{"id":"https://openalex.org/W1593955619","doi":"https://doi.org/10.1007/978-3-642-34961-4_40","title":"Commitments and Efficient Zero-Knowledge Proofs from Learning Parity with Noise","display_name":"Commitments and Efficient Zero-Knowledge Proofs from Learning Parity with Noise","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1593955619","doi":"https://doi.org/10.1007/978-3-642-34961-4_40","mag":"1593955619"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-34961-4_40","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-34961-4_40","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100661347","display_name":"Abhishek Jain","orcid":"https://orcid.org/0000-0002-3572-7643"},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Abhishek Jain","raw_affiliation_strings":["Boston University, USA","Massachusetts Institute of Technology, USA"],"affiliations":[{"raw_affiliation_string":"Boston University, USA","institution_ids":["https://openalex.org/I111088046"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042762529","display_name":"Stephan Krenn","orcid":"https://orcid.org/0000-0003-2835-9093"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Stephan Krenn","raw_affiliation_strings":["Institute of Science and Technology, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Science and Technology, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103200276","display_name":"Krzysztof Pietrzak","orcid":"https://orcid.org/0000-0002-9139-1654"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Krzysztof Pietrzak","raw_affiliation_strings":["Institute of Science and Technology, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Science and Technology, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072982334","display_name":"Aris Tentes","orcid":null},"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":false,"raw_author_name":"Aris Tentes","raw_affiliation_strings":["Department of Computer Science, New York University, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, New York University, USA","institution_ids":["https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100661347"],"corresponding_institution_ids":["https://openalex.org/I111088046","https://openalex.org/I63966007"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":5.7094,"has_fulltext":false,"cited_by_count":105,"citation_normalized_percentile":{"value":0.96558429,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"663","last_page":"680"},"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":0.9968000054359436,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9825999736785889,"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/zero-knowledge-proof","display_name":"Zero-knowledge proof","score":0.8329950571060181},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.7390628457069397},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7359152436256409},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5502576231956482},{"id":"https://openalex.org/keywords/security-parameter","display_name":"Security parameter","score":0.5418875813484192},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.5195387005805969},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.47154903411865234},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4626838266849518},{"id":"https://openalex.org/keywords/communication-complexity","display_name":"Communication complexity","score":0.44348955154418945},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.43539297580718994},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.431228369474411},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.41855743527412415},{"id":"https://openalex.org/keywords/learning-with-errors","display_name":"Learning with errors","score":0.4167737066745758},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37276381254196167},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.31506654620170593},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09766384959220886},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07144877314567566}],"concepts":[{"id":"https://openalex.org/C176329583","wikidata":"https://www.wikidata.org/wiki/Q191943","display_name":"Zero-knowledge proof","level":3,"score":0.8329950571060181},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.7390628457069397},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7359152436256409},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5502576231956482},{"id":"https://openalex.org/C2776711565","wikidata":"https://www.wikidata.org/wiki/Q7445058","display_name":"Security parameter","level":3,"score":0.5418875813484192},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.5195387005805969},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.47154903411865234},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4626838266849518},{"id":"https://openalex.org/C179145077","wikidata":"https://www.wikidata.org/wiki/Q5154130","display_name":"Communication complexity","level":2,"score":0.44348955154418945},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.43539297580718994},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.431228369474411},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41855743527412415},{"id":"https://openalex.org/C2779014939","wikidata":"https://www.wikidata.org/wiki/Q6510239","display_name":"Learning with errors","level":3,"score":0.4167737066745758},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37276381254196167},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.31506654620170593},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09766384959220886},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07144877314567566},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-34961-4_40","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-34961-4_40","pdf_url":null,"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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W139987668","https://openalex.org/W198033559","https://openalex.org/W1484557542","https://openalex.org/W1495716978","https://openalex.org/W1512460175","https://openalex.org/W1527005907","https://openalex.org/W1529679142","https://openalex.org/W1555780274","https://openalex.org/W1572614022","https://openalex.org/W1574535057","https://openalex.org/W1582538828","https://openalex.org/W1593955619","https://openalex.org/W1817312375","https://openalex.org/W1856342626","https://openalex.org/W1970808997","https://openalex.org/W1980227445","https://openalex.org/W1984685443","https://openalex.org/W1993729573","https://openalex.org/W1995897489","https://openalex.org/W2001841415","https://openalex.org/W2027471022","https://openalex.org/W2035929826","https://openalex.org/W2037038890","https://openalex.org/W2049761975","https://openalex.org/W2055863940","https://openalex.org/W2061949491","https://openalex.org/W2065151783","https://openalex.org/W2067596507","https://openalex.org/W2068189841","https://openalex.org/W2100847176","https://openalex.org/W2113333997","https://openalex.org/W2125903279","https://openalex.org/W2130389396","https://openalex.org/W2134409266","https://openalex.org/W2141395382","https://openalex.org/W2150624282","https://openalex.org/W2160584199","https://openalex.org/W2283002900","https://openalex.org/W2990399857"],"related_works":["https://openalex.org/W2466303427","https://openalex.org/W1516766811","https://openalex.org/W2157568248","https://openalex.org/W2969705217","https://openalex.org/W2809883875","https://openalex.org/W2362245488","https://openalex.org/W2035793348","https://openalex.org/W2146325043","https://openalex.org/W2949886604","https://openalex.org/W4385654212"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}