{"id":"https://openalex.org/W4410302404","doi":"https://doi.org/10.3390/cryptography9020031","title":"Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives","display_name":"Post-Quantum Homomorphic Encryption: A Case for Code-Based Alternatives","publication_year":2025,"publication_date":"2025-05-12","ids":{"openalex":"https://openalex.org/W4410302404","doi":"https://doi.org/10.3390/cryptography9020031"},"language":"en","primary_location":{"id":"doi:10.3390/cryptography9020031","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography9020031","pdf_url":"https://www.mdpi.com/2410-387X/9/2/31/pdf?version=1747054074","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"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":"Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2410-387X/9/2/31/pdf?version=1747054074","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083762560","display_name":"Siddhartha Siddhiprada Bhoi","orcid":"https://orcid.org/0009-0000-6099-9707"},"institutions":[{"id":"https://openalex.org/I2802631561","display_name":"Australian Mathematical Sciences Institute","ror":"https://ror.org/00yn60108","country_code":"AU","type":"other","lineage":["https://openalex.org/I2802631561"]},{"id":"https://openalex.org/I82951845","display_name":"RMIT University","ror":"https://ror.org/04ttjf776","country_code":"AU","type":"education","lineage":["https://openalex.org/I82951845"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Siddhartha Siddhiprada Bhoi","raw_affiliation_strings":["Department of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, Australia","Department of Mathematical Sciences, RMIT University, Melbourne VIC 3000, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, Australia","institution_ids":["https://openalex.org/I82951845","https://openalex.org/I2802631561"]},{"raw_affiliation_string":"Department of Mathematical Sciences, RMIT University, Melbourne VIC 3000, Australia","institution_ids":["https://openalex.org/I2802631561","https://openalex.org/I82951845"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090823015","display_name":"Arathi Arakala","orcid":"https://orcid.org/0000-0002-5515-175X"},"institutions":[{"id":"https://openalex.org/I2802631561","display_name":"Australian Mathematical Sciences Institute","ror":"https://ror.org/00yn60108","country_code":"AU","type":"other","lineage":["https://openalex.org/I2802631561"]},{"id":"https://openalex.org/I82951845","display_name":"RMIT University","ror":"https://ror.org/04ttjf776","country_code":"AU","type":"education","lineage":["https://openalex.org/I82951845"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Arathi Arakala","raw_affiliation_strings":["Department of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, Australia","Department of Mathematical Sciences, RMIT University, Melbourne VIC 3000, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, Australia","institution_ids":["https://openalex.org/I82951845","https://openalex.org/I2802631561"]},{"raw_affiliation_string":"Department of Mathematical Sciences, RMIT University, Melbourne VIC 3000, Australia","institution_ids":["https://openalex.org/I2802631561","https://openalex.org/I82951845"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018795892","display_name":"Amy Beth Corman","orcid":"https://orcid.org/0000-0003-3542-3807"},"institutions":[{"id":"https://openalex.org/I2802631561","display_name":"Australian Mathematical Sciences Institute","ror":"https://ror.org/00yn60108","country_code":"AU","type":"other","lineage":["https://openalex.org/I2802631561"]},{"id":"https://openalex.org/I82951845","display_name":"RMIT University","ror":"https://ror.org/04ttjf776","country_code":"AU","type":"education","lineage":["https://openalex.org/I82951845"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Amy Beth Corman","raw_affiliation_strings":["Department of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, Australia","Department of Mathematical Sciences, RMIT University, Melbourne VIC 3000, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, Australia","institution_ids":["https://openalex.org/I82951845","https://openalex.org/I2802631561"]},{"raw_affiliation_string":"Department of Mathematical Sciences, RMIT University, Melbourne VIC 3000, Australia","institution_ids":["https://openalex.org/I2802631561","https://openalex.org/I82951845"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071957313","display_name":"Asha Rao","orcid":"https://orcid.org/0000-0001-6222-282X"},"institutions":[{"id":"https://openalex.org/I2802631561","display_name":"Australian Mathematical Sciences Institute","ror":"https://ror.org/00yn60108","country_code":"AU","type":"other","lineage":["https://openalex.org/I2802631561"]},{"id":"https://openalex.org/I82951845","display_name":"RMIT University","ror":"https://ror.org/04ttjf776","country_code":"AU","type":"education","lineage":["https://openalex.org/I82951845"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Asha Rao","raw_affiliation_strings":["Department of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, Australia","Department of Mathematical Sciences, RMIT University, Melbourne VIC 3000, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, RMIT University, Melbourne, VIC 3000, Australia","institution_ids":["https://openalex.org/I82951845","https://openalex.org/I2802631561"]},{"raw_affiliation_string":"Department of Mathematical Sciences, RMIT University, Melbourne VIC 3000, Australia","institution_ids":["https://openalex.org/I2802631561","https://openalex.org/I82951845"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5083762560"],"corresponding_institution_ids":["https://openalex.org/I2802631561","https://openalex.org/I82951845"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1732},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1732},"fwci":12.0284,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.98185389,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"9","issue":"2","first_page":"31","last_page":"31"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9986000061035156,"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/T11130","display_name":"Coding theory and cryptography","score":0.9986000061035156,"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/T10237","display_name":"Cryptography and Data Security","score":0.9940999746322632,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.8788182735443115},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6011536717414856},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5730298757553101},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.5715578198432922},{"id":"https://openalex.org/keywords/homomorphic-secret-sharing","display_name":"Homomorphic secret