{"id":"https://openalex.org/W3095930832","doi":"https://doi.org/10.1145/3372297.3417894","title":"Practical Lattice-Based Zero-Knowledge Proofs for Integer Relations","display_name":"Practical Lattice-Based Zero-Knowledge Proofs for Integer Relations","publication_year":2020,"publication_date":"2020-10-30","ids":{"openalex":"https://openalex.org/W3095930832","doi":"https://doi.org/10.1145/3372297.3417894","mag":"3095930832"},"language":"en","primary_location":{"id":"doi:10.1145/3372297.3417894","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3372297.3417894","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security","raw_type":"proceedings-article"},"type":"article","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/A5074391920","display_name":"Vadim Lyubashevsky","orcid":"https://orcid.org/0009-0003-5149-264X"},"institutions":[{"id":"https://openalex.org/I4210126328","display_name":"IBM Research - Zurich","ror":"https://ror.org/02js37d36","country_code":"CH","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115","https://openalex.org/I4210126328"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Vadim Lyubashevsky","raw_affiliation_strings":["IBM Research - Zurich, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"IBM Research - Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I4210126328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065667852","display_name":"Ngoc Khanh Nguyen","orcid":"https://orcid.org/0000-0001-8240-6167"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4210126328","display_name":"IBM Research - Zurich","ror":"https://ror.org/02js37d36","country_code":"CH","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115","https://openalex.org/I4210126328"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Ngoc Khanh Nguyen","raw_affiliation_strings":["IBM Research - Zurich and ETH Zurich, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"IBM Research - Zurich and ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I4210126328","https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052994395","display_name":"Gregor Seiler","orcid":"https://orcid.org/0009-0005-5024-5123"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4210126328","display_name":"IBM Research - Zurich","ror":"https://ror.org/02js37d36","country_code":"CH","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115","https://openalex.org/I4210126328"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Gregor Seiler","raw_affiliation_strings":["IBM Research - Zurich and ETH Zurich, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"IBM Research - Zurich and ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I4210126328","https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074391920"],"corresponding_institution_ids":["https://openalex.org/I4210126328"],"apc_list":null,"apc_paid":null,"fwci":3.9768,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.94796721,"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":"1051","last_page":"1070"},"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":0.9987000226974487,"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":0.9944000244140625,"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/mathematical-proof","display_name":"Mathematical proof","score":0.8917035460472107},{"id":"https://openalex.org/keywords/zero-knowledge-proof","display_name":"Zero-knowledge proof","score":0.6687414646148682},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5827347636222839},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5765256881713867},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5679765939712524},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5311200618743896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4773012399673462},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.4283917248249054},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4094942808151245},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39318251609802246},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.18490877747535706},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15286323428153992}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8917035460472107},{"id":"https://openalex.org/C176329583","wikidata":"https://www.wikidata.org/wiki/Q191943","display_name":"Zero-knowledge proof","level":3,"score":0.6687414646148682},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5827347636222839},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5765256881713867},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5679765939712524},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5311200618743896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4773012399673462},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4283917248249054},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4094942808151245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39318251609802246},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.18490877747535706},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15286323428153992},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3372297.3417894","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3372297.3417894","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4399999976158142,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1506156414","https://openalex.org/W1970808997","https://openalex.org/W1985439922","https://openalex.org/W2067596507","https://openalex.org/W2751494174","https://openalex.org/W2765206040","https://openalex.org/W2791664942","https://openalex.org/W2886714247","https://openalex.org/W2912809249","https://openalex.org/W4240339612"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W1870614684","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W4387820098","https://openalex.org/W2022025391","https://openalex.org/W2163538620","https://openalex.org/W1970588133","https://openalex.org/W1567449721"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,104],"novel":[3],"lattice-based":[4],"zero-knowledge":[5,99],"proof":[6,20,38,52,75,100,114],"system":[7,39,101,115],"for":[8,46,77,85],"showing":[9],"that":[10],"(arbitrary-sized)":[11],"committed":[12],"integers":[13,89],"satisfy":[14],"additive":[15],"and":[16],"multiplicative":[17],"relationships.":[18],"The":[19],"sizes":[21,53],"of":[22,31,40,54,112,121],"our":[23,55,63,92,113],"schemes":[24],"are":[25],"between":[26,87],"two":[27],"to":[28],"three":[29],"orders":[30],"magnitude":[32,122],"smaller":[33],"than":[34,69,124],"in":[35,59,96],"the":[36,47,51,60,97,110],"lattice":[37],"Libert":[41],"et":[42],"al.":[43],"(CRYPTO":[44],"2018)":[45],"same":[48],"relations.":[49],"Because":[50],"protocols":[56],"grow":[57],"linearly":[58],"integer":[61],"length,":[62],"proofs":[64,93],"will":[65],"eventually":[66],"be":[67],"longer":[68],"those":[70],"produced":[71],"by":[72],"quantum-safe":[73,105,127],"succinct":[74],"systems":[76],"general":[78],"circuits":[79],"(e.g.":[80,90],"Ligero,":[81],"Aurora,":[82],"etc.).":[83],"But":[84],"relations":[86],"reasonably-sized":[88],"$512$-bit),":[91],"still":[94],"result":[95],"smallest":[98],"based":[102],"on":[103],"assumption.":[106],"Of":[107],"equal":[108],"importance,":[109],"run-time":[111],"is":[116],"at":[117],"least":[118],"an":[119],"order":[120],"faster":[123],"any":[125],"other":[126],"scheme.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}