{"id":"https://openalex.org/W4415502436","doi":"https://doi.org/10.1186/s13635-025-00218-2","title":"A fast method for finding separable Goppa polynomials used in post-quantum McEliece-based cryptography","display_name":"A fast method for finding separable Goppa polynomials used in post-quantum McEliece-based cryptography","publication_year":2025,"publication_date":"2025-10-24","ids":{"openalex":"https://openalex.org/W4415502436","doi":"https://doi.org/10.1186/s13635-025-00218-2"},"language":"en","primary_location":{"id":"doi:10.1186/s13635-025-00218-2","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13635-025-00218-2","pdf_url":"https://jis-eurasipjournals.springeropen.com/counter/pdf/10.1186/s13635-025-00218-2","source":{"id":"https://openalex.org/S5820498","display_name":"EURASIP Journal on Information Security","issn_l":"1687-4161","issn":["1687-4161","1687-417X","2510-523X"],"is_oa":true,"is_in_doaj":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Information Security","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://jis-eurasipjournals.springeropen.com/counter/pdf/10.1186/s13635-025-00218-2","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067557036","display_name":"Mariano L\u00f3pez-Garc\u00eda","orcid":"https://orcid.org/0000-0002-5556-233X"},"institutions":[{"id":"https://openalex.org/I4210133992","display_name":"Cidete (Spain)","ror":"https://ror.org/03v79p997","country_code":"ES","type":"company","lineage":["https://openalex.org/I4210133992"]},{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Mariano Lopez-Garcia","raw_affiliation_strings":["Electronic Engineering Department, Universitat Polit\u00e8cnica de Catalunya, Avda. Victor Balaguer 1, 08800, Vilanova i la Geltr\u00fa, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electronic Engineering Department, Universitat Polit\u00e8cnica de Catalunya, Avda. Victor Balaguer 1, 08800, Vilanova i la Geltr\u00fa, Spain","institution_ids":["https://openalex.org/I4210133992","https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020449505","display_name":"Enrique Cant\u00f3","orcid":"https://orcid.org/0000-0002-5674-4119"},"institutions":[{"id":"https://openalex.org/I55952717","display_name":"Universitat Rovira i Virgili","ror":"https://ror.org/00g5sqv46","country_code":"ES","type":"education","lineage":["https://openalex.org/I55952717"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Enrique Canto-Navarro","raw_affiliation_strings":["Electrical, Automatic and Electronic Engineering Department, Universitat Rovira i Virgili, Avda. Pa\u00efsos Catalans 26, 43007, Tarragona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical, Automatic and Electronic Engineering Department, Universitat Rovira i Virgili, Avda. Pa\u00efsos Catalans 26, 43007, Tarragona, Spain","institution_ids":["https://openalex.org/I55952717"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067557036"],"corresponding_institution_ids":["https://openalex.org/I4210133992","https://openalex.org/I9617848"],"apc_list":{"value":1040,"currency":"USD","value_usd":1040},"apc_paid":{"value":1040,"currency":"USD","value_usd":1040},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23271054,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2025","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9994999766349792,"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/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.6539000272750854},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.6319000124931335},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.555400013923645},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.47760000824928284},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4426000118255615},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.3869999945163727},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3783999979496002}],"concepts":[{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.6539000272750854},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.6319000124931335},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.555400013923645},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5013999938964844},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.47760000824928284},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4426000118255615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4189000129699707},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.3869999945163727},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.38109999895095825},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3783999979496002},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36739999055862427},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36090001463890076},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.34689998626708984},{"id":"https://openalex.org/C184297639","wikidata":"https://www.wikidata.org/wiki/Q177765","display_name":"Biometrics","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C16935551","wikidata":"https://www.wikidata.org/wiki/Q1042583","display_name":"McEliece cryptosystem","level":4,"score":0.3165000081062317},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.2815999984741211},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C92717368","wikidata":"https://www.wikidata.org/wiki/Q1162538","display_name":"Plaintext","level":3,"score":0.2502000033855438}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1186/s13635-025-00218-2","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13635-025-00218-2","pdf_url":"https://jis-eurasipjournals.springeropen.com/counter/pdf/10.1186/s13635-025-00218-2","source":{"id":"https://openalex.org/S5820498","display_name":"EURASIP