantulikov","orcid":null},"institutions":[{"id":"https://openalex.org/I188973947","display_name":"Novosibirsk State University","ror":"https://ror.org/04t2ss102","country_code":"RU","type":"education","lineage":["https://openalex.org/I188973947"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Bulat Zhantulikov","raw_affiliation_strings":["Novosibirsk State University, Novosibirsk, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Novosibirsk State University, Novosibirsk, Russia","institution_ids":["https://openalex.org/I188973947"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":10,"corresponding_author_ids":["https://openalex.org/A5036504001"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5597,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.72753771,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"292","last_page":"313"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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":0.9997000098228455,"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/T11567","display_name":"semigroups and automata theory","score":0.9948999881744385,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.773245632648468},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.653766393661499},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.6143481135368347},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5626078844070435},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5083944201469421},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4379897117614746},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.42708820104599},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42478665709495544},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.27386295795440674},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09878388047218323}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.773245632648468},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.653766393661499},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.6143481135368347},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5626078844070435},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5083944201469421},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4379897117614746},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.42708820104599},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42478665709495544},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.27386295795440674},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09878388047218323},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.46586/tosc.v2021.i2.292-313","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2021.i2.292-313","pdf_url":"https://tosc.iacr.org/index.php/ToSC/article/download/8912/8488","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:doaj.org/article:7ae3184896c24600af06b3fc5179a4d1","is_oa":true,"landing_page_url":"https://doaj.org/article/7ae3184896c24600af06b3fc5179a4d1","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 2021, Iss 2 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46586/tosc.v2021.i2.292-313","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2021.i2.292-313","pdf_url":"https://tosc.iacr.org/index.php/ToSC/article/download/8912/8488","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":[{"id":"https://openalex.org/G3245660431","display_name":null,"funder_award_id":"No. 075-15-2019-1613","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"},{"id":"https://openalex.org/G3776982894","display_name":null,"funder_award_id":"075-15-2019-1613","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"},{"id":"https://openalex.org/G6444257319","display_name":null,"funder_award_id":"075-15-","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"}],"funders":[{"id":"https://openalex.org/F4320327494","display_name":"Ministry of Science and Higher Education of the Russian Federation","ror":null},{"id":"https://openalex.org/F4320331675","display_name":"JetBrains Research","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3167606741.pdf","grobid_xml":"https://content.openalex.org/works/W3167606741.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W50116563","https://openalex.org/W170945785","https://openalex.org/W199966775","https://openalex.org/W1498785007","https://openalex.org/W1504341594","https://openalex.org/W1508038907","https://openalex.org/W1523702841","https://openalex.org/W1526619693","https://openalex.org/W1535006789","https://openalex.org/W1536457675","https://openalex.org/W1629301835","https://openalex.org/W1883151075","https://openalex.org/W2103641030","https://openalex.org/W2123628192","https://openalex.org/W2132271754","https://openalex.org/W2554376114","https://openalex.org/W2792256231","https://openalex.org/W2950097020","https://openalex.org/W3006144266","https://openalex.org/W3030624396","https://openalex.org/W3082483840","https://openalex.org/W4235801565","https://openalex.org/W4241072010"],"related_works":["https://openalex.org/W2070252991","https://openalex.org/W2117548279","https://openalex.org/W2807449856","https://openalex.org/W238211858","https://openalex.org/W2025727968","https://openalex.org/W2941201715","https://openalex.org/W2803761277","https://openalex.org/W4297742300","https://openalex.org/W4295096867","https://openalex.org/W4291557013"],"abstract_inverted_index":{"At":[0],"FSE":[1,77],"2004,":[2],"Lipmaa":[3],"et":[4],"al.":[5],"studied":[6],"the":[7,32,45,69,76,129,142],"additive":[8],"differential":[9,65,133],"probability":[10,28],"adp\u2295(\u03b1,\u03b2":[11],"\u2192":[12,84,88,111,115,147],"\u03b3)":[13,85,89,112],"of":[14,34,53,75,131,145],"exclusive-or":[15],"where":[16],"differences":[17],"\u03b1,\u03b2,\u03b3":[18],"\u2208":[19],"Fn2":[20],"are":[21,61],"expressed":[22],"using":[23],"addition":[24],"modulo":[25],"2n.":[26],"This":[27],"is":[29,56],"used":[30],"in":[31],"analysis":[33],"symmetric-key":[35],"primitives":[36],"that":[37,82,96,108,154],"combine":[38],"XOR":[39],"and":[40,117,149],"modular":[41],"addition,":[42],"such":[43,107,140],"as":[44,141],"increasingly":[46],"popular":[47],"Addition-Rotation-XOR":[48],"(ARX)":[49],"constructions.":[50],"The":[51],"focus":[52],"this":[54,156],"paper":[55],"on":[57],"maximal":[58],"differentials,":[59],"which":[60,80],"helpful":[62],"when":[63],"constructing":[64],"trails.":[66],"We":[67],"provide":[68],"missing":[70],"proof":[71],"for":[72,90,122],"Theorem":[73],"3":[74],"2004":[78],"paper,":[79],"states":[81],"max\u03b1,\u03b2adp\u2295(\u03b1,\u03b2":[83],"=":[86,113],"adp\u2295(0,\u03b3":[87,114,146],"all":[91,152],"\u03b3.":[92],"Furthermore,":[93],"we":[94,118,135,150],"prove":[95],"there":[97],"always":[98],"exist":[99],"either":[100],"two":[101],"or":[102],"eight":[103],"distinct":[104],"pairs":[105],"\u03b1,\u03b2":[106,110],"adp\u2295(":[109],"\u03b3),":[116,148],"obtain":[119],"recurrence":[120],"formulas":[121],"calculating":[123],"adp\u2295.":[124],"To":[125],"gain":[126],"insight":[127],"into":[128],"range":[130],"possible":[132],"probabilities,":[134],"also":[136],"study":[137],"other":[138],"properties":[139],"minimum":[143,157],"value":[144],"find":[151],"\u03b3":[153],"satisfy":[155],"value.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}