{"id":"https://openalex.org/W4409254287","doi":"https://doi.org/10.62056/abksdk5vt","title":"A divide-and-conquer sumcheck protocol","display_name":"A divide-and-conquer sumcheck protocol","publication_year":2025,"publication_date":"2025-04-08","ids":{"openalex":"https://openalex.org/W4409254287","doi":"https://doi.org/10.62056/abksdk5vt"},"language":"en","primary_location":{"id":"doi:10.62056/abksdk5vt","is_oa":true,"landing_page_url":"https://doi.org/10.62056/abksdk5vt","pdf_url":null,"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://doi.org/10.62056/abksdk5vt","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028512470","display_name":"Christophe Levrat","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Christophe Levrat","raw_affiliation_strings":["INRIA Saclay, Palaiseau"],"raw_orcid":"https://orcid.org/0009-0004-9768-5786","affiliations":[{"raw_affiliation_string":"INRIA Saclay, Palaiseau","institution_ids":["https://openalex.org/I4210126360","https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116017495","display_name":"Tanguy Medevielle","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210161663","display_name":"Institut de recherche math\u00e9matique de Rennes","ror":"https://ror.org/05y76vp22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2800285241","https://openalex.org/I28221208","https://openalex.org/I3124938446","https://openalex.org/I4210117091","https://openalex.org/I4210141950","https://openalex.org/I4210146044","https://openalex.org/I4210161663","https://openalex.org/I4399657933","https://openalex.org/I56067802","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Tanguy Medevielle","raw_affiliation_strings":["Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000"],"raw_orcid":"https://orcid.org/0009-0004-0872-5265","affiliations":[{"raw_affiliation_string":"Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000","institution_ids":["https://openalex.org/I56067802","https://openalex.org/I1294671590","https://openalex.org/I4210161663"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081157195","display_name":"Jade Nardi","orcid":"https://orcid.org/0000-0003-0901-7266"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210161663","display_name":"Institut de recherche math\u00e9matique de Rennes","ror":"https://ror.org/05y76vp22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2800285241","https://openalex.org/I28221208","https://openalex.org/I3124938446","https://openalex.org/I4210117091","https://openalex.org/I4210141950","https://openalex.org/I4210146044","https://openalex.org/I4210161663","https://openalex.org/I4399657933","https://openalex.org/I56067802","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jade Nardi","raw_affiliation_strings":["Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000"],"raw_orcid":"https://orcid.org/0000-0003-0901-7266","affiliations":[{"raw_affiliation_string":"Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000","institution_ids":["https://openalex.org/I56067802","https://openalex.org/I1294671590","https://openalex.org/I4210161663"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5028512470"],"corresponding_institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"],"apc_list":null,"apc_paid":null,"fwci":2.057,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.87389378,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"2","issue":"1","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":1.0,"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":1.0,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9966999888420105,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/divide-and-conquer-algorithms","display_name":"Divide and conquer algorithms","score":0.8359090089797974},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5683945417404175},{"id":"https://openalex.org/keywords/protocol","display_name":"Protocol (science)","score":0.5236061215400696},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.18440350890159607},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.15768718719482422}],"concepts":[{"id":"https://openalex.org/C71559656","wikidata":"https://www.wikidata.org/wiki/Q671298","display_name":"Divide and conquer algorithms","level":2,"score":0.8359090089797974},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5683945417404175},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.5236061215400696},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.18440350890159607},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.15768718719482422},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.0},{"id":"https://openalex.org/C204787440","wikidata":"https://www.wikidata.org/wiki/Q188504","display_name":"Alternative medicine","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.62056/abksdk5vt","is_oa":true,"landing_page_url":"https://doi.org/10.62056/abksdk5vt","pdf_url":null,"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"},{"id":"pmh:oai:HAL:hal-05010610v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05010610","pdf_url":"https://hal.science/hal-05010610/document","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://cic.iacr.org/","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.62056/abksdk5vt","is_oa":true,"landing_page_url":"https://doi.org/10.62056/abksdk5vt","pdf_url":null,"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":[],"awards":[{"id":"https://openalex.org/G3355261338","display_name":null,"funder_award_id":"ANR-21-CE39-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3597637701","display_name":null,"funder_award_id":"ANR-11-LABX-0020","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4830050000","display_name":null,"funder_award_id":"ANR-11-LABX-0020-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6142105111","display_name":null,"funder_award_id":"11-LABX-0020-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1599026900","https://openalex.org/W1909324101","https://openalex.org/W1968245619","https://openalex.org/W1970606468","https://openalex.org/W2053086236","https://openalex.org/W2071520502","https://openalex.org/W2080132708","https://openalex.org/W2082647621","https://openalex.org/W2536319456","https://openalex.org/W2883585522","https://openalex.org/W2885314357","https://openalex.org/W2898776076","https://openalex.org/W2902191010","https://openalex.org/W2954625838","https://openalex.org/W2968027060","https://openalex.org/W2990120385","https://openalex.org/W3159039187","https://openalex.org/W3213340422","https://openalex.org/W4233056417","https://openalex.org/W4312903934","https://openalex.org/W4385654262","https://openalex.org/W4385659358","https://openalex.org/W4390098323","https://openalex.org/W4401599157","https://openalex.org/W4403207914"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2352794675","https://openalex.org/W1539994214","https://openalex.org/W2051228988","https://openalex.org/W4247094814","https://openalex.org/W108531593","https://openalex.org/W2111712077","https://openalex.org/W8810113"],"abstract_inverted_index":{"We":[0,64,85],"present":[1,66],"a":[2,14,79,94,126],"new":[3],"sumcheck":[4,37],"protocol":[5],"called":[6],"Fold-DCS":[7,67],"(Fold-Divide-and-Conquer-Sumcheck)":[8],"for":[9],"multivariate":[10,54,80,95],"polynomials":[11],"based":[12],"on":[13],"divide-and-conquer":[15],"strategy.":[16],"Its":[17],"round":[18],"complexity":[19],"and":[20,46],"soundness":[21,47],"error":[22],"are":[23,32],"logarithmic":[24],"in":[25,34,42,68,91],"the":[26,35,50,69,73,107,119,123],"number":[27,43],"of":[28,44,52,106,118],"variables,":[29],"whereas":[30],"they":[31],"linear":[33],"classical":[36],"protocol.":[38],"This":[39],"drastic":[40],"improvement":[41],"rounds":[45],"comes":[48],"at":[49,82],"expense":[51],"exchanging":[53],"polynomials,":[55],"which":[56,112],"can":[57],"be":[58],"alleviated":[59],"using":[60],"polynomial":[61,81,96],"commitment":[62,97,109],"schemes.":[63],"first":[65],"PIOP":[70],"model,":[71],"where":[72],"prover":[74],"provides":[75],"oracle":[76,89],"access":[77,90],"to":[78,115],"each":[83],"round.":[84],"then":[86],"replace":[87,116],"this":[88,101],"practice":[92],"with":[93,102,125],"scheme;":[98],"we":[99],"illustrate":[100],"an":[103],"adapted":[104],"version":[105],"recent":[108],"scheme":[110],"Zeromorph,":[111],"allows":[113],"us":[114],"most":[117],"queries":[120],"made":[121],"by":[122],"verifier":[124],"single":[127],"batched":[128],"evaluation":[129],"check.":[130]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}
