{"id":"https://openalex.org/W7119546853","doi":"https://doi.org/10.62056/akmpdk5vt","title":"Matrix Polynomial Attack on the Megrelishvili Key Exchange Protocol","display_name":"Matrix Polynomial Attack on the Megrelishvili Key Exchange Protocol","publication_year":2026,"publication_date":"2026-01-08","ids":{"openalex":"https://openalex.org/W7119546853","doi":"https://doi.org/10.62056/akmpdk5vt"},"language":"en","primary_location":{"id":"doi:10.62056/akmpdk5vt","is_oa":true,"landing_page_url":"https://doi.org/10.62056/akmpdk5vt","pdf_url":"https://cic.iacr.org/p/2/4/16/pdf","source":{"id":"https://openalex.org/S4394708374","display_name":"IACR Communications in Cryptology","issn_l":"3006-5496","issn":["3006-5496"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320989","host_organization_name":"International Association for Cryptologic Research","host_organization_lineage":["https://openalex.org/P4310320989"],"host_organization_lineage_names":["International Association for Cryptologic Research"],"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 Communications in Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://cic.iacr.org/p/2/4/16/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119592370","display_name":"Raul Caram de Assis","orcid":"https://orcid.org/0009-0003-8572-7072"},"institutions":[{"id":"https://openalex.org/I4210103631","display_name":"Centro de Estudos e Pesquisa em Sa\u00fade Coletiva","ror":"https://ror.org/01dwh3q17","country_code":"BR","type":"nonprofit","lineage":["https://openalex.org/I4210103631"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Raul de Assis","raw_affiliation_strings":["CEPESC"],"raw_orcid":"https://orcid.org/0009-0003-8572-7072","affiliations":[{"raw_affiliation_string":"CEPESC","institution_ids":["https://openalex.org/I4210103631"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107663504","display_name":"Thiago do R\u00eago Sousa","orcid":null},"institutions":[{"id":"https://openalex.org/I4210103631","display_name":"Centro de Estudos e Pesquisa em Sa\u00fade Coletiva","ror":"https://ror.org/01dwh3q17","country_code":"BR","type":"nonprofit","lineage":["https://openalex.org/I4210103631"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Thiago do R\u00eago Sousa","raw_affiliation_strings":["CEPESC"],"raw_orcid":"https://orcid.org/0000-0002-0776-034X","affiliations":[{"raw_affiliation_string":"CEPESC","institution_ids":["https://openalex.org/I4210103631"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210103631"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03227217,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11504","display_name":"Advanced Authentication Protocols Security","score":0.5490000247955322,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11504","display_name":"Advanced Authentication Protocols Security","score":0.5490000247955322,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10237","display_name":"Cryptography and Data Security","score":0.2791000008583069,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.016599999740719795,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/polynomial","display_name":"Polynomial","score":0.5957000255584717},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.5828999876976013},{"id":"https://openalex.org/keywords/key-exchange","display_name":"Key exchange","score":0.5601999759674072},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5415999889373779},{"id":"https://openalex.org/keywords/diagonalizable-matrix","display_name":"Diagonalizable matrix","score":0.49810001254081726},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4691999852657318},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4553999900817871},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.43849998712539673}],"concepts":[{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5957000255584717},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.5828999876976013},{"id":"https://openalex.org/C99674996","wikidata":"https://www.wikidata.org/wiki/Q1414155","display_name":"Key exchange","level":4,"score":0.5601999759674072},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5415999889373779},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.536300003528595},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.49810001254081726},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4691999852657318},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4553999900817871},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.44600000977516174},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4458000063896179},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.43849998712539673},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4090999960899353},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.40709999203681946},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.39430001378059387},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3849000036716461},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3828999996185303},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.3684999942779541},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.34779998660087585},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.3296999931335449},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.3118000030517578},{"id":"https://openalex.org/C38369872","wikidata":"https://www.wikidata.org/wiki/Q7445009","display_name":"Security