{"id":"https://openalex.org/W2792143328","doi":"https://doi.org/10.3934/amc.2019016","title":"Type-preserving matrices and security of block ciphers","display_name":"Type-preserving matrices and security of block ciphers","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2792143328","doi":"https://doi.org/10.3934/amc.2019016","mag":"2792143328"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2019016","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2019016","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=b4f5a145-2c3a-41ab-a01d-b3e126878053","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=b4f5a145-2c3a-41ab-a01d-b3e126878053","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030996302","display_name":"Riccardo Aragona","orcid":"https://orcid.org/0000-0001-8834-4358"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Riccardo Aragona","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058540975","display_name":"Alessio Meneghetti","orcid":"https://orcid.org/0000-0002-5159-7252"},"institutions":[{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alessio Meneghetti","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 degli Studi di Trento, Via Sommarive 14, 38123 Povo (TN), Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 degli Studi di Trento, Via Sommarive 14, 38123 Povo (TN), Italy","institution_ids":["https://openalex.org/I193223587"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030996302"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00414675,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"2","first_page":"235","last_page":"251"},"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":0.9995999932289124,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9976000189781189,"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/gost","display_name":"GOST (hash function)","score":0.8799598217010498},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.7333013415336609},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.6886028051376343},{"id":"https://openalex.org/keywords/block-cipher","display_name":"Block cipher","score":0.6101719737052917},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.602867603302002},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4789507985115051},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.46850278973579407},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.43934395909309387},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4163692593574524},{"id":"https://openalex.org/keywords/logical-matrix","display_name":"Logical matrix","score":0.4101288318634033},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3723638951778412},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35715121030807495},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2984682321548462},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.2880963087081909},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07734954357147217}],"concepts":[{"id":"https://openalex.org/C2780233296","wikidata":"https://www.wikidata.org/wiki/Q3756229","display_name":"GOST (hash function)","level":2,"score":0.8799598217010498},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.7333013415336609},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6886028051376343},{"id":"https://openalex.org/C106544461","wikidata":"https://www.wikidata.org/wiki/Q543151","display_name":"Block cipher","level":3,"score":0.6101719737052917},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.602867603302002},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4789507985115051},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.46850278973579407},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.43934395909309387},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4163692593574524},{"id":"https://openalex.org/C163561899","wikidata":"https://www.wikidata.org/wiki/Q1994977","display_name":"Logical matrix","level":3,"score":0.4101288318634033},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3723638951778412},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35715121030807495},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2984682321548462},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.2880963087081909},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07734954357147217},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3934/amc.2019016","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2019016","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=b4f5a145-2c3a-41ab-a01d-b3e126878053","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1803.00965","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.00965","pdf_url":"https://arxiv.org/pdf/1803.00965","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2792143328","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1803.00965.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:iris.unitn.it:11572/277643","is_oa":true,"landing_page_url":"https://hdl.handle.net/11572/277643","pdf_url":null,"source":{"id":"https://openalex.org/S4306401913","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Trento)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193223587","host_organization_name":"University of Trento","host_organization_lineage":["https://openalex.org/I193223587"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ricerca.uniba.it:11586/554060","is_oa":false,"landing_page_url":"https://hdl.handle.net/11586/554060","pdf_url":null,"source":{"id":"https://openalex.org/S4377196296","display_name":"CINECA IRIS Institutional Research Information System (University of Bari Aldo Moro)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5561750","host_organization_name":"University of Bari Aldo Moro","host_organization_lineage":["https://openalex.org/I5561750"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1803.00965","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1803.00965","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.3934/amc.2019016","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2019016","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=b4f5a145-2c3a-41ab-a01d-b3e126878053","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.6100000143051147,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2792143328.pdf","grobid_xml":"https://content.openalex.org/works/W2792143328.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W100113061","https://openalex.org/W1489027369","https://openalex.org/W1511842436","https://openalex.org/W1518029257","https://openalex.org/W1535044875","https://openalex.org/W1572300106","https://openalex.org/W1605116544","https://openalex.org/W1894646615","https://openalex.org/W1971498088","https://openalex.org/W2021656681","https://openalex.org/W2030209085","https://openalex.org/W2058246021","https://openalex.org/W2127932955","https://openalex.org/W2586276142","https://openalex.org/W2798943694","https://openalex.org/W2963141981","https://openalex.org/W3100117667","https://openalex.org/W3101850477"],"related_works":["https://openalex.org/W2784122844","https://openalex.org/W2521851621","https://openalex.org/W2949188875","https://openalex.org/W2018475904","https://openalex.org/W1632354152","https://openalex.org/W1575922610","https://openalex.org/W194237467","https://openalex.org/W1575149347","https://openalex.org/W3095838963","https://openalex.org/W2023158465","https://openalex.org/W2398700359","https://openalex.org/W157243396","https://openalex.org/W1505698853","https://openalex.org/W1980129669","https://openalex.org/W1796856854","https://openalex.org/W2086970438","https://openalex.org/W2334965427","https://openalex.org/W1257619105","https://openalex.org/W2002922247","https://openalex.org/W2307673304"],"abstract_inverted_index":{"We":[0],"introduce":[1],"a":[2,45],"new":[3],"property":[4,30],"for":[5],"mixing":[6,41,73,103,109],"layers":[7,27,42,74],"which":[8],"guarantees":[9],"protection":[10],"against":[11],"algebraic":[12],"attacks":[13],"based":[14],"on":[15,52],"the":[16,19,23,53,72,84,88],"imprimitivity":[17],"of":[18,47,55,66,75,91],"group":[20,85],"generated":[21,86],"by":[22,43,87],"round":[24,89],"functions.":[25],"Mixing":[26],"satisfying":[28],"this":[29,112],"are":[31,69],"called":[32],"non-type-preserving.":[33],"Our":[34],"main":[35],"result":[36],"is":[37,105],"to":[38],"characterize":[39],"such":[40],"providing":[44],"list":[46],"necessary":[48],"and":[49,78],"sufficient":[50],"conditions":[51],"structure":[54],"their":[56],"underlying":[57],"binary":[58],"matrices.":[59],"Then":[60],"we":[61,81],"show":[62],"how":[63],"several":[64],"families":[65],"linear":[67],"maps":[68],"non-type-preserving,":[70],"including":[71],"AES,":[76],"GOST":[77],"PRESENT.":[79],"Finally":[80],"prove":[82],"that":[83],"functions":[90],"an":[92],"SPN":[93],"cipher":[94],"with":[95],"addition":[96],"modulo":[97],"$":[98,100],"2^n":[99],"as":[101],"key":[102],"function":[104],"primitive":[106],"if":[107],"its":[108],"layer":[110],"satisfies":[111],"property.":[113]},"counts_by_year":[],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}
