{"id":"https://openalex.org/W4413199142","doi":"https://doi.org/10.3390/jcp5030057","title":"Metric Differential Privacy on the Special Orthogonal Group SO(3)","display_name":"Metric Differential Privacy on the Special Orthogonal Group SO(3)","publication_year":2025,"publication_date":"2025-08-12","ids":{"openalex":"https://openalex.org/W4413199142","doi":"https://doi.org/10.3390/jcp5030057"},"language":"en","primary_location":{"id":"doi:10.3390/jcp5030057","is_oa":true,"landing_page_url":"https://doi.org/10.3390/jcp5030057","pdf_url":"https://www.mdpi.com/2624-800X/5/3/57/pdf?version=1754962551","source":{"id":"https://openalex.org/S4210232532","display_name":"Journal of Cybersecurity and Privacy","issn_l":"2624-800X","issn":["2624-800X"],"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":"Journal of Cybersecurity and Privacy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2624-800X/5/3/57/pdf?version=1754962551","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103563818","display_name":"Anna Katharina Hildebrandt","orcid":null},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]},{"id":"https://openalex.org/I4210115621","display_name":"Institut f\u00fcr Sozialforschung und Sozialwirtschaft","ror":"https://ror.org/024nzz449","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210115621"]},{"id":"https://openalex.org/I4210162871","display_name":"Saarbr\u00fccken Stadtwerke (Germany)","ror":"https://ror.org/05h5kva18","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210162871"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Anna Katharina Hildebrandt","raw_affiliation_strings":["Institute for Computer Science, Johannes Gutenberg University Mainz, 55122 Mainz, Germany","Mondata GmbH, Science Park 1, 66123 Saarbr\u00fccken, Germany","PRAIVACY UG, Science Park 1, 66123 Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Computer Science, Johannes Gutenberg University Mainz, 55122 Mainz, Germany","institution_ids":["https://openalex.org/I197323543"]},{"raw_affiliation_string":"Mondata GmbH, Science Park 1, 66123 Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210162871"]},{"raw_affiliation_string":"PRAIVACY UG, Science Park 1, 66123 Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210115621"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Anna Katharina Hildebrandt","orcid":null},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]},{"id":"https://openalex.org/I4210115621","display_name":"Institut f\u00fcr Sozialforschung und Sozialwirtschaft","ror":"https://ror.org/024nzz449","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210115621"]},{"id":"https://openalex.org/I4210162871","display_name":"Saarbr\u00fccken Stadtwerke (Germany)","ror":"https://ror.org/05h5kva18","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210162871"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Anna Katharina Hildebrandt","raw_affiliation_strings":["Institute for Computer Science, Johannes Gutenberg University Mainz, 55122 Mainz, Germany","Mondata GmbH, Science Park 1, 66123 Saarbr\u00fccken, Germany","PRAIVACY UG, Science Park 1, 66123 Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Computer Science, Johannes Gutenberg University Mainz, 55122 Mainz, Germany","institution_ids":["https://openalex.org/I197323543"]},{"raw_affiliation_string":"Mondata GmbH, Science Park 1, 66123 Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210162871"]},{"raw_affiliation_string":"PRAIVACY UG, Science Park 1, 66123 Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210115621"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018595947","display_name":"Elmar Sch\u00f6mer","orcid":"https://orcid.org/0000-0002-5652-2591"},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]},{"id":"https://openalex.org/I4210162871","display_name":"Saarbr\u00fccken Stadtwerke (Germany)","ror":"https://ror.org/05h5kva18","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210162871"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Elmar Sch\u00f6mer","raw_affiliation_strings":["Institute for Computer Science, Johannes Gutenberg University Mainz, 55122 Mainz, Germany","Mondata GmbH, Science Park 1, 66123 Saarbr\u00fccken, Germany"],"raw_orcid":"https://orcid.org/0000-0002-5652-2591","affiliations":[{"raw_affiliation_string":"Institute for Computer Science, Johannes Gutenberg University Mainz, 55122 Mainz, Germany","institution_ids":["https://openalex.org/I197323543"]},{"raw_affiliation_string":"Mondata GmbH, Science Park 1, 66123 Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210162871"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015934308","display_name":"Andreas Hildebrandt","orcid":"https://orcid.org/0000-0003-2180-6516"},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]},{"id":"https://openalex.org/I4210115621","display_name":"Institut