{"id":"https://openalex.org/W2301137331","doi":null,"title":"Hybrid Approach : a Tool for Multivariate Cryptography","display_name":"Hybrid Approach : a Tool for Multivariate Cryptography","publication_year":2010,"publication_date":"2010-06-01","ids":{"openalex":"https://openalex.org/W2301137331","mag":"2301137331"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.592.7724","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.592.7724","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"http://www-polsys.lip6.fr/~jcf/Papers/Tools2010b.pdf","raw_type":"text"},"volume":null,"type":"article","indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086790117","display_name":"Luk Bettale","orcid":"https://orcid.org/0000-0002-8799-8568","observed_orcids":["https://orcid.org/0000-0002-8799-8568"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luk Bettale","raw_affiliation_strings":["Solvers for Algebraic Systems and Applications"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Solvers for Algebraic Systems and Applications","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107405594","display_name":"Jean\u2010Charles Faug\u00e8re","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jean-charles Faug\u00e8re","raw_affiliation_strings":["Solvers for Algebraic Systems and Applications"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Solvers for Algebraic Systems and Applications","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109853693","display_name":"Ludovic Perret","orcid":"https://orcid.org/0009-0005-7453-8705","observed_orcids":["https://orcid.org/0009-0005-7453-8705"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ludovic Perret","raw_affiliation_strings":["Solvers for Algebraic Systems and Applications"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Solvers for Algebraic Systems and Applications","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3223,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.65692448,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.8960000276565552,"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":0.8960000276565552,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.04560000076889992,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.032999999821186066,"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/multivariate-cryptography","display_name":"multivariate public-key cryptography","score":0.8569999933242798},{"id":"https://openalex.org/keywords/cryptanalysis","display_name":"cryptanalysis","score":0.9430000185966492},{"id":"https://openalex.org/keywords/multivariate-polynomial-systems","display_name":"multivariate polynomial systems","score":0.6639999747276306},{"id":"https://openalex.org/keywords/grobner-bases","display_name":"Gr\u00f6bner bases","score":0.9150000214576721},{"id":"https://openalex.org/keywords/exhaustive-search","display_name":"exhaustive search","score":0.9470000267028809},{"id":"https://openalex.org/keywords/signature-forgery","display_name":"signature forgery","score":0.7549999952316284},{"id":"https://openalex.org/keywords/parameter-calibration","display_name":"parameter calibration","score":0.6539999842643738},{"id":"https://openalex.org/keywords/higher-degree-polynomials","display_name":"higher-degree polynomials","score":0.7789999842643738}],"concepts":[{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.6937131285667419},{"id":"https://openalex.org/C181149355","wikidata":"https://www.wikidata.org/wiki/Q897511","display_name":"Cryptanalysis","level":3,"score":0.690371572971344},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6729217767715454},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5943917036056519},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5508459210395813},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5333725214004517},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.5307443141937256},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.520216166973114},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.48638203740119934},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.4482837915420532},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44054895639419556},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.42818787693977356},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3905591666698456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3060561418533325},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.10115128755569458},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.592.7724","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.592.7724","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"http://www-polsys.lip6.fr/~jcf/Papers/Tools2010b.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01288901v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-01288901","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Tools'10: the Workshop on Tools for Cryptanalysis 2010, Jun 2010, London, United Kingdom. pp.15-23","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W137478731","https://openalex.org/W2029317328","https://openalex.org/W2059522106","https://openalex.org/W2131218687","https://openalex.org/W2151199568"],"related_works":["https://openalex.org/W4312813683","https://openalex.org/W2965484163","https://openalex.org/W4232705780","https://openalex.org/W2225318093","https://openalex.org/W2512006651","https://openalex.org/W4384027664","https://openalex.org/W2025209850","https://openalex.org/W2011670317","https://openalex.org/W2095023645","https://openalex.org/W2096221836"],"abstract_inverted_index":{"Abstract.":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,183],"present":[5,164],"an":[6,48,165],"algorithmic":[7],"tool":[8,146],"to":[9,29,88,98,147],"cryptanalysis":[10,77],"multivariate":[11,31,80,153],"cryptosystems.":[12],"The":[13],"presented":[14],"algorithm":[15,119,142],"is":[16,47,61,120,125,138],"a":[17,35,100,144,185],"hybrid":[18,170],"approach":[19,72,96],"that":[20,85],"mixes":[21],"exhaustive":[22,110],"search":[23,111],"with":[24,109,114],"classical":[25],"Gr\u00f6bner":[26,116],"bases":[27],"computation":[28],"solve":[30],"polynomial":[32],"systems":[33,129],"over":[34],"finite":[36],"field.":[37],"Depending":[38],"on":[39,50,67,93,127],"the":[40,43,68,133,136,149],"size":[41],"of":[42,56,70,78,107,130,135,151,168,175],"field,":[44],"our":[45,59,71,95,141,169,181],"method":[46,60],"improvement":[49],"existing":[51],"techniques.":[52],"For":[53,91],"usual":[54],"parameters":[55,150],"multivari-ate":[57],"schemes,":[58],"effective.":[62],"We":[63,162],"give":[64],"theoretical":[65],"evidences":[66],"efficiency":[69,124],"as":[73,75,122],"well":[74],"practical":[76],"several":[79],"signature":[81,102],"schemes":[82],"(TRMS,":[83],"UOV)":[84],"were":[86,157],"considered":[87],"be":[89],"secure.":[90],"instance,":[92],"TRMS,":[94],"allow":[97],"forge":[99],"valid":[101],"in":[103,160],"267":[104],"operations":[105],"instead":[106],"2160":[108],"or":[112],"283":[113],"only":[115],"bases.":[117],"Our":[118],"general":[121],"its":[123],"demonstrated":[126],"random":[128],"equations.":[131],"As":[132],"structure":[134],"cryptosystem":[137],"not":[139],"involved,":[140],"provides":[143],"generic":[145],"calibrate":[148],"any":[152],"scheme.":[154],"These":[155],"results":[156],"already":[158],"published":[159],"[5].":[161],"also":[163],"extended":[166],"version":[167],"approach,":[171],"suitable":[172],"for":[173],"polynomials":[174],"higher":[176],"degree.":[177],"To":[178],"easily":[179],"access":[180],"tools,":[182],"pro-vide":[184],"MAGMA":[186],"package":[187],"available":[188],"at":[189]},"counts_by_year":[],"updated_date":"2026-09-27T08:07:27.782135","created_date":"2025-10-10T00:00:00"}
