{"id":"https://openalex.org/W3006389067","doi":"https://doi.org/10.1109/uemcon47517.2019.8992917","title":"A New Approach Towards Fully Homomorphic Encryption Over Geometric Algebra","display_name":"A New Approach Towards Fully Homomorphic Encryption Over Geometric Algebra","publication_year":2019,"publication_date":"2019-10-01","ids":{"openalex":"https://openalex.org/W3006389067","doi":"https://doi.org/10.1109/uemcon47517.2019.8992917","mag":"3006389067"},"language":"en","primary_location":{"id":"doi:10.1109/uemcon47517.2019.8992917","is_oa":false,"landing_page_url":"https://doi.org/10.1109/uemcon47517.2019.8992917","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 10th Annual Ubiquitous Computing, Electronics &amp; Mobile Communication Conference (UEMCON)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086457258","display_name":"David W. H. A. da Silva","orcid":"https://orcid.org/0000-0003-4498-0525"},"institutions":[{"id":"https://openalex.org/I888729015","display_name":"University of Colorado Colorado Springs","ror":"https://ror.org/054spjc55","country_code":"US","type":"education","lineage":["https://openalex.org/I888729015"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David W. H. A. da Silva","raw_affiliation_strings":["Computer Science, University of Colorado C. Springs, Colorado Springs, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science, University of Colorado C. Springs, Colorado Springs, United States","institution_ids":["https://openalex.org/I888729015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103023116","display_name":"Carlos A. Paz de Ara\u00fajo","orcid":"https://orcid.org/0000-0003-3370-4242"},"institutions":[{"id":"https://openalex.org/I888729015","display_name":"University of Colorado Colorado Springs","ror":"https://ror.org/054spjc55","country_code":"US","type":"education","lineage":["https://openalex.org/I888729015"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Carlos Paz de Araujo","raw_affiliation_strings":["Electrical Engineering, University of Colorado C. Springs, Colorado Springs, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering, University of Colorado C. Springs, Colorado Springs, United States","institution_ids":["https://openalex.org/I888729015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103980869","display_name":"Edward Chow","orcid":null},"institutions":[{"id":"https://openalex.org/I888729015","display_name":"University of Colorado Colorado Springs","ror":"https://ror.org/054spjc55","country_code":"US","type":"education","lineage":["https://openalex.org/I888729015"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edward Chow","raw_affiliation_strings":["Computer Science, University of Colorado C. Springs, Colorado Springs, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science, University of Colorado C. Springs, Colorado Springs, United States","institution_ids":["https://openalex.org/I888729015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005461614","display_name":"Bryan Sosa Barillas","orcid":null},"institutions":[{"id":"https://openalex.org/I888729015","display_name":"University of Colorado Colorado Springs","ror":"https://ror.org/054spjc55","country_code":"US","type":"education","lineage":["https://openalex.org/I888729015"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bryan Sosa Barillas","raw_affiliation_strings":["Computer Science, University of Colorado C. Springs, Colorado Springs, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science, University of Colorado C. Springs, Colorado Springs, United States","institution_ids":["https://openalex.org/I888729015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I888729015"],"apc_list":null,"apc_paid":null,"fwci":0.8678,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.81847619,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"0241","last_page":"0249"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9995999932289124,"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":0.9995999932289124,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9969000220298767,"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/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.7538634538650513},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.6404847502708435},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5346404910087585},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5163218379020691},{"id":"https://openalex.org/keywords/chinese-remainder-theorem","display_name":"Chinese remainder theorem","score":0.47045862674713135},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.46165215969085693},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41559261083602905},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20605000853538513},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19424748420715332}],"concepts":[{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.7538634538650513},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.6404847502708435},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5346404910087585},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5163218379020691},{"id":"https://openalex.org/C151635116","wikidata":"https://www.wikidata.org/wiki/Q193878","display_name":"Chinese remainder theorem","level":2,"score":0.47045862674713135},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.46165215969085693},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41559261083602905},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20605000853538513},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19424748420715332},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/uemcon47517.2019.8992917","is_oa":false,"landing_page_url":"https://doi.org/10.1109/uemcon47517.2019.8992917","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 