Journal on Information Security","issn_l":"1687-4161","issn":["1687-4161","1687-417X","2510-523X"],"is_oa":true,"is_in_doaj":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Information Security","raw_type":"journal-article"},{"id":"pmh:oai:upcommons.upc.edu:2117/451581","is_oa":false,"landing_page_url":"https://hdl.handle.net/2117/451581","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:96c0d36e8e71456c97bd795dac8f2656","is_oa":true,"landing_page_url":"https://doaj.org/article/96c0d36e8e71456c97bd795dac8f2656","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"EURASIP Journal on Information Security, Vol 2025, Iss 1, Pp 1-15 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1186/s13635-025-00218-2","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13635-025-00218-2","pdf_url":"https://jis-eurasipjournals.springeropen.com/counter/pdf/10.1186/s13635-025-00218-2","source":{"id":"https://openalex.org/S5820498","display_name":"EURASIP Journal on Information Security","issn_l":"1687-4161","issn":["1687-4161","1687-417X","2510-523X"],"is_oa":true,"is_in_doaj":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Information Security","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G121809054","display_name":null,"funder_award_id":"MCIN/AEI/10","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G1855990336","display_name":null,"funder_award_id":".13039/501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2660406951","display_name":null,"funder_award_id":"/ AEI/10","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3690828678","display_name":null,"funder_award_id":"PID2019","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G425668148","display_name":null,"funder_award_id":".13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4910620720","display_name":null,"funder_award_id":"PID2019-107274RB-1000 and PID2023-148649OB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G5421974903","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8684520763","display_name":null,"funder_award_id":"PID2019","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415502436.pdf","grobid_xml":"https://content.openalex.org/works/W4415502436.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1508634734","https://openalex.org/W1521833188","https://openalex.org/W1574075570","https://openalex.org/W1770324186","https://openalex.org/W1851924232","https://openalex.org/W1942594900","https://openalex.org/W1990361074","https://openalex.org/W1999064382","https://openalex.org/W2032551902","https://openalex.org/W2066032081","https://openalex.org/W2084652510","https://openalex.org/W2092988036","https://openalex.org/W2098750211","https://openalex.org/W2102796633","https://openalex.org/W2126474167","https://openalex.org/W2136570131","https://openalex.org/W2165831888","https://openalex.org/W2167075312","https://openalex.org/W2195934234","https://openalex.org/W2313551285","https://openalex.org/W2740546450","https://openalex.org/W2795080420","https://openalex.org/W2962714692","https://openalex.org/W2964044544","https://openalex.org/W3006429091","https://openalex.org/W3159063726","https://openalex.org/W3168480899","https://openalex.org/W4240440526","https://openalex.org/W4285779221","https://openalex.org/W4293077480","https://openalex.org/W4294326404","https://openalex.org/W4313569892","https://openalex.org/W4321595467","https://openalex.org/W4394805051","https://openalex.org/W4400288226","https://openalex.org/W4401628456"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3,75],"simple":[4],"and":[5,89],"efficient":[6],"method":[7,64],"for":[8,83],"generating":[9],"Goppa":[10,70],"polynomials":[11,29,39,51,71],"used":[12],"in":[13],"post-quantum":[14],"cryptography":[15,88],"based":[16],"on":[17],"any":[18],"variant":[19],"of":[20,77,97,107],"the":[21,55,104,114,124],"McEliece":[22],"algorithm.":[23],"The":[24,62],"approach":[25],"demonstrates":[26],"that":[27,40,48,86,118],"such":[28],"can":[30,110],"be":[31,111],"constructed":[32],"more":[33],"rapidly":[34],"by":[35],"multiplying":[36],"several":[37],"low-degree":[38],"satisfy":[41],"specific":[42],"properties.":[43],"It":[44],"is":[45,65],"also":[46],"proven":[47],"employing":[49],"these":[50],"does":[52],"not":[53],"compromise":[54],"code\u2019s":[56],"error-correcting":[57],"capability":[58],"or":[59],"overall":[60],"security.":[61],"proposed":[63],"especially":[66],"advantageous":[67],"when":[68],"high-order":[69],"are":[72,100],"required.":[73],"As":[74],"proof":[76],"concept,":[78],"we":[79],"present":[80],"an":[81],"application":[82],"user":[84],"identification":[85],"combines":[87],"iris":[90,98],"biometrics.":[91],"In":[92],"this":[93],"system,":[94],"encrypted":[95,115],"versions":[96],"templates":[99],"securely":[101],"stored.":[102],"Using":[103],"homomorphic":[105],"property":[106],"McEliece,":[108],"recognition":[109],"performed":[112],"within":[113],"domain,":[116],"ensuring":[117],"biometric":[119],"data":[120],"remains":[121],"confidential":[122],"throughout":[123],"entire":[125],"process.":[126]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-24T00:00:00"}