{"id":"https://openalex.org/W2984459379","doi":"https://doi.org/10.1145/3319535.3354262","title":"Succinct Arguments for Bilinear Group Arithmetic","display_name":"Succinct Arguments for Bilinear Group Arithmetic","publication_year":2019,"publication_date":"2019-11-06","ids":{"openalex":"https://openalex.org/W2984459379","doi":"https://doi.org/10.1145/3319535.3354262","mag":"2984459379"},"language":"en","primary_location":{"id":"doi:10.1145/3319535.3354262","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3319535.3354262","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security","raw_type":"proceedings-article"},"type":"conference-paper","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/A5034642945","display_name":"Russell W. F. Lai","orcid":"https://orcid.org/0000-0001-9126-1887"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Russell W. F. Lai","raw_affiliation_strings":["Friedrich-Alexander University Erlangen-Nuremberg, Erlangen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Friedrich-Alexander University Erlangen-Nuremberg, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007500399","display_name":"Giulio Malavolta","orcid":"https://orcid.org/0009-0009-9737-0094"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Giulio Malavolta","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080799466","display_name":"Viktoria Ronge","orcid":null},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Viktoria Ronge","raw_affiliation_strings":["Friedrich-Alexander University Erlangen-Nuremberg, Erlangen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Friedrich-Alexander University Erlangen-Nuremberg, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"2057","last_page":"2074"},"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":0.9897000193595886,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/random-oracle","display_name":"Random oracle","score":0.8056545853614807},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7321566939353943},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.6796678304672241},{"id":"https://openalex.org/keywords/cryptographic-primitive","display_name":"Cryptographic primitive","score":0.5405577421188354},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.53780597448349},{"id":"https://openalex.org/keywords/zero-knowledge-proof","display_name":"Zero-knowledge proof","score":0.5366783738136292},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.5067010521888733},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.47949033975601196},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.47651422023773193},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4760677218437195},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4730716645717621},{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.4625171422958374},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.45354121923446655},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4500024914741516},{"id":"https://openalex.org/keywords/gas-meter-prover","display_name":"Gas meter prover","score":0.414816677570343},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.4033423662185669},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38005316257476807},{"id":"https://openalex.org/keywords/cryptographic-protocol","display_name":"Cryptographic protocol","score":0.36130887269973755},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3342564105987549},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.25645047426223755},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16711747646331787},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.13736116886138916},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.12944814562797546},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12798452377319336}],"concepts":[{"id":"https://openalex.org/C94284585","wikidata":"https://www.wikidata.org/wiki/Q228184","display_name":"Random oracle","level":4,"score":0.8056545853614807},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7321566939353943},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.6796678304672241},{"id":"https://openalex.org/C15927051","wikidata":"https://www.wikidata.org/wiki/Q246593","display_name":"Cryptographic primitive","level":4,"score":0.5405577421188354},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.53780597448349},{"id":"https://openalex.org/C176329583","wikidata":"https://www.wikidata.org/wiki/Q191943","display_name":"Zero-knowledge proof","level":3,"score":0.5366783738136292},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.5067010521888733},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.47949033975601196},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.47651422023773193},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4760677218437195},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4730716645717621},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.4625171422958374},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.45354121923446655},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4500024914741516},{"id":"https://openalex.org/C159718280","wikidata":"https://www.wikidata.org/wiki/Q5526353","display_name":"Gas meter prover","level":3,"score":0.414816677570343},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.4033423662185669},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38005316257476807},{"id":"https://openalex.org/C33884865","wikidata":"https://www.wikidata.org/wiki/Q1254335","display_name":"Cryptographic protocol","level":3,"score":0.36130887269973755},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3342564105987549},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.25645047426223755},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16711747646331787},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.13736116886138916},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.12944814562797546},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12798452377319336},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3319535.3354262","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3319535.3354262","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.6100000143051147,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W4180724","https://openalex.org/W41098585","https://openalex.org/W146078955","https://openalex.org/W170174611","https://openalex.org/W1527414074","https://openalex.org/W1548963432","https://openalex.org/W2013689473","https://openalex.org/W2089537103","https://openalex.org/W2108834246","https://openalex.org/W2141395382","https://openalex.org/W2143374261","https://openalex.org/W2159339434","https://openalex.org/W2473389213","https://openalex.org/W2765206040","https://openalex.org/W4300889023"],"related_works":["https://openalex.org/W2149634854","https://openalex.org/W3030245161","https://openalex.org/W2562305209","https://openalex.org/W2096571200","https://openalex.org/W2809883875","https://openalex.org/W3030523870","https://openalex.org/W4389777186","https://openalex.org/W3210659843","https://openalex.org/W2397501045","https://openalex.org/W2392770010"],"abstract_inverted_index":{"In":[0,80,167],"their":[1,56],"celebrated":[2],"work,":[3,82],"Groth":[4,49],"and":[5,50,117,129,131],"Sahai":[6,51],"[EUROCRYPT'08,":[7],"SICOMP'":[8],"12]":[9],"constructed":[10],"non-interactive":[11,136],"zero-knowledge":[12,103],"(NIZK)":[13],"proofs":[14],"for":[15,105],"general":[16,91],"bilinear":[17,92],"group":[18,93,119,152],"arithmetic":[19,94,153],"relations,":[20,107],"which":[21],"spawned":[22],"the":[23,32,45,62,65,70,78,85,109,115,122,138,142,147,187],"entire":[24],"subfield":[25],"of":[26,31,34,40,48,64,77,87,90,121,150,179,190],"structure-preserving":[27,191],"cryptography.":[28],"This":[29],"branch":[30],"theory":[33],"cryptography":[35,192],"focuses":[36],"on":[37],"modular":[38],"design":[39],"advanced":[41,184],"cryptographic":[42],"primitives.":[43],"Although":[44],"proof":[46,71],"systems":[47,196],"are":[52],"a":[53,59,101,176],"powerful":[54],"toolkit,":[55],"efficiency":[57],"hits":[58],"barrier":[60],"when":[61],"size":[63,72],"witness":[66],"is":[67,73,112],"large,":[68],"as":[69,175],"linear":[74],"in":[75,96,114,141,164,186],"that":[76],"witness.":[79,123],"this":[81],"we":[83,99],"revisit":[84],"problem":[86],"proving":[88],"knowledge":[89],"relations":[95,154],"zero-knowledge.":[97],"Specifically,":[98],"construct":[100],"succinct":[102],"argument":[104,125,171],"such":[106],"where":[108],"communication":[110],"complexity":[111],"logarithmic":[113],"integer":[116,157],"source":[118],"components":[120],"Our":[124],"has":[126],"public-coin":[127],"setup":[128],"verifier":[130],"can":[132,161,173],"therefore":[133],"be":[134,162],"turned":[135],"using":[137],"Fiat-Shamir":[139],"transformation":[140],"random":[143],"oracle":[144],"model.":[145],"For":[146],"special":[148],"case":[149],"non-bilinear":[151,165],"with":[155,197],"only":[156],"unknowns,":[158],"our":[159,170],"system":[160,172],"instantiated":[163],"groups.":[166],"many":[168],"applications,":[169],"serve":[174],"drop-in":[177],"replacement":[178],"Groth-Sahai":[180],"proofs,":[181],"turning":[182],"existing":[183],"primitives":[185],"vast":[188],"literature":[189],"into":[193],"practically":[194],"efficient":[195],"short":[198],"proofs.":[199]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
