{"id":"https://openalex.org/W7125530180","doi":"https://doi.org/10.3390/e28010130","title":"Logarithmic-Size Post-Quantum Linkable Ring Signatures Based on Aggregation Operations","display_name":"Logarithmic-Size Post-Quantum Linkable Ring Signatures Based on Aggregation Operations","publication_year":2026,"publication_date":"2026-01-22","ids":{"openalex":"https://openalex.org/W7125530180","doi":"https://doi.org/10.3390/e28010130","pmid":"https://pubmed.ncbi.nlm.nih.gov/41594037"},"language":"en","primary_location":{"id":"doi:10.3390/e28010130","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28010130","pdf_url":"https://www.mdpi.com/1099-4300/28/1/130/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/28/1/130/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123655608","display_name":"Minghui Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]},{"id":"https://openalex.org/I4210142167","display_name":"DigitalSpace (United States)","ror":"https://ror.org/04h1th525","country_code":"US","type":"company","lineage":["https://openalex.org/I4210142167"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Minghui Zheng","raw_affiliation_strings":["School of Cyberspace Security, Sichuan University, Chengdu 610065, China","School of Intelligent Science and Engineering, Hubei Minzu University, 39 Xueyuan Road, Enshi 445000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Cyberspace Security, Sichuan University, Chengdu 610065, China","institution_ids":["https://openalex.org/I4210142167"]},{"raw_affiliation_string":"School of Intelligent Science and Engineering, Hubei Minzu University, 39 Xueyuan Road, Enshi 445000, China","institution_ids":["https://openalex.org/I145897649"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123702798","display_name":"Shicheng Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shicheng Huang","raw_affiliation_strings":["School of Intelligent Science and Engineering, Hubei Minzu University, 39 Xueyuan Road, Enshi 445000, China"],"raw_orcid":"https://orcid.org/0009-0009-9674-0380","affiliations":[{"raw_affiliation_string":"School of Intelligent Science and Engineering, Hubei Minzu University, 39 Xueyuan Road, Enshi 445000, China","institution_ids":["https://openalex.org/I145897649"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089126301","display_name":"Deju Kong","orcid":null},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]},{"id":"https://openalex.org/I4210142167","display_name":"DigitalSpace (United States)","ror":"https://ror.org/04h1th525","country_code":"US","type":"company","lineage":["https://openalex.org/I4210142167"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Deju Kong","raw_affiliation_strings":["School of Cyberspace Security, Sichuan University, Chengdu 610065, China","School of Intelligent Science and Engineering, Hubei Minzu University, 39 Xueyuan Road, Enshi 445000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Cyberspace Security, Sichuan University, Chengdu 610065, China","institution_ids":["https://openalex.org/I4210142167"]},{"raw_affiliation_string":"School of Intelligent Science and Engineering, Hubei Minzu University, 39 Xueyuan Road, Enshi 445000, China","institution_ids":["https://openalex.org/I145897649"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123643749","display_name":"Xing Fu","orcid":null},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xing Fu","raw_affiliation_strings":["School of Intelligent Science and Engineering, Hubei Minzu University, 39 Xueyuan Road, Enshi 445000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Intelligent Science and Engineering, Hubei Minzu University, 39 Xueyuan Road, Enshi 445000, China","institution_ids":["https://openalex.org/I145897649"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123699483","display_name":"Qiancheng Yao","orcid":null},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiancheng Yao","raw_affiliation_strings":["School of Intelligent Science and Engineering, Hubei Minzu University, 39 Xueyuan Road, Enshi 445000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Intelligent Science and Engineering, Hubei Minzu University, 39 Xueyuan Road, Enshi 445000, China","institution_ids":["https://openalex.org/I145897649"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123705075","display_name":"Wenyi Hou","orcid":null},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenyi Hou","raw_affiliation_strings":["School of Intelligent Science and Engineering, Hubei Minzu University, 39 Xueyuan Road, Enshi 445000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Intelligent Science and Engineering, Hubei Minzu University, 39 Xueyuan Road, Enshi 445000, China","institution_ids":["https://openalex.org/I145897649"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08890144,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"1","first_page":"130","last_page":"130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9746000170707703,"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":0.9746000170707703,"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":0.006099999882280827,"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/T10270","display_name":"Blockchain Technology Applications and Security","score":0.0031999999191612005,"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/ring-signature","display_name":"Ring signature","score":0.9610000252723694},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5383999943733215},{"id":"https://openalex.org/keywords/random-oracle","display_name":"Random oracle","score":0.51910001039505},{"id":"https://openalex.org/keywords/signature","display_name":"Signature (topology)","score":0.5138000249862671},{"id":"https://openalex.org/keywords/hash-function","display_name":"Hash function","score":0.5102999806404114},{"id":"https://openalex.org/keywords/anonymity","display_name":"Anonymity","score":0.5052000284194946},{"id":"https://openalex.org/keywords/merkle-signature-scheme","display_name":"Merkle signature scheme","score":0.48330000042915344},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.48240000009536743},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.4763000011444092}],"concepts":[{"id":"https://openalex.org/C168941894","wikidata":"https://www.wikidata.org/wiki/Q3483645","display_name":"Ring