{"id":"https://openalex.org/W4389035934","doi":"https://doi.org/10.1007/s10207-023-00781-0","title":"De Bello Homomorphico: Investigation of the extensibility of the OpenFHE library with basic mathematical functions by means of common approaches using the example of the CKKS cryptosystem","display_name":"De Bello Homomorphico: Investigation of the extensibility of the OpenFHE library with basic mathematical functions by means of common approaches using the example of the CKKS cryptosystem","publication_year":2023,"publication_date":"2023-11-27","ids":{"openalex":"https://openalex.org/W4389035934","doi":"https://doi.org/10.1007/s10207-023-00781-0"},"language":"en","primary_location":{"id":"doi:10.1007/s10207-023-00781-0","doi":"https://doi.org/10.1007/s10207-023-00781-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10207-023-00781-0","pdf_url":null,"source":{"id":"https://openalex.org/S164062316","display_name":"International Journal of Information Security","issn_l":"1615-5262","issn":["1615-5262","1615-5270"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-2","poland-100","russia-white-list-2"],"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":"International Journal of Information Security","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s10207-023-00781-0","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083668224","display_name":"Thomas Prantl","orcid":"https://orcid.org/0000-0003-4044-8494","observed_orcids":["https://orcid.org/0000-0003-4044-8494"]},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Thomas Prantl","raw_affiliation_strings":["University of W\u00fcrzburg, W\u00fcrzburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of W\u00fcrzburg, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067465169","display_name":"Lukas Horn","orcid":"https://orcid.org/0009-0004-4959-1371","observed_orcids":["https://orcid.org/0009-0004-4959-1371"]},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lukas Horn","raw_affiliation_strings":["University of W\u00fcrzburg, W\u00fcrzburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of W\u00fcrzburg, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081560419","display_name":"Simon Engel","orcid":"https://orcid.org/0009-0005-3354-4746","observed_orcids":["https://orcid.org/0009-0005-3354-4746"]},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Simon Engel","raw_affiliation_strings":["University of W\u00fcrzburg, W\u00fcrzburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of W\u00fcrzburg, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001534207","display_name":"Lukas Iffl\u00e4nder","orcid":"https://orcid.org/0000-0002-8506-2758","observed_orcids":["https://orcid.org/0000-0002-8506-2758"]},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lukas Iffl\u00e4nder","raw_affiliation_strings":["University of W\u00fcrzburg, W\u00fcrzburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of W\u00fcrzburg, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013237962","display_name":"Lukas Beierlieb","orcid":"https://orcid.org/0000-0003-2512-9292","observed_orcids":["https://orcid.org/0000-0003-2512-9292"]},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lukas Beierlieb","raw_affiliation_strings":["University of W\u00fcrzburg, W\u00fcrzburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of W\u00fcrzburg, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085116380","display_name":"Christian Krupitzer","orcid":"https://orcid.org/0000-0002-7275-0738","observed_orcids":["https://orcid.org/0000-0002-7275-0738"]},"institutions":[{"id":"https://openalex.org/I110079840","display_name":"University of Hohenheim","ror":"https://ror.org/00b1c9541","country_code":"DE","type":"education","lineage":["https://openalex.org/I110079840"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Krupitzer","raw_affiliation_strings":["University of Hohenheim, Stuttgart, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Hohenheim, Stuttgart, Germany","institution_ids":["https://openalex.org/I110079840"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063155276","display_name":"Andr\u00e9 Bauer","orcid":"https://orcid.org/0000-0002-5582-8812","observed_orcids":["https://orcid.org/0000-0002-5582-8812"]},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andr\u00e9 Bauer","raw_affiliation_strings":["University of Chicago, Chicago, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092855510","display_name":"Mansi Sakarvadia","orcid":"https://orcid.org/0000-0002-0041-0160","observed_orcids":["https://orcid.org/0000-0002-0041-0160"]},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mansi Sakarvadia","raw_affiliation_strings":["University of Chicago, Chicago, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032231503","display_name":"Ian T Foster","orcid":"https://orcid.org/0000-0003-2129-5269","observed_orcids":["https://orcid.org/0000-0003-2129-5269"]},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ian Foster","raw_affiliation_strings":["University of