{"id":"https://openalex.org/W2969458085","doi":"https://doi.org/10.3390/e21090826","title":"On Share Conversions for Private Information Retrieval","display_name":"On Share Conversions for Private Information Retrieval","publication_year":2019,"publication_date":"2019-08-23","ids":{"openalex":"https://openalex.org/W2969458085","doi":"https://doi.org/10.3390/e21090826","mag":"2969458085"},"language":"en","primary_location":{"id":"doi:10.3390/e21090826","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21090826","pdf_url":"https://www.mdpi.com/1099-4300/21/9/826/pdf?version=1566558884","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/21/9/826/pdf?version=1566558884","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038243550","display_name":"Anat Paskin-Cherniavsky","orcid":"https://orcid.org/0000-0001-6566-2644"},"institutions":[{"id":"https://openalex.org/I52170813","display_name":"Ariel University","ror":"https://ror.org/03nz8qe97","country_code":"IL","type":"education","lineage":["https://openalex.org/I52170813"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Anat Paskin-Cherniavsky","raw_affiliation_strings":["Computer Science Department, Ariel University, Ariel 40700, Israel"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Ariel University, Ariel 40700, Israel","institution_ids":["https://openalex.org/I52170813"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018787107","display_name":"Leora Schmerler","orcid":"https://orcid.org/0000-0002-6934-8246"},"institutions":[{"id":"https://openalex.org/I52170813","display_name":"Ariel University","ror":"https://ror.org/03nz8qe97","country_code":"IL","type":"education","lineage":["https://openalex.org/I52170813"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Leora Schmerler","raw_affiliation_strings":["Computer Science Department, Ariel University, Ariel 40700, Israel"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Ariel University, Ariel 40700, Israel","institution_ids":["https://openalex.org/I52170813"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038243550"],"corresponding_institution_ids":["https://openalex.org/I52170813"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1447,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.57781176,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"21","issue":"9","first_page":"826","last_page":"826"},"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":0.9973000288009644,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5683708786964417},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.5260767340660095},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.5008511543273926},{"id":"https://openalex.org/keywords/server","display_name":"Server","score":0.4701172113418579},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4468980133533478},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.43883568048477173},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.43750476837158203},{"id":"https://openalex.org/keywords/secret-sharing","display_name":"Secret sharing","score":0.4359320104122162},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3931206166744232},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35976165533065796},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3322782516479492},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21430179476737976},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.11401009559631348},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.0973808765411377},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.09042668342590332}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5683708786964417},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.5260767340660095},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.5008511543273926},{"id":"https://openalex.org/C93996380","wikidata":"https://www.wikidata.org/wiki/Q44127","display_name":"Server","level":2,"score":0.4701172113418579},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4468980133533478},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.43883568048477173},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.43750476837158203},{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.4359320104122162},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3931206166744232},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35976165533065796},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3322782516479492},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21430179476737976},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.11401009559631348},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0973808765411377},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.09042668342590332},{"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e21090826","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21090826","pdf_url":"https://www.mdpi.com/1099-4300/21/9/826/pdf?version=1566558884","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:620464967b1349108f59b0ecfd48b684","is_oa":true,"landing_page_url":"https://doaj.org/article/620464967b1349108f59b0ecfd48b684","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 21, Iss 9, p 826 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/9/826/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21090826","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Entropy","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7515355","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7515355","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e21090826","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21090826","pdf_url":"https://www.mdpi.com/1099-4300/21/9/826/pdf?version=1566558884","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2969458085.pdf","grobid_xml":"https://content.openalex.org/works/W2969458085.