{"id":"https://openalex.org/W3126804674","doi":"https://doi.org/10.1145/3460120.3484556","title":"QuickSilver: Efficient and Affordable Zero-Knowledge Proofs for Circuits and Polynomials over Any Field","display_name":"QuickSilver: Efficient and Affordable Zero-Knowledge Proofs for Circuits and Polynomials over Any Field","publication_year":2021,"publication_date":"2021-11-12","ids":{"openalex":"https://openalex.org/W3126804674","doi":"https://doi.org/10.1145/3460120.3484556","mag":"3126804674"},"language":"en","primary_location":{"id":"doi:10.1145/3460120.3484556","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3460120.3484556","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security","raw_type":"proceedings-article"},"type":"preprint","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/A5078827448","display_name":"Kang Yang","orcid":"https://orcid.org/0000-0002-7453-4043"},"institutions":[{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Kang Yang","raw_affiliation_strings":["State Key Laboratory of Cryptology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Cryptology, Beijing, China","institution_ids":["https://openalex.org/I4210132990"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022559893","display_name":"Pratik Sarkar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pratik Sarkar","raw_affiliation_strings":["Boston University, Boston, MA, USA"],"affiliations":[{"raw_affiliation_string":"Boston University, Boston, MA, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030545742","display_name":"Chenkai Weng","orcid":"https://orcid.org/0000-0003-2436-9366"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chenkai Weng","raw_affiliation_strings":["Northwestern University, Evanston, IL, USA"],"affiliations":[{"raw_affiliation_string":"Northwestern University, Evanston, IL, USA","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077754703","display_name":"Xiao Wang","orcid":"https://orcid.org/0000-0002-5991-7417"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiao Wang","raw_affiliation_strings":["Northwestern University, Evanston, IL, USA"],"affiliations":[{"raw_affiliation_string":"Northwestern University, Evanston, IL, USA","institution_ids":["https://openalex.org/I111979921"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5078827448"],"corresponding_institution_ids":["https://openalex.org/I4210132990"],"apc_list":null,"apc_paid":null,"fwci":0.2799,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61382503,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"2021","issue":null,"first_page":"2986","last_page":"3001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9986000061035156,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9923999905586243,"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/computer-science","display_name":"Computer science","score":0.6367910504341125},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.5607271790504456},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.535313606262207},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5148743391036987},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4731513261795044},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4729328453540802},{"id":"https://openalex.org/keywords/memory-footprint","display_name":"Memory footprint","score":0.47167760133743286},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.45095884799957275},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4426301419734955},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4343080520629883},{"id":"https://openalex.org/keywords/communication-complexity","display_name":"Communication complexity","score":0.41773465275764465},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3871804177761078},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3426903486251831},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3360867500305176},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.30662375688552856},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2462673783302307},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10565277934074402}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6367910504341125},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.5607271790504456},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.535313606262207},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5148743391036987},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4731513261795044},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4729328453540802},{"id":"https://openalex.org/C74912251","wikidata":"https://www.wikidata.org/wiki/Q6815727","display_name":"Memory footprint","level":2,"score":0.47167760133743286},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.45095884799957275},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4426301419734955},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4343080520629883},{"id":"https://openalex.org/C179145077","wikidata":"https://www.wikidata.org/wiki/Q5154130","display_name":"Communication complexity","level":2,"score":0.41773465275764465},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3871804177761078},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3426903486251831},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3360867500305176},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.30662375688552856},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2462673783302307},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10565277934074402},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3460120.3484556","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3460120.3484556","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security","raw_type":"proceedings-article"},{"id":"mag:3126804674","is_oa":false,"landing_page_url":"https://eprint.iacr.org/2021/076.