{"id":"https://openalex.org/W7147693889","doi":"https://doi.org/10.1007/s10623-026-01836-8","title":"The matrix subcode equivalence problem and its application to signature with MPC-in-the-head","display_name":"The matrix subcode equivalence problem and its application to signature with MPC-in-the-head","publication_year":2026,"publication_date":"2026-03-31","ids":{"openalex":"https://openalex.org/W7147693889","doi":"https://doi.org/10.1007/s10623-026-01836-8"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-026-01836-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-026-01836-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-026-01836-8.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10623-026-01836-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030839978","display_name":"Magali Bardet","orcid":null},"institutions":[{"id":"https://openalex.org/I4210108118","display_name":"Laboratoire d'Informatique, du Traitement de l'Information et des Syst\u00e8mes","ror":"https://ror.org/01f1vfy95","country_code":"FR","type":"facility","lineage":["https://openalex.org/I141576021","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210108118","https://openalex.org/I62396329","https://openalex.org/I88814501"]},{"id":"https://openalex.org/I62396329","display_name":"Universit\u00e9 de Rouen Normandie","ror":"https://ror.org/03nhjew95","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I62396329"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Magali Bardet","raw_affiliation_strings":["LITIS, University of Rouen Normandie, Rouen, France"],"affiliations":[{"raw_affiliation_string":"LITIS, University of Rouen Normandie, Rouen, France","institution_ids":["https://openalex.org/I4210108118","https://openalex.org/I62396329"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132671033","display_name":"Charles Brion","orcid":null},"institutions":[{"id":"https://openalex.org/I4210108118","display_name":"Laboratoire d'Informatique, du Traitement de l'Information et des Syst\u00e8mes","ror":"https://ror.org/01f1vfy95","country_code":"FR","type":"facility","lineage":["https://openalex.org/I141576021","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210108118","https://openalex.org/I62396329","https://openalex.org/I88814501"]},{"id":"https://openalex.org/I62396329","display_name":"Universit\u00e9 de Rouen Normandie","ror":"https://ror.org/03nhjew95","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I62396329"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Charles Brion","raw_affiliation_strings":["LITIS, University of Rouen Normandie, Rouen, France"],"affiliations":[{"raw_affiliation_string":"LITIS, University of Rouen Normandie, Rouen, France","institution_ids":["https://openalex.org/I4210108118","https://openalex.org/I62396329"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132655161","display_name":"Philippe Gaborit","orcid":null},"institutions":[{"id":"https://openalex.org/I4210093397","display_name":"XLIM","ror":"https://ror.org/00f7srh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I32881790","https://openalex.org/I4210093397","https://openalex.org/I4210095849","https://openalex.org/I65806277"]},{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Philippe Gaborit","raw_affiliation_strings":["XLIM, University of Limoges, Limoges, France"],"affiliations":[{"raw_affiliation_string":"XLIM, University of Limoges, Limoges, France","institution_ids":["https://openalex.org/I4210093397","https://openalex.org/I65806277"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034378743","display_name":"Mercedes Haiech","orcid":null},"institutions":[{"id":"https://openalex.org/I4210093397","display_name":"XLIM","ror":"https://ror.org/00f7srh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I32881790","https://openalex.org/I4210093397","https://openalex.org/I4210095849","https://openalex.org/I65806277"]},{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mercedes Haiech","raw_affiliation_strings":["XLIM, University of Limoges, Limoges, France"],"affiliations":[{"raw_affiliation_string":"XLIM, University of Limoges, Limoges, France","institution_ids":["https://openalex.org/I4210093397","https://openalex.org/I65806277"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5092491315","display_name":"Romaric Neveu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210093397","display_name":"XLIM","ror":"https://ror.org/00f7srh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I32881790","https://openalex.org/I4210093397","https://openalex.org/I4210095849","https://openalex.org/I65806277"]},{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Romaric Neveu","raw_affiliation_strings":["XLIM, University of Limoges, Limoges, France"],"affiliations":[{"raw_affiliation_string":"XLIM, University of Limoges, Limoges, France","institution_ids":["https://openalex.org/I4210093397","https://openalex.org/I65806277"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5092491315"],"corresponding_institution_ids":["https://openalex.org/I4210093397","https://openalex.org/I65806277"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.90428147,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"94","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.5494999885559082,"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/T10237","display_name":"Cryptography and Data Security","score":0.5494999885559082,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.11749999970197678,"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":0.09799999743700027,"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/equivalence","display_name":"Equivalence (formal languages)","score":0.5555999875068665},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.5450000166893005},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.46070000529289246},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43479999899864197},{"id":"https://openalex.org/keywords/hamming-bound","display_name":"Hamming bound","score":0.3919999897480011},{"id":"https://openalex.org/keywords/hamming-graph","display_name":"Hamming