{"id":"https://openalex.org/W7167910735","doi":"https://doi.org/10.48550/arxiv.2607.08042","title":"Degree-Constrained Interval Optimization for Minimax Polynomial Approximation in Homomorphic Encryption","display_name":"Degree-Constrained Interval Optimization for Minimax Polynomial Approximation in Homomorphic Encryption","publication_year":2026,"publication_date":"2026-07-09","ids":{"openalex":"https://openalex.org/W7167910735","doi":"https://doi.org/10.48550/arxiv.2607.08042"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.08042","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.08042","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.08042","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061899832","display_name":"Jiheon Woo","orcid":"https://orcid.org/0000-0001-9122-5691"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Woo, Jiheon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5140388149","display_name":"Donggyun Ryu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ryu, Donggyun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5140427039","display_name":"Yongjune Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Yongjune","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.5411999821662903,"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":0.5411999821662903,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.1420000046491623,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.05849999934434891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.758899986743927},{"id":"https://openalex.org/keywords/minimax-approximation-algorithm","display_name":"Minimax approximation algorithm","score":0.6664999723434448},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.542900025844574},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5260000228881836},{"id":"https://openalex.org/keywords/stable-polynomial","display_name":"Stable polynomial","score":0.5037000179290771},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.45969998836517334},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.4375999867916107},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.41029998660087585},{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.4032999873161316}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.758899986743927},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7117000222206116},{"id":"https://openalex.org/C117148685","wikidata":"https://www.wikidata.org/wiki/Q6865376","display_name":"Minimax approximation algorithm","level":2,"score":0.6664999723434448},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.542900025844574},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5260000228881836},{"id":"https://openalex.org/C45025165","wikidata":"https://www.wikidata.org/wiki/Q13424738","display_name":"Stable polynomial","level":5,"score":0.5037000179290771},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.45969998836517334},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.4375999867916107},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.41029998660087585},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.4032999873161316},{"id":"https://openalex.org/C173047080","wikidata":"https://www.wikidata.org/wiki/Q6400676","display_name":"Kharitonov's theorem","level":5,"score":0.38749998807907104},{"id":"https://openalex.org/C9353750","wikidata":"https://www.wikidata.org/wiki/Q5384549","display_name":"Equioscillation theorem","level":5,"score":0.38019999861717224},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.3783000111579895},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36910000443458557},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36809998750686646},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.36730000376701355},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.36399999260902405},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.36230000853538513},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36160001158714294},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.35409998893737793},{"id":"https://openalex.org/C97395012","wikidata":"https://www.wikidata.org/wiki/Q1422356","display_name":"Reciprocal polynomial","level":4,"score":0.3197999894618988},{"id":"https://openalex.org/C2780861221","wikidata":"https://www.wikidata.org/wiki/Q913849","display_name":"Minimax theorem","level":3,"score":0.30880001187324524},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C99140742","wikidata":"https://www.wikidata.org/wiki/Q843550","display_name":"Polynomial-time approximation scheme","level":3,"score":0.2955000102519989},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.2930999994277954},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.2653999924659729},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.263700008392334}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.08042","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.08042","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.08042","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.08042","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Homomorphic":[0],"encryption":[1],"(HE)":[2],"enables":[3],"privacy-preserving":[4],"inference":[5],"under":[6,82],"arithmetic":[7],"constraints":[8],"that":[9,167],"restrict":[10],"encrypted":[11],"evaluation":[12],"to":[13,73,106,114,186],"additions":[14],"and":[15,134,152,176],"multiplications.":[16],"As":[17],"a":[18,42,53,65,68,83,95,145],"result,":[19],"non-polynomial":[20],"activation":[21],"functions":[22,132],"must":[23],"be":[24],"replaced":[25],"by":[26,37],"polynomial":[27,30,59,137,156],"approximations.":[28],"Among":[29],"approximation":[31,50,62,80,102,174],"methods,":[32],"minimax":[33,58,79,127,173],"approximation,":[34],"typically":[35],"computed":[36],"the":[38,48,61,78,101,108,115,149,169],"Remez":[39],"algorithm,":[40],"is":[41,64,104],"standard":[43],"approach":[44],"because":[45],"it":[46],"minimizes":[47],"maximum":[49],"error":[51,81,110,175],"over":[52],"given":[54],"design":[55,150],"interval.":[56],"For":[57],"design,":[60],"interval":[63,70,97,103,151],"critical":[66],"hyperparameter:":[67],"wider":[69],"improves":[71],"robustness":[72],"large-magnitude":[74],"inputs":[75],"while":[76],"increasing":[77],"fixed":[84],"degree":[85],"budget.":[86],"In":[87],"this":[88,92,183],"paper,":[89],"we":[90,125],"formulate":[91],"trade-off":[93,170],"as":[94],"distribution-aware":[96],"optimization":[98],"problem,":[99],"where":[100],"chosen":[105],"minimize":[107],"mean-squared":[109],"(MSE)":[111],"with":[112,129,194],"respect":[113],"pre-activation":[116],"distribution":[117],"of":[118],"interest.":[119],"To":[120],"effectively":[121],"control":[122],"outside-interval":[123,177],"inputs,":[124],"combine":[126],"polynomials":[128,141],"domain":[130,139],"extension":[131,140],"(DEFs)":[133],"their":[135],"HE-realizable":[136,187],"counterparts,":[138],"(DEPs),":[142],"which":[143],"approximate":[144],"clipping":[146,178],"operation":[147],"outside":[148],"thereby":[153],"suppress":[154],"uncontrolled":[155],"extrapolation.":[157],"We":[158,180],"first":[159],"derive":[160],"an":[161,191,195],"analytically":[162],"tractable":[163],"DEF-based":[164],"proxy":[165],"objective":[166,185],"captures":[168],"between":[171],"within-interval":[172],"error.":[179],"then":[181],"connect":[182],"idealized":[184],"DEP":[188],"constructions":[189],"through":[190],"implementation-error":[192],"decomposition":[193],"accompanying":[196],"upper":[197],"bound.":[198]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-11T00:00:00"}