Chicago, Chicago, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013790674","display_name":"Samuel Kounev","orcid":"https://orcid.org/0000-0001-9742-2063","observed_orcids":["https://orcid.org/0000-0001-9742-2063"]},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Samuel Kounev","raw_affiliation_strings":["University of W\u00fcrzburg, W\u00fcrzburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of W\u00fcrzburg, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5083668224"],"corresponding_institution_ids":["https://openalex.org/I25974101"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":{"value":3190,"currency":"USD","value_usd":3190},"fwci":0.732,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.69651913,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"23","issue":"2","first_page":"1149","last_page":"1169"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11614","display_name":"Cloud Data Security Solutions","score":0.0008999999845400453,"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"}},{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.0003000000142492354,"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/homomorphic-encryption","display_name":"homomorphic encryption","score":0.9779999852180481},{"id":"https://openalex.org/keywords/openfhe","display_name":"OpenFHE","score":0.8199999928474426},{"id":"https://openalex.org/keywords/division","display_name":"division","score":0.6209999918937683},{"id":"https://openalex.org/keywords/exponential-function","display_name":"exponential function","score":0.6399999856948853},{"id":"https://openalex.org/keywords/square-roots","display_name":"square roots","score":0.925000011920929},{"id":"https://openalex.org/keywords/logarithms","display_name":"logarithms","score":0.9869999885559082},{"id":"https://openalex.org/keywords/cloud-data-privacy","display_name":"cloud data privacy","score":0.6930000185966492},{"id":"https://openalex.org/keywords/time-series-forecasting","display_name":"time series forecasting","score":0.6669999957084656}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8386906385421753},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.8230764865875244},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.759236216545105},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.635622501373291},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6296589374542236},{"id":"https://openalex.org/C79974875","wikidata":"https://www.wikidata.org/wiki/Q483639","display_name":"Cloud computing","level":2,"score":0.5642312169075012},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.550408661365509},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5145037174224854},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.49075111746788025},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4898652732372284},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.48935598134994507},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44328078627586365},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.28192758560180664},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26733922958374023},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.1597650647163391},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.14865809679031372},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.12044867873191833},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11523881554603577},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.09369897842407227},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10207-023-00781-0","doi":"https://doi.org/10.1007/s10207-023-00781-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10207-023-00781-0","pdf_url":null,"source":{"id":"https://openalex.org/S164062316","display_name":"International Journal of Information Security","issn_l":"1615-5262","issn":["1615-5262","1615-5270"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-2","poland-100","russia-white-list-2"],"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":"International Journal of Information Security","raw_type":"journal-article"},{"id":"pmh:oai:opus.bibliothek.uni-wuerzburg.de:38315","doi":null,"is_oa":true,"landing_page_url":"https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/38315","pdf_url":"https://opus.bibliothek.uni-wuerzburg.de/files/38315/s10207-023-00781-0.pdf","source":{"id":"https://openalex.org/S4306401635","display_name":"Online Publication Service of W\u00fcrzburg University (W\u00fcrzburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I25974101","host_organization_name":"University of W\u00fcrzburg","host_organization_lineage":["https://openalex.org/I25974101"],"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":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10207-023-00781-0","doi":"https://doi.org/10.1007/s10207-023-00781-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10207-023-00781-0","pdf_url":null,"source":{"id":"https://openalex.org/S164062316","display_name":"International Journal of Information Security","issn_l":"1615-5262","issn":["1615-5262","1615-5270"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-2","poland-100","russia-white-list-2"],"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":"International Journal of Information Security","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320325356","display_name":"Julius-Maximilians-Universit\u00e4t W\u00fcrzburg","ror":"https://ror.org/00fbnyb24"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389035934.pdf","grobid_xml":"https://content.openalex.org/works/W4389035934.