graph","score":0.3711000084877014},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.3601999878883362}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7098000049591064},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5555999875068665},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.5450000166893005},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.46070000529289246},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43479999899864197},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.3919999897480011},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37720000743865967},{"id":"https://openalex.org/C29696283","wikidata":"https://www.wikidata.org/wiki/Q369440","display_name":"Hamming graph","level":5,"score":0.3711000084877014},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.3601999878883362},{"id":"https://openalex.org/C112932734","wikidata":"https://www.wikidata.org/wiki/Q2322550","display_name":"Hamming(7,4)","level":5,"score":0.34630000591278076},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2969000041484833},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.288100004196167},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C61987429","wikidata":"https://www.wikidata.org/wiki/Q3064355","display_name":"M-matrix","level":3,"score":0.2773999869823456},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26829999685287476},{"id":"https://openalex.org/C90230998","wikidata":"https://www.wikidata.org/wiki/Q3406746","display_name":"Hadamard product","level":3,"score":0.2513999938964844},{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.250900000333786}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10623-026-01836-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-026-01836-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-026-01836-8.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10623-026-01836-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-026-01836-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-026-01836-8.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320337210","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7147693889.pdf","grobid_xml":"https://content.openalex.org/works/W7147693889.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W90698540","https://openalex.org/W1527005907","https://openalex.org/W1589034595","https://openalex.org/W2082432729","https://openalex.org/W2119117325","https://openalex.org/W2140204181","https://openalex.org/W2156052684","https://openalex.org/W2168676717","https://openalex.org/W2593199740","https://openalex.org/W2889463786","https://openalex.org/W2891063150","https://openalex.org/W3003231116","https://openalex.org/W3214573664","https://openalex.org/W3214651532","https://openalex.org/W4312296614","https://openalex.org/W4365936127","https://openalex.org/W4377082027","https://openalex.org/W4384010644","https://openalex.org/W4385648276","https://openalex.org/W4387623737","https://openalex.org/W4389843994","https://openalex.org/W4390672596","https://openalex.org/W4392742631","https://openalex.org/W4396509812","https://openalex.org/W4399477263","https://openalex.org/W4401753138","https://openalex.org/W4405207973","https://openalex.org/W4405263008","https://openalex.org/W4408238662","https://openalex.org/W4411365431"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Nowadays,":[1],"equivalence":[2,37,45,180],"problems":[3],"are":[4],"widely":[5],"used":[6],"in":[7,28,48,177,189,207,259],"cryptography,":[8],"most":[9,24],"notably":[10],"to":[11,71,79,89,96,119,128,156,201,302,325],"establish":[12],"cryptosystems":[13],"such":[14],"as":[15,22,186],"digital":[16],"signatures,":[17],"with":[18,167,214,236,283,297],"MEDS,":[19,303],"LESS,":[20],"PERK":[21],"the":[23,29,35,43,49,60,66,75,90,113,120,133,138,145,151,157,171,178,184,190,197,208,215,260,304,311,314,337,340],"recent":[25],"ones.":[26],"However,":[27],"context":[30],"of":[31,137,196,217,227,240,262,287,313,316,339],"matrix":[32,134],"codes,":[33],"only":[34],"code":[36,102,135,179],"problem":[38,155],"has":[39],"been":[40],"studied,":[41],"while":[42],"subcode":[44,106,158],"is":[46,126,183,306,334],"well-defined":[47],"Hamming":[50,121,191],"metric.":[51,192],"In":[52,273],"this":[53,168,275],"work,":[54],"we":[55,73,110,161,222,309],"introduce":[56],"two":[57],"new":[58,85,270,276],"problems:":[59],"Matrix":[61,68,91,114,152,209],"Subcode":[62,69,115,122],"Equivalence":[63,93,116,123,154,211],"Problem":[64,117],"and":[65,104,147,160,308,318],"Inhomogeneous":[67],"Problem,":[70],"which":[72,125,182,256],"apply":[74],"Multi-Party-Computation-in-the-Head":[76],"(MPCitH)":[77],"paradigm":[78],"build":[80],"a":[81,101,105,224,237,252,269,284,322,330],"signature":[82,225,254,264,277,293,299,305,317,331,342],"scheme.":[83,343],"These":[84],"problems,":[86],"closely":[87],"related":[88],"Code":[92,153,210],"problem,":[94,124],"ask":[95],"find":[97,166],"an":[98],"isometry":[99],"given":[100],"C":[103],"D":[107],".":[108],"Furthermore,":[109],"prove":[111],"that":[112,170,333],"reduces":[118],"known":[127],"be":[129],"NP-Complete,":[130],"thus":[131,250],"introducing":[132],"version":[136],"Permuted":[139],"Kernel":[140],"Problem.":[141],"We":[142,165,249,327],"also":[143,295,328],"adapt":[144],"combinatorial":[146],"algebraic":[148],"algorithms":[149,172],"for":[150],"case,":[159,181],"analyze":[162],"their":[163],"complexities.":[164],"analysis":[169,195],"perform":[173],"much":[174,204],"worse":[175],"than":[176,206,281],"same":[185],"what":[187],"happens":[188],"Finally,":[193],"our":[194],"attacks":[198],"allows":[199],"us":[200],"take":[202],"parameters":[203],"smaller":[205,285],"case.":[212],"Coupled":[213],"effectiveness":[216],"Threshold-Computation-in-the-Head":[218],"or":[219],"VOLE-in-the-Head":[220],",":[221],"obtain":[223,251,329],"size":[226,286,312,332,338],"$$\\approx":[228,241],"$$":[229,242],"<mml:math":[230,243],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[231,244],"<mml:mo>\u2248</mml:mo>":[232,245],"</mml:math>":[233,246],"4800":[234],"Bytes,":[235],"public":[238,288,319],"key":[239,289,320],"275":[247],"Bytes.":[248],"reasonable":[253],"size,":[255],"brings":[257],"diversity":[258],"landscape":[261],"post-quantum":[263],"schemes,":[265],"by":[266,321],"relying":[267],"on":[268],"hard":[271],"problem.":[272],"particular,":[274],"scheme":[278],"performs":[279],"better":[280],"SPHINCS+,":[282],"+":[290],"signature.":[291],"Our":[292],"compares":[294],"well":[296],"other":[298],"schemes:":[300],"compared":[301],"smaller,":[307],"reduced":[310],"sum":[315],"factor":[323],"close":[324],"5.":[326],"almost":[335],"half":[336],"CROSS":[341]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2026-04-02T00:00:00"}