analysis","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.26809999346733093},{"id":"https://openalex.org/C135530808","wikidata":"https://www.wikidata.org/wiki/Q3306713","display_name":"Key-agreement protocol","level":5,"score":0.26579999923706055},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2540000081062317}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.62056/akmpdk5vt","is_oa":true,"landing_page_url":"https://doi.org/10.62056/akmpdk5vt","pdf_url":"https://cic.iacr.org/p/2/4/16/pdf","source":{"id":"https://openalex.org/S4394708374","display_name":"IACR Communications in Cryptology","issn_l":"3006-5496","issn":["3006-5496"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320989","host_organization_name":"International Association for Cryptologic Research","host_organization_lineage":["https://openalex.org/P4310320989"],"host_organization_lineage_names":["International Association for Cryptologic Research"],"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 Communications in Cryptology","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.62056/akmpdk5vt","is_oa":true,"landing_page_url":"https://doi.org/10.62056/akmpdk5vt","pdf_url":"https://cic.iacr.org/p/2/4/16/pdf","source":{"id":"https://openalex.org/S4394708374","display_name":"IACR Communications in Cryptology","issn_l":"3006-5496","issn":["3006-5496"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320989","host_organization_name":"International Association for Cryptologic Research","host_organization_lineage":["https://openalex.org/P4310320989"],"host_organization_lineage_names":["International Association for Cryptologic Research"],"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 Communications in Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6572617888450623,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7119546853.pdf","grobid_xml":"https://content.openalex.org/works/W7119546853.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1965506160","https://openalex.org/W2156186849","https://openalex.org/W2168676717","https://openalex.org/W2317037120","https://openalex.org/W2594072575","https://openalex.org/W2765297546","https://openalex.org/W2769514460","https://openalex.org/W2795884581","https://openalex.org/W2901413339","https://openalex.org/W2974904852","https://openalex.org/W3120491398","https://openalex.org/W3156072796","https://openalex.org/W4400648863"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,48],"article":[2],"we":[3,54,131],"explain":[4],"what":[5],"the":[6,18,27,30,34,37,56,68,72,79,82,101,106,120,139,148,161,183,186],"Megrelishvili":[7,38],"Key":[8,21],"Exchange":[9,22],"Protocol":[10],"(MKE)":[11],"is":[12],"and":[13,42,78,178],"compare":[14],"it":[15],"briefly":[16],"to":[17,33,44,75,91,118,126,136,166],"older":[19],"Diffie-Hellman":[20],"Protocol.":[23],"We":[24,169],"clarify":[25],"how":[26],"security":[28],"of":[29,36,47,147,160,185,193],"MKE":[31,69,107,162],"relates":[32],"hardness":[35],"Vector-Matrix":[39],"Problem":[40,59],"(MVMP)":[41],"also":[43,170],"a":[45,133,152,167,190],"generalization":[46],"problem,":[49],"introduced":[50],"by":[51],"us,":[52],"which":[53],"call":[55],"Matrix":[57],"Polynomial":[58],"(MPP).":[60],"There":[61],"were":[62],"previous":[63],"sub-exponential":[64],"time":[65,124,154],"attacks":[66],"on":[67,100],"[AW16,":[70],"AMP18],":[71],"first":[73,140],"applying":[74],"arbitrary":[76],"instances":[77],"latter":[80],"requiring":[81],"public":[83],"matrix":[84],"<mml:math":[85],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[86],"<mml:mrow>":[87],"<mml:mi>M</mml:mi>":[88],"</mml:mrow>":[89],"</mml:math>":[90],"be":[92],"diagonalizable":[93],"\u2014":[94],"as":[95,97,142,144],"well":[96],"an":[98],"attack":[99],"one-way":[102],"function":[103],"used":[104],"in":[105,122],"[Meg14]":[108],"that":[109,156],"required":[110],"special":[111],"conditions,":[112],"but":[113],"when":[114],"applicable":[115],"would":[116],"allow":[117],"break":[119],"protocol":[121],"polynomial":[123,153],"according":[125],"our":[127,145,194],"running-time":[128],"analysis.":[129],"Here":[130],"adopt":[132],"bottom-up":[134],"approach":[135],"construct":[137],"for":[138,189],"time,":[141],"far":[143],"review":[146],"relevant":[149],"literature":[150],"reveals,":[151],"algorithm":[155],"solves":[157],"any":[158],"instance":[159],"through":[163],"its":[164],"reduction":[165],"MPP.":[168],"introduce":[171],"some":[172],"key":[173],"concepts":[174],"from":[175],"linear":[176],"algebra":[177],"Krylov":[179],"subspace":[180],"theory":[181],"into":[182],"context":[184],"MKE,":[187],"allowing":[188],"clearer":[191],"understanding":[192],"attack.":[195]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-01-09T00:00:00"}
