{"id":"https://openalex.org/W1987890787","doi":"https://doi.org/10.1137/s0097539791220688","title":"On the Composition of Zero-Knowledge Proof Systems","display_name":"On the Composition of Zero-Knowledge Proof Systems","publication_year":1996,"publication_date":"1996-02-01","ids":{"openalex":"https://openalex.org/W1987890787","doi":"https://doi.org/10.1137/s0097539791220688","mag":"1987890787"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539791220688","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539791220688","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-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/A5013698877","display_name":"Oded Goldreich","orcid":"https://orcid.org/0000-0002-4329-135X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Oded Goldreich","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5057824781","display_name":"Hugo Krawczyk","orcid":"https://orcid.org/0000-0003-3130-1888"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hugo Krawczyk","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013698877"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.6778,"has_fulltext":false,"cited_by_count":427,"citation_normalized_percentile":{"value":0.98105934,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"25","issue":"1","first_page":"169","last_page":"192"},"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9988999962806702,"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":0.9958000183105469,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/zero-knowledge-proof","display_name":"Zero-knowledge proof","score":0.9656964540481567},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7752633094787598},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5541092753410339},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5291973352432251},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4147789478302002},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40469974279403687},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.321159303188324}],"concepts":[{"id":"https://openalex.org/C176329583","wikidata":"https://www.wikidata.org/wiki/Q191943","display_name":"Zero-knowledge proof","level":3,"score":0.9656964540481567},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7752633094787598},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5541092753410339},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5291973352432251},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4147789478302002},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40469974279403687},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.321159303188324},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0097539791220688","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539791220688","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1502416796","https://openalex.org/W1539572409","https://openalex.org/W1970606468","https://openalex.org/W1985623009","https://openalex.org/W2000850689","https://openalex.org/W2011112377","https://openalex.org/W2019038806","https://openalex.org/W2035693183","https://openalex.org/W2038517014","https://openalex.org/W2130993035","https://openalex.org/W2151433956","https://openalex.org/W4210300416","https://openalex.org/W4238472918","https://openalex.org/W4250445866"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W1970588133","https://openalex.org/W2022025391","https://openalex.org/W2163538620","https://openalex.org/W1567449721","https://openalex.org/W2952570804","https://openalex.org/W2408612903","https://openalex.org/W4389292261","https://openalex.org/W974961824","https://openalex.org/W2030257803"],"abstract_inverted_index":{"The":[0],"wide":[1],"applicability":[2],"of":[3,11,33,43,46,55,69,88,97,129,182,188,196,203],"zero-knowledge":[4,34,37,47,56,70,89,98,114,163,191,206],"interactive":[5,104,132],"proofs":[6,14,105,109,133,164],"comes":[7],"from":[8,171],"the":[9,28,41,44,52,66,85,95,126,130,152,172,185,194,201],"possibility":[10],"using":[12,197],"these":[13,159],"as":[15],"subroutines":[16],"in":[17,119,144,156,200],"cryptographic":[18],"protocols.":[19,99],"A":[20],"basic":[21],"question":[22],"concerning":[23],"this":[24],"use":[25],"is":[26,36,57],"whether":[27],"(sequential":[29],"and/or":[30],"parallel)":[31],"composition":[32,45],"protocols":[35,48,192],"too.":[38],"We":[39,80,100],"demonstrate":[40],"limitations":[42],"by":[49],"proving":[50],"that":[51,64,102,110,125],"original":[53],"definition":[54],"not":[58,75,147],"closed":[59,76],"under":[60,77],"sequential":[61],"composition;":[62],"and":[63,106,141,193],"even":[65],"strong":[67],"formulations":[68],"(e.g.,":[71],"black-box":[72,112,148],"simulation)":[73],"are":[74,111,146,155,179],"parallel":[78,160],"execution.":[79],"present":[81],"lower":[82],"bounds":[83],"on":[84,175],"round":[86,186],"complexity":[87,187],"proofs,":[90],"with":[91],"significant":[92],"implications":[93],"for":[94,117,136,184],"parallelization":[96],"prove":[101],"three-round":[103],"constant-round":[107,205],"Arthur-Merlin":[108],"simulation":[113,149],"exist":[115],"only":[116],"languages":[118,154],"BPP.":[120],"In":[121],"particular,":[122],"it":[123],"follows":[124],"\u201cparallel":[127],"versions\u201d":[128],"first":[131],"systems":[134],"presented":[135],"quadratic":[137],"residuosity,":[138],"graph":[139],"isomorphism,":[140],"any":[142],"language":[143],"NP,":[145],"zero-knowledge,":[150],"unless":[151],"corresponding":[153],"BPP":[157],"Whether":[158],"versions":[161],"constitute":[162],"was":[165],"an":[166],"intriguing":[167],"open":[168],"questions":[169],"arising":[170],"early":[173],"works":[174],"zero-knowledge.":[176],"Other":[177],"consequences":[178],"a":[180],"proof":[181],"optimality":[183],"various":[189],"known":[190],"necessity":[195],"secret":[198],"coins":[199],"design":[202],"\u201cparallelizable\u201d":[204],"proofs.":[207]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":23},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":20}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}