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2764847869","display_name":"IACR Cryptology ePrint Archive","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":["https://openalex.org/P4322614454"],"host_organization_lineage_names":["Cryptology ePrint Archive"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Cryptology ePrint Archive","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.41999998688697815}],"awards":[{"id":"https://openalex.org/G4499938846","display_name":null,"funder_award_id":"62102037, 61932019, 62022018","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6812776702","display_name":null,"funder_award_id":"2016240,1931714,1414119","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8463217817","display_name":null,"funder_award_id":"HR001120C0087","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W264971478","https://openalex.org/W1499934958","https://openalex.org/W1505629034","https://openalex.org/W1826277484","https://openalex.org/W1980227445","https://openalex.org/W2039605106","https://openalex.org/W2040168265","https://openalex.org/W2058648304","https://openalex.org/W2144238522","https://openalex.org/W2146099890","https://openalex.org/W2173120240","https://openalex.org/W2473389213","https://openalex.org/W2520099014","https://openalex.org/W2534243026","https://openalex.org/W2604366484","https://openalex.org/W2724596564","https://openalex.org/W2883585522","https://openalex.org/W2890999648","https://openalex.org/W2891063150","https://openalex.org/W2954625838","https://openalex.org/W2964279767","https://openalex.org/W2967347604","https://openalex.org/W2972152617","https://openalex.org/W2988839516","https://openalex.org/W2990120385","https://openalex.org/W3003231116","https://openalex.org/W3012999251","https://openalex.org/W3015343560","https://openalex.org/W3015408680","https://openalex.org/W3023964980","https://openalex.org/W3031679272","https://openalex.org/W3095923304","https://openalex.org/W3097836574","https://openalex.org/W3190538822","https://openalex.org/W3192802957","https://openalex.org/W4300889023"],"related_works":["https://openalex.org/W3157630909","https://openalex.org/W2407813796","https://openalex.org/W1981985056","https://openalex.org/W3082217300","https://openalex.org/W2959417844","https://openalex.org/W2167110608","https://openalex.org/W2776756296","https://openalex.org/W2739302581","https://openalex.org/W2951500762","https://openalex.org/W2100945076","https://openalex.org/W2295468561","https://openalex.org/W3107664768","https://openalex.org/W2951774635","https://openalex.org/W3047574331","https://openalex.org/W3008867583","https://openalex.org/W3091480782","https://openalex.org/W2026162734","https://openalex.org/W2398167647","https://openalex.org/W2951189305","https://openalex.org/W2462789209"],"abstract_inverted_index":{"Zero-knowledge":[0],"(ZK)":[1],"proofs":[2],"with":[3,23,80,201,256,280],"an":[4],"optimal":[5],"memory":[6,26,34,42],"footprint":[7],"have":[8],"attracted":[9],"a":[10,24,96,99,105,182,197,202],"lot":[11],"of":[12,83,108,190,199,222,233,237,240,267,272,286],"attention,":[13],"because":[14],"such":[15],"protocols":[16,60],"can":[17,193,206,252],"easily":[18],"prove":[19,167,253],"very":[20,123],"large":[21],"computation":[22,92,122,147,192],"small":[25],"requirement.":[27],"Such":[28],"ZK":[29,59,102,249],"protocol":[30,103,160],"only":[31,161,216,288],"needs":[32,162,289],"O(M)":[33],"for":[35,78,115,176],"both":[36],"parties,":[37],"where":[38,90,188],"M":[39],"is":[40,93],"the":[41,46,49,66,71,87,91,121,138,186,191,211,214,219,227,230,238,247,260,265,270],"required":[43],"to":[44,137,166,210,242,259],"verify":[45],"statement":[47],"in":[48,61,146,151,225],"clear.":[50],"In":[51,86,185],"this":[52,62],"paper,":[53],"we":[54,142,205,251],"propose":[55],"several":[56],"new":[57],"constant-round":[58],"setting,":[63],"which":[64,129],"improve":[65],"concrete":[67],"efficiency":[68,133],"and,":[69],"at":[70],"same":[72],"time,":[73],"enable":[74],"sublinear":[75,209],"amortized":[76],"communication":[77,106,208,215,257],"circuits":[79],"some":[81],"notion":[82],"relaxed":[84],"uniformity.":[85],"circuit-based":[88],"model,":[89],"represented":[94,195],"as":[95,196],"circuit":[97],"over":[98,181],"field,":[100],"our":[101,127,159,278],"achieves":[104],"complexity":[107],"1":[109,284],"field":[110,117],"element":[111],"per":[112],"non-linear":[113],"gate":[114],"any":[116],"size":[118],"while":[119],"keeping":[120],"cheap.":[124],"We":[125],"implemented":[126],"protocol,":[128,250],"shows":[130],"extremely":[131],"high":[132],"and":[134,148,229,283,292],"affordability.":[135],"Compared":[136],"previous":[139],"best-known":[140],"implementation,":[141,279],"achieve":[143,207],"6x--7x":[144],"improvement":[145,150],"3x--7x":[149],"communication.":[152],"When":[153],"running":[154],"on":[155,218],"intro-level":[156],"AWS":[157],"instances,":[158],"one":[163,168,177,281],"US":[164,174],"dollar":[165],"trillion":[169,178],"AND":[170],"gates":[171,180],"(or":[172],"2.5":[173],"dollars":[175],"multiplication":[179,255,271],"61-bit":[183],"field).":[184],"setting":[187],"part":[189],"be":[194],"set":[198],"polynomials":[200,228],"\"degree-separated\"":[203],"format,":[204],"polynomial":[212],"size:":[213],"depends":[217],"total":[220],"number":[221,239,266],"distinct":[223],"variables":[224],"all":[226,234,244],"highest":[231],"degree":[232],"polynomials,":[235],"independent":[236],"multiplications":[241],"compute":[243],"polynomials.":[245],"Using":[246],"improved":[248],"matrix":[254],"proportional":[258],"input":[261],"size,":[262],"rather":[263],"than":[264],"multiplications.":[268],"Proving":[269],"two":[273],"1024":[274,276],"x":[275],"matrices,":[277],"thread":[282],"GB":[285],"memory,":[287],"10":[290],"seconds":[291],"communicates":[293],"25":[294],"MB.":[295]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