sharing","score":0.522211492061615},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4690571129322052},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3609585762023926},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3527827262878418},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.351839154958725},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.22188091278076172},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10858523845672607},{"id":"https://openalex.org/keywords/secure-multi-party-computation","display_name":"Secure multi-party computation","score":0.0965988039970398},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05562230944633484}],"concepts":[{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.8788182735443115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6011536717414856},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5730298757553101},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.5715578198432922},{"id":"https://openalex.org/C132161212","wikidata":"https://www.wikidata.org/wiki/Q5891458","display_name":"Homomorphic secret sharing","level":4,"score":0.522211492061615},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4690571129322052},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3609585762023926},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3527827262878418},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.351839154958725},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.22188091278076172},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10858523845672607},{"id":"https://openalex.org/C18396474","wikidata":"https://www.wikidata.org/wiki/Q2465888","display_name":"Secure multi-party computation","level":3,"score":0.0965988039970398},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05562230944633484},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/cryptography9020031","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography9020031","pdf_url":"https://www.mdpi.com/2410-387X/9/2/31/pdf?version=1747054074","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"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":"Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:634d7aa3beb64e3d945849fc4858d49a","is_oa":true,"landing_page_url":"https://doaj.org/article/634d7aa3beb64e3d945849fc4858d49a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cryptography, Vol 9, Iss 2, p 31 (2025)","raw_type":"article"},{"id":"pmh:oai:figshare.com:article/29231195","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"Journal contribution"}],"best_oa_location":{"id":"doi:10.3390/cryptography9020031","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography9020031","pdf_url":"https://www.mdpi.com/2410-387X/9/2/31/pdf?version=1747054074","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"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":"Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410302404.pdf","grobid_xml":"https://content.openalex.org/works/W4410302404.grobid-xml"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W36213310","https://openalex.org/W56544557","https://openalex.org/W118080808","https://openalex.org/W913176383","https://openalex.org/W1675339804","https://openalex.org/W1965275036","https://openalex.org/W1972913305","https://openalex.org/W1992282993","https://openalex.org/W2025108828","https://openalex.org/W2031533839","https://openalex.org/W2035929826","https://openalex.org/W2046874530","https://openalex.org/W2048994663","https://openalex.org/W2108834246","https://openalex.org/W2110775981","https://openalex.org/W2132172731","https://openalex.org/W2137147061","https://openalex.org/W2156030242","https://openalex.org/W2171001107","https://openalex.org/W2176745559","https://openalex.org/W2177209050","https://openalex.org/W2226167778","https://openalex.org/W2408211519","https://openalex.org/W2480523195","https://openalex.org/W2512450221","https://openalex.org/W2566390621","https://openalex.org/W2768174108","https://openalex.org/W2914095959","https://openalex.org/W2938052850","https://openalex.org/W3018474919","https://openalex.org/W3116456096","https://openalex.org/W3176410512","https://openalex.org/W3205079182","https://openalex.org/W4297991408","https://openalex.org/W4366605688","https://openalex.org/W4388830940","https://openalex.org/W4390481773","https://openalex.org/W4390865640","https://openalex.org/W4391916556","https://openalex.org/W4406086392","https://openalex.org/W4409862611","https://openalex.org/W6603570079","https://openalex.org/W6604593047","https://openalex.org/W6606067566","https://openalex.org/W6636236547","https://openalex.org/W6638402721","https://openalex.org/W6689604759","https://openalex.org/W6762012821","https://openalex.org/W6768459703","https://openalex.org/W6778434676","https://openalex.org/W6797158879"],"related_works":["https://openalex.org/W4316659877","https://openalex.org/W3035389378","https://openalex.org/W2607647996","https://openalex.org/W3183645941","https://openalex.org/W2911298733","https://openalex.org/W2949835517","https://openalex.org/W1540514112","https://openalex.org/W2292786713","https://openalex.org/W3163109844","https://openalex.org/W4388857498"],"abstract_inverted_index":{"Homomorphic":[0],"Encryption":[1],"(HE)":[2],"allows":[3],"secure":[4],"and":[5,23,53,80,102,105,111],"privacy-protected":[6],"computation":[7],"on":[8,35,63],"encrypted":[9],"data":[10],"without":[11],"the":[12,44,73,94,121],"need":[13],"to":[14,59,76,88,133],"decrypt":[15],"it.":[16],"Since":[17],"Shor\u2019s":[18],"algorithm":[19],"rendered":[20],"prime":[21],"factorisation":[22],"discrete":[24],"logarithm-based":[25],"ciphers":[26,61],"insecure":[27],"with":[28],"quantum":[29],"computations,":[30],"researchers":[31],"have":[32,55,119],"been":[33,56],"working":[34],"building":[36,77],"post-quantum":[37,90,135],"homomorphic":[38,113,137],"encryption":[39,83,114],"(PQHE)":[40],"algorithms.":[41,91],"Most":[42],"of":[43,72,97,123],"current":[45,74],"PQHE":[46,78],"algorithms":[47],"are":[48],"secured":[49],"by":[50],"Lattice-based":[51],"problems":[52],"there":[54],"limited":[57],"attempts":[58],"build":[60],"based":[62],"error-correcting":[64],"code-based":[65,82,99,112,124,136],"problems.":[66],"This":[67],"review":[68],"presents":[69],"an":[70],"overview":[71],"approaches":[75],"schemes":[79],"justifies":[81],"as":[84],"a":[85],"novel":[86],"way":[87],"diversify":[89],"We":[92,108,126],"present":[93],"mathematical":[95],"underpinnings":[96],"existing":[98],"cryptographic":[100],"frameworks":[101],"their":[103],"security":[104],"efficiency":[106],"guarantees.":[107],"compare":[109],"lattice-based":[110],"solutions":[115],"identifying":[116],"challenges":[117],"that":[118],"inhibited":[120],"progress":[122],"schemes.":[125],"finally":[127],"propose":[128],"five":[129],"new":[130],"research":[131],"directions":[132],"advance":[134],"encryption.":[138]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
