{"id":"https://openalex.org/W2971070390","doi":"https://doi.org/10.1515/jmc-2020-0077","title":"The Eleventh Power Residue Symbol","display_name":"The Eleventh Power Residue Symbol","publication_year":2020,"publication_date":"2020-11-17","ids":{"openalex":"https://openalex.org/W2971070390","doi":"https://doi.org/10.1515/jmc-2020-0077","mag":"2971070390"},"language":"en","primary_location":{"id":"doi:10.1515/jmc-2020-0077","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2020-0077","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2020-0077/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2020-0077/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074996766","display_name":"Marc J\u00f3ye","orcid":"https://orcid.org/0000-0003-4433-2333"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Marc Joye","raw_affiliation_strings":["Zama , Paris , France"],"affiliations":[{"raw_affiliation_string":"Zama , Paris , France","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110730807","display_name":"Oleksandra Lapiha","orcid":null},"institutions":[{"id":"https://openalex.org/I4210162280","display_name":"Laboratoire de G\u00e9ologie de l\u2019\u00c9cole Normale Sup\u00e9rieure","ror":"https://ror.org/05vg9cw43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I4210148025","https://openalex.org/I4210162280"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Oleksandra Lapiha","raw_affiliation_strings":["\u00c9cole normale sup\u00e9rieure , Paris , France",",\u00c9cole Normale Sup\u00e9rieure, Paris, France#TAB#"],"affiliations":[{"raw_affiliation_string":"\u00c9cole normale sup\u00e9rieure , Paris , France","institution_ids":["https://openalex.org/I4210162280"]},{"raw_affiliation_string":",\u00c9cole Normale Sup\u00e9rieure, Paris, France#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030914695","display_name":"Ky Nguyen","orcid":"https://orcid.org/0000-0002-3867-4209"},"institutions":[{"id":"https://openalex.org/I4210162280","display_name":"Laboratoire de G\u00e9ologie de l\u2019\u00c9cole Normale Sup\u00e9rieure","ror":"https://ror.org/05vg9cw43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I4210148025","https://openalex.org/I4210162280"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ky Nguyen","raw_affiliation_strings":["\u00c9cole normale sup\u00e9rieure , Paris , France",",\u00c9cole Normale Sup\u00e9rieure, Paris, France#TAB#"],"affiliations":[{"raw_affiliation_string":"\u00c9cole normale sup\u00e9rieure , Paris , France","institution_ids":["https://openalex.org/I4210162280"]},{"raw_affiliation_string":",\u00c9cole Normale Sup\u00e9rieure, Paris, France#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112710845","display_name":"David Naccache","orcid":"https://orcid.org/0000-0002-8651-6555"},"institutions":[{"id":"https://openalex.org/I4210162280","display_name":"Laboratoire de G\u00e9ologie de l\u2019\u00c9cole Normale Sup\u00e9rieure","ror":"https://ror.org/05vg9cw43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I4210148025","https://openalex.org/I4210162280"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"David Naccache","raw_affiliation_strings":["\u00c9cole normale sup\u00e9rieure , Paris , France",",\u00c9cole Normale Sup\u00e9rieure, Paris, France#TAB#"],"affiliations":[{"raw_affiliation_string":"\u00c9cole normale sup\u00e9rieure , Paris , France","institution_ids":["https://openalex.org/I4210162280"]},{"raw_affiliation_string":",\u00c9cole Normale Sup\u00e9rieure, Paris, France#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5074996766"],"corresponding_institution_ids":[],"apc_list":{"value":1000,"currency":"EUR","value_usd":1078},"apc_paid":{"value":1000,"currency":"EUR","value_usd":1078},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00623307,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"1","first_page":"111","last_page":"122"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.8680999875068665,"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"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.8680999875068665,"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/T10237","display_name":"Cryptography and Data Security","score":0.03970000147819519,"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/T11130","display_name":"Coding theory and cryptography","score":0.03550000116229057,"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/eleventh","display_name":"Eleventh","score":0.9130682945251465},{"id":"https://openalex.org/keywords/residue","display_name":"Residue (chemistry)","score":0.7249813079833984},{"id":"https://openalex.org/keywords/symbol","display_name":"Symbol (formal)","score":0.5299378633499146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49372872710227966},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4478154182434082},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.40488722920417786},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3517313003540039},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.13292571902275085},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11888304352760315},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09222900867462158}],"concepts":[{"id":"https://openalex.org/C2779796141","wikidata":"https://www.wikidata.org/wiki/Q1930430","display_name":"Eleventh","level":2,"score":0.9130682945251465},{"id":"https://openalex.org/C2781338088","wikidata":"https://www.wikidata.org/wiki/Q903495","display_name":"Residue (chemistry)","level":2,"score":0.7249813079833984},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.5299378633499146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49372872710227966},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4478154182434082},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.40488722920417786},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3517313003540039},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.13292571902275085},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11888304352760315},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09222900867462158},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/jmc-2020-0077","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2020-0077","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2020-0077/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},{"id":"mag:2971070390","is_oa":false,"landing_page_url":"https://eprint.iacr.org/2019/870.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2764847869","display_name":"IACR Cryptology ePrint Archive","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":["https://openalex.org/P4322614454"],"host_organization_lineage_names":["Cryptology ePrint Archive"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Cryptology ePrint Archive","raw_type":null}],"best_oa_location":{"id":"doi:10.1515/jmc-2020-0077","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2020-0077","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2020-0077/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2971070390.pdf","grobid_xml":"https://content.openalex.org/works/W2971070390.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1536619066","https://openalex.org/W2024918898","https://openalex.org/W2039316044","https://openalex.org/W2043823960","https://openalex.org/W2052806472","https://openalex.org/W2090015297","https://openalex.org/W2093850334","https://openalex.org/W2152971985","https://openalex.org/W2736884784","https://openalex.org/W2783802424","https://openalex.org/W4210300416","https://openalex.org/W4230210810","https://openalex.org/W4251872739","https://openalex.org/W6816014058"],"related_works":["https://openalex.org/W2982644245","https://openalex.org/W2481351478","https://openalex.org/W2319104924","https://openalex.org/W2314068679","https://openalex.org/W2316986633","https://openalex.org/W2807810044","https://openalex.org/W278524583","https://openalex.org/W3036742354","https://openalex.org/W2887334276","https://openalex.org/W2986651339","https://openalex.org/W2262444255","https://openalex.org/W3026825838","https://openalex.org/W2515102960","https://openalex.org/W2820498674","https://openalex.org/W2800565850","https://openalex.org/W2330452458"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"presents":[3],"an":[4,55],"efficient":[5],"algorithm":[6,57,77],"for":[7,68],"computing":[8],"11":[9,44,48],"th":[10,49,71],"-power":[11,72],"residue":[12,73],"symbols":[13],"in":[14,80],"the":[15,69,81],"cyclo-tomic":[16],"field":[17],"<m:math":[18],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[19],"<m:mrow>":[20,22,24,27],"<m:mi>\u211a</m:mi>":[21],"<m:mo>(</m:mo>":[23],"<m:msub>":[25],"<m:mi>\u03b6</m:mi>":[26],"<m:mn>11</m:mn>":[28],"</m:mrow>":[29,31,33,35],"</m:msub>":[30],"<m:mo>)</m:mo>":[32],"<m:mo>,</m:mo>":[34],"</m:math>":[36],"$":[37,42],"\\mathbb{Q}\\left(":[38],"{{\\zeta":[39],"}_{11}}":[40],"\\right),":[41],"where":[43],"is":[45],"a":[46],"primitive":[47],"root":[50],"of":[51,83],"unity.":[52],"It":[53],"extends":[54],"earlier":[56],"due":[58],"to":[59],"Caranay":[60],"and":[61],"Scheidler":[62],"(Int.":[63],"J.":[64],"Number":[65],"Theory,":[66],"2010)":[67],"7":[70],"symbol.":[74],"The":[75],"new":[76],"finds":[78],"applications":[79],"implementation":[82],"certain":[84],"cryptographic":[85],"schemes.":[86]},"counts_by_year":[],"updated_date":"2026-03-17T09:09:15.849793","created_date":"2025-10-10T00:00:00"}
