{"id":"https://openalex.org/W2951336038","doi":"https://doi.org/10.1007/s00145-019-09340-0","title":"Multilinear Maps from Obfuscation","display_name":"Multilinear Maps from Obfuscation","publication_year":2020,"publication_date":"2020-01-02","ids":{"openalex":"https://openalex.org/W2951336038","doi":"https://doi.org/10.1007/s00145-019-09340-0","mag":"2951336038"},"language":"en","primary_location":{"id":"doi:10.1007/s00145-019-09340-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00145-019-09340-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00145-019-09340-0.pdf","source":{"id":"https://openalex.org/S190936789","display_name":"Journal of Cryptology","issn_l":"0933-2790","issn":["0933-2790","1432-1378"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptology","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00145-019-09340-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066696423","display_name":"M. Albrecht","orcid":"https://orcid.org/0000-0003-1835-052X"},"institutions":[{"id":"https://openalex.org/I184558857","display_name":"Royal Holloway University of London","ror":"https://ror.org/04g2vpn86","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I184558857"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Martin R. Albrecht","raw_affiliation_strings":["Royal Holloway, University of London, London, United Kingdom","Royal Holloway University of London Egham UK"],"affiliations":[{"raw_affiliation_string":"Royal Holloway, University of London, London, United Kingdom","institution_ids":["https://openalex.org/I184558857"]},{"raw_affiliation_string":"Royal Holloway University of London Egham UK","institution_ids":["https://openalex.org/I184558857"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067769910","display_name":"Pooya Farshim","orcid":"https://orcid.org/0000-0003-2746-3585"},"institutions":[{"id":"https://openalex.org/I126231945","display_name":"Queen's University Belfast","ror":"https://ror.org/00hswnk62","country_code":"GB","type":"education","lineage":["https://openalex.org/I126231945"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]}],"countries":["FR","GB"],"is_corresponding":false,"raw_author_name":"Pooya Farshim","raw_affiliation_strings":["DI/ENS and CNRS, PSL University, Paris, France","Queen\u2019s University Belfast, Belfast, UK"],"affiliations":[{"raw_affiliation_string":"DI/ENS and CNRS, PSL University, Paris, France","institution_ids":["https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Queen\u2019s University Belfast, Belfast, UK","institution_ids":["https://openalex.org/I126231945"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Shuai Han","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN","DE"],"is_corresponding":false,"raw_author_name":"Shuai Han","raw_affiliation_strings":["Shanghai Jiao Tong University, Shanghai, China","Karlsruhe Institute of Technology, Karlsruhe, Germany"],"affiliations":[{"raw_affiliation_string":"Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"Karlsruhe Institute of Technology, Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003704447","display_name":"Dennis Hofheinz","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I184558857","display_name":"Royal Holloway University of London","ror":"https://ror.org/04g2vpn86","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I184558857"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Dennis Hofheinz","raw_affiliation_strings":["Karlsruhe Institute of Technology, Karlsruhe, Germany","Royal Holloway University of London Egham UK"],"affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology, Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"Royal Holloway University of London Egham UK","institution_ids":["https://openalex.org/I184558857"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036580999","display_name":"Enrique Larraia","orcid":null},"institutions":[{"id":"https://openalex.org/I184558857","display_name":"Royal Holloway University of London","ror":"https://ror.org/04g2vpn86","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I184558857"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Enrique Larraia","raw_affiliation_strings":["Royal Holloway, University of London, London, United Kingdom","Royal Holloway University of London Egham UK"],"affiliations":[{"raw_affiliation_string":"Royal Holloway, University of London, London, United Kingdom","institution_ids":["https://openalex.org/I184558857"]},{"raw_affiliation_string":"Royal Holloway University of London Egham UK","institution_ids":["https://openalex.org/I184558857"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072987600","display_name":"Kenneth G. Paterson","orcid":"https://orcid.org/0000-0002-5145-4489"},"institutions":[{"id":"https://openalex.org/I184558857","display_name":"Royal Holloway University of London","ror":"https://ror.org/04g2vpn86","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I184558857"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Kenneth G. Paterson","raw_affiliation_strings":["Royal Holloway, University of London, London, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Royal Holloway, University of London, London, United Kingdom","institution_ids":["https://openalex.org/I184558857"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5066696423"],"corresponding_institution_ids":["https://openalex.org/I184558857"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.00595562,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"33","issue":"3","first_page":"1080","last_page":"1113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9993000030517578,"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":0.9993000030517578,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9936000108718872,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9513999819755554,"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/multilinear-map","display_name":"Multilinear