{"id":"https://openalex.org/W7124997565","doi":"https://doi.org/10.3390/cryptography10010007","title":"Autopotency and Conjugacy of Non-Diagonalizable Matrices for Challenge\u2013Response Authentication","display_name":"Autopotency and Conjugacy of Non-Diagonalizable Matrices for Challenge\u2013Response Authentication","publication_year":2026,"publication_date":"2026-01-18","ids":{"openalex":"https://openalex.org/W7124997565","doi":"https://doi.org/10.3390/cryptography10010007"},"language":"en","primary_location":{"id":"doi:10.3390/cryptography10010007","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography10010007","pdf_url":"https://www.mdpi.com/2410-387X/10/1/7/pdf?version=1768981443","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2410-387X/10/1/7/pdf?version=1768981443","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015292323","display_name":"Daniel Alarc\u00f3n-Narv\u00e1ez","orcid":null},"institutions":[{"id":"https://openalex.org/I157492648","display_name":"Autonomous University of Queretaro","ror":"https://ror.org/00v8fdc16","country_code":"MX","type":"education","lineage":["https://openalex.org/I157492648"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Daniel Alarc\u00f3n-Narv\u00e1ez","raw_affiliation_strings":["Computer Science, Autonomous University of Quer\u00e9taro (UAQ), Av. de las Ciencias, Quer\u00e9taro 76230, Quer\u00e9taro, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science, Autonomous University of Quer\u00e9taro (UAQ), Av. de las Ciencias, Quer\u00e9taro 76230, Quer\u00e9taro, Mexico","institution_ids":["https://openalex.org/I157492648"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123414620","display_name":"Luis Adri\u00e1n Lizama-P\u00e9rez","orcid":null},"institutions":[{"id":"https://openalex.org/I75778554","display_name":"Federico Santa Mar\u00eda Technical University","ror":"https://ror.org/05510vn56","country_code":"CL","type":"education","lineage":["https://openalex.org/I75778554"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Luis Adri\u00e1n Lizama-P\u00e9rez","raw_affiliation_strings":["Department of Electronics, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Av. Vicu\u00f1a Mackenna, San Joaqu\u00edn 8940897, Chile"],"raw_orcid":"https://orcid.org/0000-0001-5109-2927","affiliations":[{"raw_affiliation_string":"Department of Electronics, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Av. Vicu\u00f1a Mackenna, San Joaqu\u00edn 8940897, Chile","institution_ids":["https://openalex.org/I75778554"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031392892","display_name":"Fausto Abraham Jacques-Garc\u00eda","orcid":"https://orcid.org/0000-0001-8522-0368"},"institutions":[{"id":"https://openalex.org/I157492648","display_name":"Autonomous University of Queretaro","ror":"https://ror.org/00v8fdc16","country_code":"MX","type":"education","lineage":["https://openalex.org/I157492648"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Fausto Abraham Jacques-Garc\u00eda","raw_affiliation_strings":["Computer Science, Autonomous University of Quer\u00e9taro (UAQ), Av. de las Ciencias, Quer\u00e9taro 76230, Quer\u00e9taro, Mexico"],"raw_orcid":"https://orcid.org/0000-0001-8522-0368","affiliations":[{"raw_affiliation_string":"Computer Science, Autonomous University of Quer\u00e9taro (UAQ), Av. de las Ciencias, Quer\u00e9taro 76230, Quer\u00e9taro, Mexico","institution_ids":["https://openalex.org/I157492648"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015292323"],"corresponding_institution_ids":["https://openalex.org/I157492648"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1732},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1732},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14234852,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"1","first_page":"7","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.28760001063346863,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.28760001063346863,"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/T11130","display_name":"Coding theory and cryptography","score":0.15279999375343323,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.12540000677108765,"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/conjugacy-class","display_name":"Conjugacy class","score":0.7475000023841858},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.5133000016212463},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.47189998626708984},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4690999984741211},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4499000012874603},{"id":"https://openalex.org/keywords/authentication","display_name":"Authentication (law)","score":0.4397999942302704},{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.4092000126838684},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4041999876499176},{"id":"https://openalex.org/keywords/authentication-protocol","display_name":"Authentication protocol","score":0.37380000948905945}],"concepts":[{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.7475000023841858},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6955999732017517},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.5133000016212463},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.47189998626708984},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4690999984741211},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4499000012874603},{"id":"https://openalex.org/C148417208","wikidata":"https://www.wikidata.org/wiki/Q4825882","display_name":"Authentication (law)","level":2,"score":0.4397999942302704},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4390000104904175},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.4092000126838684},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4041999876499176},{"id":"https://openalex.org/C21564112","wikidata":"https://www.wikidata.org/wiki/Q4825885","display_name":"Authentication protocol","level":3,"score":0.37380000948905945},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3714999854564667},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.34139999747276306},{"id":"https://openalex.org/C159718280","wikidata":"https://www.wikidata.org/wiki/Q5526353","display_name":"Gas meter prover","level":3,"score":0.3321000039577484},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.3296000063419342},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.30329999327659607},{"id":"https://openalex.org/C103275481","wikidata":"https://www.wikidata.org/wiki/Q6787889","display_name":"Matrix representation","level":3,"score":0.30169999599456787},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2687000036239624},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.26429998874664307},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2630999982357025},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.2619999945163727},{"id":"https://openalex.org/C15927051","wikidata":"https://www.wikidata.org/wiki/Q246593","display_name":"Cryptographic primitive","level":4,"score":0.2597000002861023},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.2531999945640564},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2506999969482422},{"id":"https://openalex.org/C33884865","wikidata":"https://www.wikidata.org/wiki/Q1254335","display_name":"Cryptographic protocol","level":3,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/cryptography10010007","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography10010007","pdf_url":"https://www.mdpi.com/2410-387X/10/1/7/pdf?version=1768981443","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e2e8958fa0334844ad5c28446bc86ca5","is_oa":false,"landing_page_url":"https://doaj.org/article/e2e8958fa0334844ad5c28446bc86ca5","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cryptography, Vol 10, Iss 1, p 7 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/cryptography10010007","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography10010007","pdf_url":"https://www.mdpi.com/2410-387X/10/1/7/pdf?version=1768981443","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7124997565.pdf","grobid_xml":"https://content.openalex.org/works/W7124997565.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W634784785","https://openalex.org/W1510717485","https://openalex.org/W1536729852","https://openalex.org/W1568587963","https://openalex.org/W2113446256","https://openalex.org/W2128718974","https://openalex.org/W2791664942","https://openalex.org/W2866028610","https://openalex.org/W2895182117","https://openalex.org/W3097058029","https://openalex.org/W4229706427","https://openalex.org/W4296842505","https://openalex.org/W4385805359","https://openalex.org/W4401575566","https://openalex.org/W4403291154","https://openalex.org/W4405425791","https://openalex.org/W4406271161"],"related_works":[],"abstract_inverted_index":{"We":[0,125],"present":[1],"an":[2,48,106],"algebraic":[3,129,164,201],"framework":[4,181],"for":[5,67,85,207],"constructing":[6],"challenge\u2013response":[7],"authentication":[8,108,197],"protocols":[9],"based":[10],"on":[11,22,33],"powers":[12],"of":[13,59,93,117,133,166],"non-diagonalizable":[14,147,184],"matrices":[15,26,65],"over":[16],"finite":[17],"fields.":[18],"The":[19,51,90,180],"construction":[20,168],"relies":[21],"upper":[23],"triangular":[24],"Toeplitz":[25,150],"with":[27],"a":[28,56,71,86,205],"single":[29],"Jordan":[30],"block":[31],"and":[32,45,79,136,142,149,169,187,203,210],"their":[34],"structured":[35,188],"power":[36,81],"expansions,":[37],"which":[38,111],"induce":[39],"nonlinear":[40],"relations":[41,190],"between":[42],"matrix":[43,60,185],"parameters":[44],"exponents":[46],"through":[47],"autopotency":[49],"phenomenon.":[50],"protocol":[52],"is":[53,74,83,96],"built":[54],"from":[55,63,139,162],"cyclic":[57],"family":[58,92],"products":[61,95],"derived":[62],"secret":[64,87],"(Ai)i=1n\u2282GLk(Fp):":[66],"each":[68],"index":[69],"i,":[70],"product":[72],"Pi=AiAi+1\u2026Ai+n\u22121":[73],"formed":[75],"(indices":[76],"modulo":[77],"n),":[78],"its":[80],"Pi(x)":[82],"published":[84],"exponent":[88],"x.":[89],"resulting":[91],"powered":[94,140],"linked":[97],"by":[98,120],"conjugation":[99],"via":[100],"the":[101,112,115,127,145,163,167],"unknown":[102],"factors":[103,119],"Ai,":[104],"enabling":[105],"interactive":[107],"mechanism":[109],"in":[110,131,199],"prover":[113],"demonstrates":[114],"knowledge":[116],"selected":[118],"satisfying":[121],"explicit":[122],"conjugacy":[123,137,189],"relations.":[124],"formalize":[126],"underlying":[128],"problems":[130],"terms":[132],"factor":[134],"recovery":[135],"identification":[138],"products,":[141],"analyze":[143],"how":[144,183],"enforced":[146],"structure":[148],"constraints":[151],"lead":[152],"to":[153,175,194],"coupled":[154],"multivariate":[155],"polynomial":[156],"systems.":[157],"These":[158],"systems":[159],"arise":[160],"naturally":[161],"design":[165],"do":[170],"not":[171],"admit":[172],"immediate":[173],"reductions":[174],"classical":[176],"discrete":[177],"logarithm":[178],"settings.":[179],"illustrates":[182],"structures":[186],"can":[191],"be":[192],"used":[193],"define":[195],"concrete":[196],"primitives":[198],"noncommutative":[200],"settings,":[202],"provides":[204],"basis":[206],"further":[208],"cryptanalytic":[209],"cryptographic":[211],"investigation.":[212]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2026-01-21T00:00:00"}
