{"id":"https://openalex.org/W4297999087","doi":"https://doi.org/10.1515/jmc-2021-0054","title":"Integer polynomial recovery from outputs and its application to cryptanalysis of a protocol for secure sorting","display_name":"Integer polynomial recovery from outputs and its application to cryptanalysis of a protocol for secure sorting","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4297999087","doi":"https://doi.org/10.1515/jmc-2021-0054"},"language":"en","primary_location":{"id":"doi:10.1515/jmc-2021-0054","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2021-0054","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2021-0054/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2021-0054/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008324213","display_name":"S. Sree Vivek","orcid":"https://orcid.org/0000-0002-8426-0859"},"institutions":[{"id":"https://openalex.org/I181514455","display_name":"International Institute of Information Technology Bangalore","ror":"https://ror.org/05h9eqy10","country_code":"IN","type":"education","lineage":["https://openalex.org/I181514455"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Srinivas Vivek","raw_affiliation_strings":["IIIT Bangalore, Electronics City, Hosur Road , Bangalore , 560100, Karnataka , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IIIT Bangalore, Electronics City, Hosur Road , Bangalore , 560100, Karnataka , India","institution_ids":["https://openalex.org/I181514455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080861797","display_name":"Shyam Murthy","orcid":"https://orcid.org/0000-0002-0222-322X"},"institutions":[{"id":"https://openalex.org/I181514455","display_name":"International Institute of Information Technology Bangalore","ror":"https://ror.org/05h9eqy10","country_code":"IN","type":"education","lineage":["https://openalex.org/I181514455"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Shyam Murthy","raw_affiliation_strings":["IIIT Bangalore, Electronics City, Hosur Road , Bangalore , 560100, Karnataka , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IIIT Bangalore, Electronics City, Hosur Road , Bangalore , 560100, Karnataka , India","institution_ids":["https://openalex.org/I181514455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079010262","display_name":"Deepak Kumaraswamy","orcid":"https://orcid.org/0000-0003-0245-9520"},"institutions":[{"id":"https://openalex.org/I11880225","display_name":"National Institute of Technology Karnataka","ror":"https://ror.org/01hz4v948","country_code":"IN","type":"education","lineage":["https://openalex.org/I11880225"]},{"id":"https://openalex.org/I42014448","display_name":"Sardar Vallabhbhai National Institute of Technology Surat","ror":"https://ror.org/02y394t43","country_code":"IN","type":"education","lineage":["https://openalex.org/I42014448"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Deepak Kumaraswamy","raw_affiliation_strings":["Department of Computer Science and Engineering, National Institute of Technology , Surathkal , Karnataka , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, National Institute of Technology , Surathkal , Karnataka , India","institution_ids":["https://openalex.org/I11880225","https://openalex.org/I42014448"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080861797"],"corresponding_institution_ids":["https://openalex.org/I181514455"],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":{"value":0,"currency":"USD","value_usd":0},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.08878708,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"16","issue":"1","first_page":"251","last_page":"277"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9991999864578247,"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":0.9991000294685364,"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/polynomial","display_name":"Polynomial","score":0.7224075198173523},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.7207421064376831},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5961838364601135},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5144579410552979},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5122568011283875},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4667171835899353},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15751662850379944}],"concepts":[{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.7224075198173523},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7207421064376831},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5961838364601135},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5144579410552979},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5122568011283875},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4667171835899353},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15751662850379944},{"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:10.1515/jmc-2021-0054","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2021-0054","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2021-0054/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6e9778c8fa6a4cbdad8a3f08b89407ae","is_oa":true,"landing_page_url":"https://doaj.org/article/6e9778c8fa6a4cbdad8a3f08b89407ae","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Mathematical