f\u00fcr Sozialforschung und Sozialwirtschaft","ror":"https://ror.org/024nzz449","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210115621"]},{"id":"https://openalex.org/I4210162871","display_name":"Saarbr\u00fccken Stadtwerke (Germany)","ror":"https://ror.org/05h5kva18","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210162871"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andreas Hildebrandt","raw_affiliation_strings":["Institute for Computer Science, Johannes Gutenberg University Mainz, 55122 Mainz, Germany","Mondata GmbH, Science Park 1, 66123 Saarbr\u00fccken, Germany","PRAIVACY UG, Science Park 1, 66123 Saarbr\u00fccken, Germany"],"raw_orcid":"https://orcid.org/0000-0003-2180-6516","affiliations":[{"raw_affiliation_string":"Institute for Computer Science, Johannes Gutenberg University Mainz, 55122 Mainz, Germany","institution_ids":["https://openalex.org/I197323543"]},{"raw_affiliation_string":"Mondata GmbH, Science Park 1, 66123 Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210162871"]},{"raw_affiliation_string":"PRAIVACY UG, Science Park 1, 66123 Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210115621"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015934308","display_name":"Andreas Hildebrandt","orcid":"https://orcid.org/0000-0003-2180-6516"},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]},{"id":"https://openalex.org/I4210115621","display_name":"Institut f\u00fcr Sozialforschung und Sozialwirtschaft","ror":"https://ror.org/024nzz449","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210115621"]},{"id":"https://openalex.org/I4210162871","display_name":"Saarbr\u00fccken Stadtwerke (Germany)","ror":"https://ror.org/05h5kva18","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210162871"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Andreas Hildebrandt","raw_affiliation_strings":["Institute for Computer Science, Johannes Gutenberg University Mainz, 55122 Mainz, Germany","Mondata GmbH, Science Park 1, 66123 Saarbr\u00fccken, Germany","PRAIVACY UG, Science Park 1, 66123 Saarbr\u00fccken, Germany"],"raw_orcid":"https://orcid.org/0000-0003-2180-6516","affiliations":[{"raw_affiliation_string":"Institute for Computer Science, Johannes Gutenberg University Mainz, 55122 Mainz, Germany","institution_ids":["https://openalex.org/I197323543"]},{"raw_affiliation_string":"Mondata GmbH, Science Park 1, 66123 Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210162871"]},{"raw_affiliation_string":"PRAIVACY UG, Science Park 1, 66123 Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210115621"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015934308"],"corresponding_institution_ids":["https://openalex.org/I197323543","https://openalex.org/I4210115621","https://openalex.org/I4210162871"],"apc_list":{"value":1000,"currency":"CHF","value_usd":1207},"apc_paid":{"value":1000,"currency":"CHF","value_usd":1207},"fwci":1.0988,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.83973866,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"5","issue":"3","first_page":"57","last_page":"57"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9998999834060669,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9998999834060669,"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/T11980","display_name":"Human Mobility and Location-Based Analysis","score":0.9577999711036682,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9448000192642212,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/differential-privacy","display_name":"Differential privacy","score":0.8938107490539551},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.642548143863678},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6052242517471313},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.5087435841560364},{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.4766993224620819},{"id":"https://openalex.org/keywords/laplace-distribution","display_name":"Laplace distribution","score":0.44977399706840515},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35623711347579956},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32952257990837097},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.26914942264556885},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.2036738097667694},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14139840006828308},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09217676520347595}],"concepts":[{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.8938107490539551},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.642548143863678},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6052242517471313},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.5087435841560364},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.4766993224620819},{"id":"https://openalex.org/C183057437","wikidata":"https://www.wikidata.org/wiki/Q671617","display_name":"Laplace