map","score":0.9724597334861755},{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.685502827167511},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.6506563425064087},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6191247701644897},{"id":"https://openalex.org/keywords/obfuscation","display_name":"Obfuscation","score":0.5900065898895264},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.46905115246772766},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4336186349391937},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4235672354698181},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.3692275881767273},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3369213938713074},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33370399475097656},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24484920501708984},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22850480675697327}],"concepts":[{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.9724597334861755},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.685502827167511},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.6506563425064087},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6191247701644897},{"id":"https://openalex.org/C40305131","wikidata":"https://www.wikidata.org/wiki/Q2616305","display_name":"Obfuscation","level":2,"score":0.5900065898895264},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.46905115246772766},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4336186349391937},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4235672354698181},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.3692275881767273},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3369213938713074},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33370399475097656},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24484920501708984},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22850480675697327},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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":7,"locations":[{"id":"doi:10.1007/s00145-019-09340-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00145-019-09340-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00145-019-09340-0.pdf","source":{"id":"https://openalex.org/S190936789","display_name":"Journal of Cryptology","issn_l":"0933-2790","issn":["0933-2790","1432-1378"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:EVASTAR-Karlsruhe.de:1000105369","is_oa":true,"landing_page_url":"https://publikationen.bibliothek.kit.edu/1000105369","pdf_url":null,"source":{"id":"https://openalex.org/S4306401992","display_name":"Repository KITopen (Karlsruhe Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102335020","host_organization_name":"Karlsruhe Institute of Technology","host_organization_lineage":["https://openalex.org/I102335020"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of cryptology, 33, 1080\u20131113","raw_type":"doc-type:article"},{"id":"pmh:oai:eprints.whiterose.ac.uk:169875","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400854","display_name":"White Rose Research Online (University of Leeds, The University of Sheffield, University of York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800616092","host_organization_name":"White Rose University Consortium","host_organization_lineage":["https://openalex.org/I2800616092"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/463573","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/463573","pdf_url":"http://hdl.handle.net/20.500.11850/463573","source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Cryptology, 33","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"mag:2951336038","is_oa":false,"landing_page_url":"https://eprint.iacr.org/2015/780.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},{"id":"doi:10.3929/ethz-b-000463573","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000463573","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5445/ir/1000105369","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000105369","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s00145-019-09340-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00145-019-09340-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00145-019-09340-0.pdf","source":{"id":"https://openalex.org/S190936789","display_name":"Journal of Cryptology","issn_l":"0933-2790","issn":["0933-2790","1432-1378"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4298364007","display_name":"Multilinear Maps in Cryptography","funder_award_id":"EP/L018543/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4869689085","display_name":null,"funder_award_id":"FP7/2007-2013","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4870564573","display_name":null,"funder_award_id":"EP/S020330/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G762232396","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7766065054","display_name":null,"funder_award_id":"EP/L018543/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8452545418","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2951336038.pdf","grobid_xml":"https://content.openalex.org/works/W2951336038.