10th Annual Ubiquitous Computing, Electronics &amp; Mobile Communication Conference (UEMCON)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6100000143051147,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W56544557","https://openalex.org/W150064776","https://openalex.org/W150223756","https://openalex.org/W341789076","https://openalex.org/W619515706","https://openalex.org/W913176383","https://openalex.org/W1494049356","https://openalex.org/W1585680900","https://openalex.org/W1586781146","https://openalex.org/W1595771334","https://openalex.org/W1607431452","https://openalex.org/W1658453268","https://openalex.org/W1785033518","https://openalex.org/W1850468005","https://openalex.org/W1966725992","https://openalex.org/W1979120705","https://openalex.org/W1992282993","https://openalex.org/W2007466965","https://openalex.org/W2015663895","https://openalex.org/W2021258994","https://openalex.org/W2031533839","https://openalex.org/W2050174852","https://openalex.org/W2053148809","https://openalex.org/W2070357636","https://openalex.org/W2098290658","https://openalex.org/W2116021467","https://openalex.org/W2117463337","https://openalex.org/W2117475864","https://openalex.org/W2129580084","https://openalex.org/W2130618508","https://openalex.org/W2142399242","https://openalex.org/W2156030242","https://openalex.org/W2159579247","https://openalex.org/W2176745559","https://openalex.org/W2177209050","https://openalex.org/W2226167778","https://openalex.org/W2233194383","https://openalex.org/W2395482502","https://openalex.org/W2399908350","https://openalex.org/W2400239211","https://openalex.org/W2489339293","https://openalex.org/W2518938922","https://openalex.org/W2533462565","https://openalex.org/W2554750353","https://openalex.org/W2606882085","https://openalex.org/W2898352792","https://openalex.org/W2949694298","https://openalex.org/W2950663030","https://openalex.org/W2952541202","https://openalex.org/W2952982365","https://openalex.org/W3028867652","https://openalex.org/W3030180915","https://openalex.org/W3148044822","https://openalex.org/W6606067566","https://openalex.org/W6635080486","https://openalex.org/W6679427637","https://openalex.org/W6697696596","https://openalex.org/W6712075820","https://openalex.org/W6712787161","https://openalex.org/W6764751714","https://openalex.org/W6765188004","https://openalex.org/W6777979691","https://openalex.org/W6778434676"],"related_works":["https://openalex.org/W3011940778","https://openalex.org/W2567319923","https://openalex.org/W4221119508","https://openalex.org/W276198277","https://openalex.org/W2124202597","https://openalex.org/W2340393497","https://openalex.org/W2471310969","https://openalex.org/W1592523240","https://openalex.org/W2963369796","https://openalex.org/W3006389067"],"abstract_inverted_index":{"The":[0,22,52,114],"ability":[1],"to":[2,30,48,87,138,202,206,221],"compute":[3],"on":[4,33,105,168],"encrypted":[5,34],"data":[6,35],"in":[7,17,57,68,121,128,140,191],"a":[8,12,146,181,214],"meaningful":[9],"way":[10,47],"is":[11,36,44,80,85,174],"subject":[13],"of":[14,24,91,103,117,134,149,188,196,216],"increasing":[15],"interest":[16],"both":[18,81],"academia":[19],"and":[20,43,63,83,110,145,154,209],"industry.":[21],"type":[23],"encryption":[25,139],"that":[26,79,125,170],"allows":[27,200],"any":[28],"function":[29],"be":[31,88],"evaluated":[32],"called":[37],"fully":[38],"homomorphic":[39,219],"encryption,":[40],"or":[41],"FHE,":[42],"one":[45],"promising":[46],"achieve":[49],"secure":[50,84],"computation.":[51],"problem":[53,74],"was":[54],"first":[55,64],"stated":[56],"1978":[58],"by":[59,66],"Rivest":[60],"et":[61],"al.":[62],"realized":[65],"Gentry":[67],"2009,":[69],"but":[70],"remains":[71],"an":[72,76,157],"open":[73],"since":[75],"FHE":[77,94,161,172,224],"scheme":[78,173],"efficient":[82],"yet":[86],"presented.":[89],"Most":[90],"the":[92,101,122,132,150,165,192],"prominent":[93],"schemes":[95,119],"follow":[96],"Gentry's":[97],"blueprint":[98],"which":[99,199],"concentrates":[100],"efforts":[102],"researchers":[104],"very":[106],"similar":[107,123],"algebraic":[108,189],"structures":[109,190],"noise":[111],"management":[112],"techniques.":[113],"intrinsic":[115],"complexity":[116],"these":[118],"results":[120],"shortfalls":[124],"they":[126],"share":[127],"efficiency.":[129],"We":[130,163],"introduce":[131],"application":[133],"Geometric":[135],"Algebra":[136],"(GA)":[137],"conjunction":[141],"with":[142],"p-adic":[143],"arithmetic":[144],"modified":[147],"version":[148],"Chinese":[151],"Remainder":[152],"Theorem":[153],"we":[155,179],"demonstrate":[156],"efficient,":[158],"noise-free,":[159],"symmetric-key":[160],"scheme.":[162],"focus":[164],"security":[166],"analysis":[167],"demonstrating":[169],"our":[171],"not":[175],"linearly":[176],"decryptable.":[177],"Further,":[178],"discuss":[180],"practical":[182],"approach":[183],"for":[184],"generalizing":[185],"different":[186],"types":[187],"geometric":[193],"product":[194],"space":[195],"two":[197],"dimensions,":[198],"us":[201],"export":[203],"GA":[204],"operations":[205],"other":[207],"algebras":[208],"vice-versa.":[210],"Our":[211],"construction":[212],"supports":[213],"variety":[215],"applications,":[217],"from":[218],"obfuscation":[220],"general":[222],"purpose":[223],"computations.":[225]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