distribution","level":3,"score":0.44977399706840515},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35623711347579956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32952257990837097},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.26914942264556885},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.2036738097667694},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14139840006828308},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09217676520347595},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/jcp5030057","is_oa":true,"landing_page_url":"https://doi.org/10.3390/jcp5030057","pdf_url":"https://www.mdpi.com/2624-800X/5/3/57/pdf?version=1754962551","source":{"id":"https://openalex.org/S4210232532","display_name":"Journal of Cybersecurity and Privacy","issn_l":"2624-800X","issn":["2624-800X"],"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":"Journal of Cybersecurity and Privacy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:eb02a6f0cfb64aafaf8478198d71cc12","is_oa":true,"landing_page_url":"https://doaj.org/article/eb02a6f0cfb64aafaf8478198d71cc12","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 Cybersecurity and Privacy, Vol 5, Iss 3, p 57 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/jcp5030057","is_oa":true,"landing_page_url":"https://doi.org/10.3390/jcp5030057","pdf_url":"https://www.mdpi.com/2624-800X/5/3/57/pdf?version=1754962551","source":{"id":"https://openalex.org/S4210232532","display_name":"Journal of Cybersecurity and Privacy","issn_l":"2624-800X","issn":["2624-800X"],"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":"Journal of Cybersecurity and Privacy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4413199142.pdf","grobid_xml":"https://content.openalex.org/works/W4413199142.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1658920975","https://openalex.org/W2016959837","https://openalex.org/W2035868186","https://openalex.org/W2318908986","https://openalex.org/W2894779347","https://openalex.org/W2901147448","https://openalex.org/W2963515066","https://openalex.org/W3027483882","https://openalex.org/W3102917240","https://openalex.org/W3199411828","https://openalex.org/W3212753401","https://openalex.org/W4205228770","https://openalex.org/W6663662237","https://openalex.org/W6753006236"],"related_works":["https://openalex.org/W3171066746","https://openalex.org/W3166730876","https://openalex.org/W2989546622","https://openalex.org/W4385694606","https://openalex.org/W2254375831","https://openalex.org/W3091150767","https://openalex.org/W4297752560","https://openalex.org/W1683740614","https://openalex.org/W3008292135","https://openalex.org/W4366999619"],"abstract_inverted_index":{"Differential":[0],"privacy":[1,14,42,84,103,134],"(DP)":[2],"is":[3,69,149],"an":[4],"important":[5],"framework":[6],"to":[7,29,80,85,112,118,124,137],"provide":[8],"strong":[9],"theoretical":[10],"guarantees":[11],"on":[12,98,106,153],"the":[13,37,45,54,107,126,142,150,157,170],"and":[15,33,47,100,155,177],"utility":[16],"of":[17,39,49,66,115,172],"released":[18],"data.":[19],"Since":[20],"its":[21],"introduction":[22,38],"in":[23,51,57,90,130],"2006,":[24],"DP":[25,50,117],"has":[26,43],"been":[27],"applied":[28],"various":[30],"data":[31,55,67],"types":[32],"domains.":[34],"More":[35],"recently,":[36],"metric":[40,60,63,82,116,152],"differential":[41,83],"improved":[44],"applicability":[46],"interpretability":[48],"cases":[52],"where":[53,147],"resides":[56],"more":[58],"general":[59],"spaces.":[61],"In":[62,74,110],"DP,":[64],"indistinguishability":[65],"points":[68],"modulated":[70],"by":[71],"their":[72,180],"distance.":[73],"this":[75],"work,":[76],"we":[77,121,168],"demonstrate":[78,122],"how":[79,123],"extend":[81],"datasets":[86],"representing":[87],"three-dimensional":[88],"rotations":[89],"SO(3)":[91,131],"through":[92],"two":[93],"mechanisms:":[94],"a":[95,101,165],"Laplace":[96,143],"mechanism":[97,104,144,159],"SO(3),":[99,154],"novel":[102],"based":[105],"Bingham":[108,158],"distribution.":[109],"contrast":[111],"other":[113],"applications":[114],"directional":[119],"data,":[120],"handle":[125],"antipodal":[127],"symmetry":[128],"inherent":[129],"while":[132],"transferring":[133],"from":[135,174],"S3":[136],"SO(3).":[138],"We":[139],"show":[140],"that":[141,156],"fulfills":[145,160],"\u03f5\u03d5-privacy,":[146],"\u03d5":[148],"geodesic":[151],"\u03f5\u02dc\u03d5-privacy":[161],"with":[162],"\u03f5\u02dc=\u03c04\u03f5.":[163],"Through":[164],"simulation":[166],"study,":[167],"compare":[169],"distribution":[171],"samples":[173],"both":[175],"mechanisms":[176],"argue":[178],"about":[179],"respective":[181],"privacy\u2013utility":[182],"tradeoffs.":[183]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