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W7540341","https://openalex.org/W9192823","https://openalex.org/W25973253","https://openalex.org/W55405330","https://openalex.org/W57039937","https://openalex.org/W61175307","https://openalex.org/W186896240","https://openalex.org/W199192073","https://openalex.org/W754106230","https://openalex.org/W1462154385","https://openalex.org/W1487683390","https://openalex.org/W1547517307","https://openalex.org/W1563479433","https://openalex.org/W1564449568","https://openalex.org/W1603256047","https://openalex.org/W1871911207","https://openalex.org/W1915197037","https://openalex.org/W1949164874","https://openalex.org/W2054904172","https://openalex.org/W2073210531","https://openalex.org/W2085983185","https://openalex.org/W2141395382","https://openalex.org/W2169673773","https://openalex.org/W2172174332","https://openalex.org/W2179825755","https://openalex.org/W2295328551","https://openalex.org/W2394843291","https://openalex.org/W2397835572","https://openalex.org/W2398614482","https://openalex.org/W2399042670","https://openalex.org/W2414682689","https://openalex.org/W2470510195","https://openalex.org/W2500250645","https://openalex.org/W2613226212","https://openalex.org/W2614022109","https://openalex.org/W2752847244","https://openalex.org/W2792195188","https://openalex.org/W2792957989","https://openalex.org/W2949731975","https://openalex.org/W3121827341","https://openalex.org/W3216853462"],"related_works":["https://openalex.org/W2196940748","https://openalex.org/W3013890204","https://openalex.org/W3029183001","https://openalex.org/W3082860856","https://openalex.org/W2768736126","https://openalex.org/W2395286272","https://openalex.org/W2047256651","https://openalex.org/W2293639154","https://openalex.org/W2755430954","https://openalex.org/W2799069235","https://openalex.org/W2952119761","https://openalex.org/W2398607975","https://openalex.org/W3028729311","https://openalex.org/W2407438300","https://openalex.org/W2954683065","https://openalex.org/W2408347115","https://openalex.org/W1492314155","https://openalex.org/W2951086828","https://openalex.org/W2949458889","https://openalex.org/W2148888468"],"abstract_inverted_index":{"Abstract":[0],"We":[1,36,223],"provide":[2,37],"constructions":[3,25,43],"of":[4,26,49,101,119,165,228,281,289],"multilinear":[5,30,47,267,284],"groups":[6,86,171,276],"equipped":[7],"with":[8,67],"natural":[9],"hard":[10],"problems":[11],"from":[12,29,269],"indistinguishability":[13,27,235],"obfuscation,":[14,236],"homomorphic":[15,250],"encryption,":[16],"and":[17,44,65,91,176,182,245,248,277,283],"NIZKs.":[18],"This":[19],"complements":[20],"known":[21],"results":[22],"on":[23,116,185,225],"the":[24,33,50,99,102,117,125,143,186,201,220,253,279,287,290],"obfuscators":[28],"maps":[31,285],"in":[32,194,219,231,273],"reverse":[34],"direction.":[35],"two":[38],"distinct,":[39],"but":[40,213],"closely":[41],"related":[42],"show":[45,278],"that":[46],"analogues":[48],"$${\\text":[51,108,131,188],"{DDH}}":[52,109,132,189],"$$":[53,70,104,110,127,133,190,204],"<mml:math":[54,71,82,89,94,105,111,128,134,160,168,174,179,191,205,257],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mtext>DDH</mml:mtext></mml:math>":[55,112,135,192],"assumption":[56,136,193],"hold":[57],"for":[58,84,123,142,162,252],"them.":[59],"Our":[60,138],"first":[61],"construction":[62,140],"is":[63,141],"symmetric":[64],"comes":[66],"a":[68,120,163,214,226,261],"$$\\kappa":[69,103,126,166,203],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03ba</mml:mi></mml:math>":[72,106,129,206],"-linear":[73,107],"map":[74],"$$\\mathbf{e":[75,147],"}:":[76,148],"{{\\mathbb":[77],"{G}}}^\\kappa":[78],"\\longrightarrow":[79,157],"{\\mathbb":[80,149,154,158],"{G}}_T$$":[81,93,159,178],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>e</mml:mi><mml:mo>:</mml:mo><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mi>\u03ba</mml:mi></mml:msup><mml:mo>\u27f6</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:mrow></mml:math>":[83],"prime-order":[85,170],"$${\\mathbb":[87,92,172,177],"{G}}$$":[88],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>G</mml:mi></mml:math>":[90],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>G</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math>":[95,180],".":[96,259],"To":[97],"establish":[98],"hardness":[100],"problem,":[113],"we":[114,264],"rely":[115,224],"existence":[118,288],"base":[121,196],"group":[122,254],"which":[124],"-strong":[130],"holds.":[137],"second":[139],"asymmetric":[144],"setting,":[145],"where":[146],"{G}}_1":[150],"\\times":[151,153],"\\cdots":[152],"{G}}_{\\kappa":[155],"}":[156],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>e</mml:mi><mml:mo>:</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>\u00d7</mml:mo><mml:mo>\u22ef</mml:mo><mml:mo>\u00d7</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mi>\u03ba</mml:mi></mml:msub><mml:mo>\u27f6</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:mrow></mml:math>":[161],"collection":[164],"+1$$":[167],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>\u03ba</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>":[169],"{G}}_i$$":[173],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>G</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math>":[175],",":[181],"relies":[183],"only":[184],"1-strong":[187],"its":[195],"group.":[197],"In":[198],"both":[199],"constructions,":[200],"linearity":[202],"can":[207],"be":[208],"set":[209],"to":[210],"any":[211],"arbitrary":[212],"priori":[215],"fixed":[216],"polynomial":[217],"value":[218],"security":[221],"parameter.":[222],"number":[227],"powerful":[229],"tools":[230],"our":[232],"constructions:":[233],"probabilistic":[234],"dual-mode":[237],"NIZK":[238],"proof":[239],"systems":[240],"(with":[241],"perfect":[242],"soundness,":[243],"witness-indistinguishability,":[244],"zero":[246],"knowledge),":[247],"additively":[249],"encryption":[251],"$$\\mathbb":[255],"{Z}_N^{+}$$":[256],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msubsup><mml:mi>Z</mml:mi><mml:mi>N</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:math>":[258],"At":[260],"high":[262],"level,":[263],"enable":[265],"\u201cbootstrapping\u201d":[266],"assumptions":[268],"their":[270],"simpler":[271],"counterparts":[272],"standard":[274],"cryptographic":[275],"equivalence":[280],"PIO":[282],"under":[286],"aforementioned":[291],"primitives.":[292]},"counts_by_year":[{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