Cryptology, Vol 16, Iss 1, Pp 251-277 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/jmc-2021-0054","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2021-0054","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2021-0054/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320322753","display_name":"Infosys Foundation","ror":"https://ror.org/03bs18y54"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4297999087.pdf","grobid_xml":"https://content.openalex.org/works/W4297999087.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W56544557","https://openalex.org/W754106230","https://openalex.org/W1608796955","https://openalex.org/W1895952394","https://openalex.org/W1997509004","https://openalex.org/W2010756295","https://openalex.org/W2017464959","https://openalex.org/W2031533839","https://openalex.org/W2032431003","https://openalex.org/W2051847955","https://openalex.org/W2074356711","https://openalex.org/W2104987248","https://openalex.org/W2107764994","https://openalex.org/W2147258429","https://openalex.org/W2157915592","https://openalex.org/W2160108357","https://openalex.org/W2177209050","https://openalex.org/W2295292576","https://openalex.org/W2345615338","https://openalex.org/W2536125594","https://openalex.org/W2571885312","https://openalex.org/W2768174108","https://openalex.org/W2773194476","https://openalex.org/W2798340061","https://openalex.org/W2905257503","https://openalex.org/W2942255051","https://openalex.org/W2982485243","https://openalex.org/W3005886042","https://openalex.org/W3101568060","https://openalex.org/W3114221980","https://openalex.org/W3124717507","https://openalex.org/W3217440957"],"related_works":["https://openalex.org/W2050668358","https://openalex.org/W2080268478","https://openalex.org/W1978042415","https://openalex.org/W2014538672","https://openalex.org/W1967784590","https://openalex.org/W3041670244","https://openalex.org/W2610653156","https://openalex.org/W2260999558","https://openalex.org/W96597593","https://openalex.org/W2265876396"],"abstract_inverted_index":{"Abstract":[0],"We":[1,100],"investigate":[2],"the":[3,17,57,60,83,86,89,94,97,114,127,134,139,144,174,190,208,211,222],"problem":[4],"of":[5,27,74,85,88,96,116,123,137,146,148,176,192,224],"recovering":[6,138],"integer":[7,18,25,32,61,132,180,198],"inputs":[8,38,62,185,212],"(up":[9,63],"to":[10,55,64,182,187],"an":[11,53,65,219],"affine":[12,66],"scaling)":[13],"when":[14],"given":[15],"only":[16,126,188],"monotonic":[19,33,179],"polynomial":[20,34,58,90,92,98,128,181,199,209],"outputs.":[21],"Given":[22],"n":[23,24,45],"outputs":[26,175],"a":[28,120,149,214],"degree-":[29],"d":[30,31,47,49],"whose":[35],"coefficients":[36],"and":[37,44,59,112,210],"are":[39],"integers":[40],"within":[41,213],"known":[42],"bounds":[43],"\u226b":[46],"n\\gg":[48],",":[50],"we":[51,202,205],"give":[52],"algorithm":[54,118],"recover":[56,207],"scaling).":[67],"A":[68],"heuristic":[69],"expected":[70],"time":[71],"complexity":[72],"analysis":[73],"our":[75,117,197],"method":[76],"shows":[77],"that":[78,167,204],"it":[79],"is":[80],"exponential":[81],"in":[82,93],"size":[84,95],"degree":[87],"but":[91],"coefficients.":[99],"conduct":[101],"experiments":[102],"with":[103],"real-world":[104],"data":[105,141,166],"as":[106,108,143],"well":[107],"randomly":[109,177],"chosen":[110,178],"parameters":[111],"demonstrate":[113],"effectiveness":[115],"over":[119],"wide":[121],"range":[122],"parameters.":[124],"Using":[125],"evaluations":[129],"at":[130],"specific":[131],"points,":[133],"apparent":[135],"hardness":[136],"input":[140,193],"served":[142],"basis":[145],"security":[147],"recent":[150],"protocol":[151,172,223],"proposed":[152],"by":[153],"Kesarwani":[154,225],"et":[155,226],"al.":[156,227],"for":[157],"secure":[158,169],"k":[159,160],"-nearest":[161],"neighbor":[162],"computation":[163],"on":[164,221],"encrypted":[165],"involved":[168],"sorting.":[170],"The":[171],"uses":[173],"hide":[183],"its":[184],"except":[186],"reveal":[189],"ordering":[191],"data.":[194],"By":[195],"using":[196],"recovery":[200],"algorithm,":[201],"show":[203],"can":[206],"few":[215],"seconds,":[216],"thereby":[217],"demonstrating":[218],"attack":[220]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2022-10-01T00:00:00"}