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W7185409","https://openalex.org/W129305155","https://openalex.org/W150223756","https://openalex.org/W1536392520","https://openalex.org/W1910065018","https://openalex.org/W1971286892","https://openalex.org/W1983892874","https://openalex.org/W2031533839","https://openalex.org/W2042519306","https://openalex.org/W2068279394","https://openalex.org/W2099662985","https://openalex.org/W2102030985","https://openalex.org/W2118663079","https://openalex.org/W2129745056","https://openalex.org/W2134978206","https://openalex.org/W2137269967","https://openalex.org/W2152209375","https://openalex.org/W2157253445","https://openalex.org/W2164327070","https://openalex.org/W2207441427","https://openalex.org/W2282950146","https://openalex.org/W2285574614","https://openalex.org/W2290980804","https://openalex.org/W2620783544","https://openalex.org/W2768174108","https://openalex.org/W2768505000","https://openalex.org/W2794888826","https://openalex.org/W2811248283","https://openalex.org/W2885347723","https://openalex.org/W2899140612","https://openalex.org/W2944259260","https://openalex.org/W2944535446","https://openalex.org/W2957780493","https://openalex.org/W2978874100","https://openalex.org/W2989605743","https://openalex.org/W3031471216","https://openalex.org/W3042644725","https://openalex.org/W3114221980","https://openalex.org/W3155526168","https://openalex.org/W3173128495","https://openalex.org/W3181751708","https://openalex.org/W4221159209","https://openalex.org/W4249630244","https://openalex.org/W4285284542","https://openalex.org/W6602143840","https://openalex.org/W6777472928"],"related_works":["https://openalex.org/W4411230702","https://openalex.org/W7138010493","https://openalex.org/W4416961900","https://openalex.org/W1924686635","https://openalex.org/W4409724164","https://openalex.org/W2189043898","https://openalex.org/W2911789111","https://openalex.org/W2547665653","https://openalex.org/W7070457218","https://openalex.org/W3095628233"],"abstract_inverted_index":{"Abstract":[0],"Cloud":[1],"computing":[2],"has":[3],"become":[4],"increasingly":[5],"popular":[6],"due":[7],"to":[8,14,24,43,58,120,145,190],"its":[9],"scalability,":[10],"cost-effectiveness,":[11],"and":[12,33,45,67,83,92,168],"ability":[13],"handle":[15],"large":[16],"volumes":[17],"of":[18,99,142,165,173,197,201],"data.":[19],"However,":[20],"entrusting":[21],"(sensitive)":[22],"data":[23,31,47],"a":[25,49,147,177],"third":[26],"party":[27],"raises":[28],"concerns":[29],"about":[30],"security":[32],"privacy.":[34],"Homomorphic":[35],"encryption":[36,62],"is":[37,127,163,169],"one":[38],"solution":[39],"that":[40,105],"allows":[41],"users":[42,185],"store":[44],"process":[46],"in":[48,129,170],"public":[50],"cloud":[51,54],"without":[52],"the":[53,76,85,96,100,123,140,153,157,166,171,192,198,202],"provider":[55],"having":[56],"access":[57],"it.":[59],"Currently,":[60],"homomorphic":[61],"libraries":[63],"only":[64],"support":[65],"addition":[66],"multiplication;":[68],"other":[69],"mathematical":[70,207],"functions":[71],"must":[72],"be":[73,109],"implemented":[74],"by":[75],"user.":[77],"To":[78,103],"this":[79,112,181],"end,":[80],"we":[81,116,183],"discuss":[82],"implement":[84],"division,":[86],"exponential,":[87],"square":[88],"root,":[89],"logarithm,":[90],"minimum,":[91],"maximum":[93],"function,":[94],"using":[95],"CKKS":[97,199],"cryptosystem":[98,200],"OpenFHE":[101,203],"library.":[102],"demonstrate":[104],"complex":[106],"applications":[107],"can":[108],"realized":[110],"with":[111,186,205],"extended":[113],"function":[114,162,195],"set,":[115],"have":[117],"used":[118,128],"it":[119],"homomorphically":[121],"realize":[122],"Box\u2013Cox":[124],"transform,":[125],"which":[126],"many":[130],"real-world":[131],"applications,":[132],"e.g.,":[133],"time-series":[134],"forecasts.":[135],"Our":[136],"results":[137],"show":[138],"how":[139,189],"number":[141],"iterations":[143],"required":[144],"achieve":[146],"given":[148],"accuracy":[149],"varies":[150],"depending":[151],"on":[152,176,188],"function.":[154],"In":[155],"addition,":[156],"execution":[158],"time":[159],"for":[160],"each":[161],"independent":[164],"input":[167],"range":[172],"ten":[174],"seconds":[175],"reference":[178],"machine.":[179],"With":[180],"work,":[182],"provide":[184],"insights":[187],"extend":[191],"original":[193],"restricted":[194],"set":[196],"library":[204],"basic":[206],"functions.":[208]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":2}],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2023-11-28T00:00:00"}