{"id":"https://openalex.org/W4389011127","doi":"https://doi.org/10.1007/978-3-031-48621-0_14","title":"Multilinear Schwartz-Zippel Mod N and\u00a0Lattice-Based Succinct Arguments","display_name":"Multilinear Schwartz-Zippel Mod N and\u00a0Lattice-Based Succinct Arguments","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4389011127","doi":"https://doi.org/10.1007/978-3-031-48621-0_14"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-48621-0_14","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-48621-0_14","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-48621-0_14.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-48621-0_14.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050862609","display_name":"Benedikt B\u00fcnz","orcid":"https://orcid.org/0000-0003-2082-4480"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Benedikt B\u00fcnz","raw_affiliation_strings":["New York University, New York, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"New York University, New York, USA","institution_ids":["https://openalex.org/I57206974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037983878","display_name":"Ben Fisch","orcid":"https://orcid.org/0009-0007-1154-2277"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ben Fisch","raw_affiliation_strings":["Yale University, New Haven, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yale University, New Haven, USA","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050862609"],"corresponding_institution_ids":["https://openalex.org/I57206974"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.5593,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.91378223,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"394","last_page":"423"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9889000058174133,"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/T10270","display_name":"Blockchain Technology Applications and Security","score":0.987500011920929,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multilinear-map","display_name":"Multilinear map","score":0.807628870010376},{"id":"https://openalex.org/keywords/lattice-problem","display_name":"Lattice problem","score":0.6084365844726562},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5940143465995789},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5756658315658569},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5359576344490051},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.5184992551803589},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5001921653747559},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47768455743789673},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.46289458870887756},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.4615018963813782},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.45488834381103516},{"id":"https://openalex.org/keywords/zero-knowledge-proof","display_name":"Zero-knowledge proof","score":0.4389134347438812},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.43153342604637146},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4173923134803772},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19591209292411804},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19408509135246277},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17826223373413086},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12568342685699463},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.10257112979888916},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08759531378746033},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0872918963432312}],"concepts":[{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.807628870010376},{"id":"https://openalex.org/C168482242","wikidata":"https://www.wikidata.org/wiki/Q6497128","display_name":"Lattice problem","level":3,"score":0.6084365844726562},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5940143465995789},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5756658315658569},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5359576344490051},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.5184992551803589},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5001921653747559},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47768455743789673},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.46289458870887756},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.4615018963813782},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.45488834381103516},{"id":"https://openalex.org/C176329583","wikidata":"https://www.wikidata.org/wiki/Q191943","display_name":"Zero-knowledge proof","level":3,"score":0.4389134347438812},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.43153342604637146},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4173923134803772},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19591209292411804},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19408509135246277},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17826223373413086},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12568342685699463},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.10257112979888916},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08759531378746033},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0872918963432312},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-48621-0_14","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-48621-0_14","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-48621-0_14.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-48621-0_14","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-48621-0_14","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-48621-0_14.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[{"display_name":"Partnerships for the goals","score":0.4000000059604645,"id":"https://metadata.un.org/sdg/17"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389011127.pdf","grobid_xml":"https://content.openalex.org/works/W4389011127.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W39036742","https://openalex.org/W1599026900","https://openalex.org/W1985439922","https://openalex.org/W2026036943","https://openalex.org/W2038761522","https://openalex.org/W2080132708","https://openalex.org/W2473389213","https://openalex.org/W2612871929","https://openalex.org/W2794842518","https://openalex.org/W2883585522","https://openalex.org/W2883748642","https://openalex.org/W2885172320","https://openalex.org/W2967946631","https://openalex.org/W2990120385","https://openalex.org/W3013005985","https://openalex.org/W3031397331","https://openalex.org/W3031679272","https://openalex.org/W3037467273","https://openalex.org/W3147459559","https://openalex.org/W3159039187","https://openalex.org/W3159513901","https://openalex.org/W3164004061","https://openalex.org/W3187842930","https://openalex.org/W3192802957","https://openalex.org/W3204983216","https://openalex.org/W4211086354","https://openalex.org/W4298286978","https://openalex.org/W4312232931","https://openalex.org/W4312753175","https://openalex.org/W4317928254"],"related_works":["https://openalex.org/W2466303427","https://openalex.org/W2035793348","https://openalex.org/W1516766811","https://openalex.org/W2157568248","https://openalex.org/W2969705217","https://openalex.org/W2809883875","https://openalex.org/W2362245488","https://openalex.org/W2384324714","https://openalex.org/W2997604978","https://openalex.org/W2949331520"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-09T13:55:54.758798","created_date":"2025-10-10T00:00:00"}