{"id":"https://openalex.org/W7130532392","doi":"https://doi.org/10.48550/arxiv.2602.16156","title":"Weak Zero-Knowledge and One-Way Functions","display_name":"Weak Zero-Knowledge and One-Way Functions","publication_year":2026,"publication_date":"2026-02-18","ids":{"openalex":"https://openalex.org/W7130532392","doi":"https://doi.org/10.48550/arxiv.2602.16156"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.16156","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123631769","display_name":"Rohit Chatterjee","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chatterjee, Rohit","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126384529","display_name":"Yunqi Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yunqi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032319697","display_name":"Prashant Nalini Vasudevan","orcid":"https://orcid.org/0000-0001-6880-795X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vasudevan, Prashant Nalini","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"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/T10237","display_name":"Cryptography and Data Security","score":0.5112000107765198,"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":0.5112000107765198,"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":0.1784999966621399,"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":0.11050000041723251,"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/mathematical-proof","display_name":"Mathematical proof","score":0.9049999713897705},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5365999937057495},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33250001072883606},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.33250001072883606},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.3319000005722046},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.31130000948905945}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.9049999713897705},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7031000256538391},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5365999937057495},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4611999988555908},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33250001072883606},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.33250001072883606},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.31130000948905945},{"id":"https://openalex.org/C105355099","wikidata":"https://www.wikidata.org/wiki/Q720931","display_name":"One-way function","level":3,"score":0.25780001282691956},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2554999887943268},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2522999942302704},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2515000104904175},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.16156","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.16156","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.16156","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.16156","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,5,38,50,119],"implications":[3],"of":[4,7],"existence":[6],"weak":[8],"Zero-Knowledge":[9],"(ZK)":[10],"protocols":[11,18],"for":[12,81,157],"worst-case":[13,43],"hard":[14,44],"languages.":[15],"These":[16],"are":[17,42,111],"that":[19,32,40,88],"have":[20,58,94,105,139,165],"completeness,":[21],"soundness,":[22],"and":[23,29,98],"zero-knowledge":[24],"errors":[25,110],"(denoted":[26],"$\u03b5_c$,":[27],"$\u03b5_s$,":[28],"$\u03b5_z$,":[30],"respectively)":[31],"might":[33],"not":[34],"be":[35],"negligible.":[36,112],"Under":[37],"assumption":[39],"there":[41],"languages":[45,55,91,136,162],"in":[46,56,92,137,163],"NP,":[47],"we":[48],"show":[49],"following:":[51],"1.":[52],"If":[53,134],"all":[54,77,90,109,135,161],"NP":[57,93,138,164],"NIZK":[59,96,106],"proofs":[60,97,107,143,169],"or":[61,144,170],"arguments":[62,145,171],"satisfying":[63,146,172],"$":[64,123,127,147,173],"\u03b5_c+\u03b5_s+":[65],"\u03b5_z":[66],"&lt;":[67,125,149,175],"1":[68,126,150,176],"$,":[69,151,177],"then":[70,102,152,178],"One-Way":[71],"Functions":[72],"(OWFs)":[73],"exist.":[74,154,181],"This":[75],"covers":[76],"possible":[78],"non-trivial":[79],"values":[80],"these":[82,114],"error":[83],"rates.":[84],"It":[85],"additionally":[86],"implies":[87],"if":[89],"such":[95],"$\u03b5_c$":[99],"is":[100],"negligible,":[101],"they":[103],"also":[104],"where":[108],"Previously,":[113],"results":[115],"were":[116],"known":[117],"under":[118],"more":[120],"restrictive":[121],"condition":[122],"\u03b5_c+\\sqrt{\u03b5_s}+\u03b5_z":[124],"[Chakraborty":[128],"et":[129],"al.,":[130],"CRYPTO":[131],"2025].":[132],"2.":[133],"$k$-round":[140,166],"public-coin":[141,167],"ZK":[142,168],"\u03b5_c+\u03b5_s+(2k-1).\u03b5_z":[148],"OWFs":[153,180],"3.":[155],"If,":[156],"some":[158],"constant":[159],"$k$,":[160],"\u03b5_c+\u03b5_s+k.\u03b5_z":[174],"infinitely-often":[179]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-02-20T00:00:00"}