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W51265332","https://openalex.org/W147290027","https://openalex.org/W1934398053","https://openalex.org/W1998698985","https://openalex.org/W2006453614","https://openalex.org/W2027317757","https://openalex.org/W2027471022","https://openalex.org/W2027857542","https://openalex.org/W2036602082","https://openalex.org/W2039991502","https://openalex.org/W2073346043","https://openalex.org/W2120282110","https://openalex.org/W2121640981","https://openalex.org/W2154654620","https://openalex.org/W2177108502","https://openalex.org/W2570927556","https://openalex.org/W2990399857","https://openalex.org/W3103511209"],"related_works":["https://openalex.org/W2388464034","https://openalex.org/W2533125852","https://openalex.org/W2140460949","https://openalex.org/W2105580438","https://openalex.org/W2057435755","https://openalex.org/W2018782216","https://openalex.org/W1994257264","https://openalex.org/W1984242286","https://openalex.org/W2062000137","https://openalex.org/W2052758143"],"abstract_inverted_index":{"Beimel":[0,272,427],"et":[1,273,428],"al.":[2,274,429],"in":[3,29,199,357,426,479],"CCC":[4],"12\u2019":[5],"put":[6],"forward":[7],"a":[8,37,51,59,68,133,139,154,163,169,180,185,196,294,323,347,399,450],"paradigm":[9,413],"for":[10,21,88,138,189,252,365,375,391,417],"constructing":[11],"Private":[12],"Information":[13],"Retrieval":[14],"(PIR)":[15],"schemes,":[16],"capturing":[17],"several":[18,190],"previous":[19],"constructions":[20],"k":[22],"\u2265":[23],"3":[24,75,211,333],"servers.":[25],"A":[26],"key":[27],"component":[28],"the":[30,64,119,129,151,213,217,222,230,248,297,303,372,377,423,465,468],"paradigm,":[31,65],"applicable":[32],"to":[33,50,81,118,150,312,315,384,415,431,461,464],"three-server":[34,214,340,471],"PIR,":[35],"is":[36,115,233,398,444],"share":[38,69,113,135,359,387],"conversion":[39,70,114,136,187,295,388,451],"scheme":[40],"from":[41,71],"corresponding":[42],"linear":[43,156,424],"three-party":[44],"secret":[45],"sharing":[46,83,181],"schemes":[47],"with":[48,116,216,309,321,481],"respect":[49,117],"certain":[52,155,482],"type":[53],"of":[54,63,131,153,178,192,234,256,271,296,306,350,401,436,467,470],"\u201cmodified":[55],"universal\u201d":[56],"relation.":[57],"In":[58,242,447],"useful":[60,363],"particular":[61],"instantiation":[62],"they":[66,166],"used":[67],"(":[72,141,237,257,325],"2":[73,94,102,110,146,206,209,262,284,286,330],",":[74,92,95,144,147,173,207,260,263,282,292,328,395],")":[76,149,176,240,265,331,334],"-CNF":[77],"over":[78,84,158],"Z":[79,85,159,419],"m":[80,104,125,172,238,322,394,397,420],"three-additive":[82],"p":[86,90,93,96,98,101,106,109,142,145,148,160,175,201,203,208,258,261,264,280,283,288,290,326,329],"\u03b2":[87],"primes":[89],"1":[91,99,107,143,204,259,281,291,327],"where":[97,396],"\u2260":[100],"and":[103,287],"=":[105,202,205,210,289],"\u00b7":[108],".":[111,126,161,241],"The":[112,410],"modified":[120],"universal":[121],"relation":[122],"C":[123,392],"S":[124,393],"They":[127,183],"reduced":[128],"question":[130,270],"whether":[132,386],"suitable":[134,186],"exists":[137,188],"triple":[140],"(in)solvability":[152],"system":[157],"Assuming":[162],"solution":[164],"exists,":[165],"also":[167],"provided":[168],"efficient":[170],"(in":[171],"log":[174],"construction":[177,458],"such":[179,307,418,449],"scheme.":[182],"proved":[184],"triples":[191,335],"small":[193],"numbers":[194],"using":[195],"computer":[197],"program;":[198],"particular,":[200],"yielded":[212],"PIR":[215,313,341,351,472],"best":[218],"communication":[219,342,473],"complexity":[220,343,474],"at":[221],"time.":[223],"This":[224],"approach":[225],"quickly":[226],"becomes":[227],"infeasible":[228],"as":[229,389],"resulting":[231],"matrix":[232],"size":[235],"\u0398":[236],"4":[239],"this":[243],"work,":[244],"we":[245,276,353,369,380],"prove":[246,277],"that":[247,278,371],"solvability":[249],"condition":[250,425],"holds":[251],"an":[253,268],"infinite":[254],"family":[255,349],"\u2019s,":[266],"answering":[267],"open":[269],"Concretely,":[275],"if":[279],"&gt;":[285,332],"then":[293],"required":[298],"form":[299],"exists.":[300,409],"We":[301],"leave":[302],"full":[304],"characterization":[305],"triples,":[308],"potential":[310],"applications":[311],"complexity,":[314],"future":[316],"work.":[317],"Although":[318],"larger":[319],"(particularly":[320],"x":[324],"do":[336],"not":[337],"yield":[338],"improved":[339],"via":[344],"BIKO\u2019s":[345,457],"construction,":[346],"richer":[348],"protocols":[352],"obtain":[354],"by":[355],"plugging":[356,454],"our":[358,442],"conversions":[360],"might":[361],"have":[362],"properties":[364],"other":[366],"applications.":[367],"Moreover,":[368],"hope":[370,443],"analytic":[373],"techniques":[374],"understanding":[376],"relevant":[378],"matrices":[379],"developed":[381],"would":[382,459],"help":[383],"understand":[385],"above":[390],"product":[400],"more":[402,437],"than":[403,438],"two":[404,439],"(say":[405],"three)":[406],"distinct":[407],"primes,":[408,440],"general":[411],"BIKO":[412],"generalizes":[414,430],"work":[416],"\u2019s.":[421],"Furthermore,":[422],"m\u2019s,":[432],"which":[433],"are":[434],"products":[435],"so":[441],"somewhat":[445],"justified.":[446],"case":[448],"does":[452],"exist,":[453],"it":[455],"into":[456],"lead":[460],"major":[462],"improvement":[463],"state":[466],"art":[469],"(reducing":[475],"Communication":[476],"Complexity":[477],"(CC)":[478],"correspondence":[480],"matching":[483],"vector":[484],"families).":[485]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