signature","level":4,"score":0.9610000252723694},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7379999756813049},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5383999943733215},{"id":"https://openalex.org/C94284585","wikidata":"https://www.wikidata.org/wiki/Q228184","display_name":"Random oracle","level":4,"score":0.51910001039505},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.5138000249862671},{"id":"https://openalex.org/C99138194","wikidata":"https://www.wikidata.org/wiki/Q183427","display_name":"Hash function","level":2,"score":0.5102999806404114},{"id":"https://openalex.org/C178005623","wikidata":"https://www.wikidata.org/wiki/Q308859","display_name":"Anonymity","level":2,"score":0.5052000284194946},{"id":"https://openalex.org/C40404285","wikidata":"https://www.wikidata.org/wiki/Q1921816","display_name":"Merkle signature scheme","level":5,"score":0.48330000042915344},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.48240000009536743},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.4763000011444092},{"id":"https://openalex.org/C118463975","wikidata":"https://www.wikidata.org/wiki/Q220849","display_name":"Digital signature","level":3,"score":0.427700012922287},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4262999892234802},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C205383636","wikidata":"https://www.wikidata.org/wiki/Q14746","display_name":"Merkle tree","level":4,"score":0.39160001277923584},{"id":"https://openalex.org/C520049643","wikidata":"https://www.wikidata.org/wiki/Q189760","display_name":"Voting","level":3,"score":0.38280001282691956},{"id":"https://openalex.org/C2780612046","wikidata":"https://www.wikidata.org/wiki/Q926161","display_name":"Electronic voting","level":4,"score":0.36469998955726624},{"id":"https://openalex.org/C19163912","wikidata":"https://www.wikidata.org/wiki/Q7681779","display_name":"Tamper resistance","level":2,"score":0.35100001096725464},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.34880000352859497},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34850001335144043},{"id":"https://openalex.org/C18899389","wikidata":"https://www.wikidata.org/wiki/Q2736593","display_name":"Blind signature","level":4,"score":0.28949999809265137},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.27900001406669617},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C141492731","wikidata":"https://www.wikidata.org/wiki/Q1052621","display_name":"Message authentication code","level":3,"score":0.2732999920845032},{"id":"https://openalex.org/C97399411","wikidata":"https://www.wikidata.org/wiki/Q825367","display_name":"Coin flipping","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C123201435","wikidata":"https://www.wikidata.org/wiki/Q456632","display_name":"Information privacy","level":2,"score":0.2563999891281128}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e28010130","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28010130","pdf_url":"https://www.mdpi.com/1099-4300/28/1/130/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:41594037","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41594037","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:3c99ef1f6f9a43abaa8552eec5b84ee0","is_oa":true,"landing_page_url":"https://doaj.org/article/3c99ef1f6f9a43abaa8552eec5b84ee0","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":"Entropy, Vol 28, Iss 1, p 130 (2026)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:12840541","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC12840541/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e28010130","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28010130","pdf_url":"https://www.mdpi.com/1099-4300/28/1/130/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7910454273223877,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7125530180.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1533905858","https://openalex.org/W1783862658","https://openalex.org/W2071576863","https://openalex.org/W2129483619","https://openalex.org/W2791664942","https://openalex.org/W3003209651","https://openalex.org/W3170925853","https://openalex.org/W3185221375","https://openalex.org/W4385834407","https://openalex.org/W4402210788","https://openalex.org/W4402571252","https://openalex.org/W4404321370","https://openalex.org/W4404834516","https://openalex.org/W4414066615"],"related_works":[],"abstract_inverted_index":{"Linkable":[0],"ring":[1,7,38,65,105,121,175,192,216,230],"signatures":[2,39],"are":[3],"a":[4,101,117,126,143],"type":[5],"of":[6,15,54,80,92,159,173,179,190],"signature":[8,66,82,106,146,231,246],"scheme":[9,107,115,147,168,182,223],"that":[10,165],"can":[11],"protect":[12],"the":[13,19,24,29,51,78,90,140,157,166,170,181,184,195,203,215,225],"anonymity":[14],"signers":[16],"while":[17],"allowing":[18],"public":[20,123],"to":[21,129,148,219],"verify":[22],"whether":[23],"same":[25,30],"signer":[26],"has":[27],"signed":[28],"message":[31],"multiple":[32],"times.":[33],"This":[34],"functionality":[35],"makes":[36],"linkable":[37,64,104,174,191],"suitable":[40],"for":[41,139],"applications":[42],"such":[43,72],"as":[44,73],"cryptocurrencies":[45],"and":[46,58,84,133,187,243],"anonymous":[47],"voting":[48],"systems,":[49],"achieving":[50],"dual":[52],"goals":[53],"identity":[55],"privacy":[56,208],"protection":[57],"misuse":[59],"prevention.":[60],"However,":[61],"existing":[62,226],"post-quantum":[63,81,93,103,144,150,229],"schemes":[67],"often":[68],"suffer":[69],"from":[70,89,120],"issues":[71],"excessive":[74],"linear":[75],"data":[76],"growth":[77],"adoption":[79],"algorithms,":[83],"high":[85],"circuit":[86],"complexity":[87],"resulting":[88],"use":[91],"zero-knowledge":[94,151],"proof":[95,152],"protocols.":[96],"To":[97],"address":[98],"these":[99],"issues,":[100],"logarithmic-size":[102],"based":[108],"on":[109],"aggregation":[110,196],"operations":[111],"is":[112],"proposed.":[113],"The":[114],"constructs":[116],"Merkle":[118],"tree":[119],"members'":[122],"keys":[124],"via":[125],"hash":[127],"algorithm":[128],"achieve":[130],"logarithmic-scale":[131],"signing":[132,204,237],"verification":[134,241],"operations.":[135],"Moreover,":[136,194],"it":[137],"introduces,":[138],"first":[141],"time,":[142,238,242],"aggregate":[145],"replace":[149],"protocols,":[153],"thereby":[154],"effectively":[155],"avoiding":[156],"construction":[158],"complex":[160],"circuits.":[161],"Scheme":[162],"analysis":[163],"confirms":[164],"proposed":[167],"meets":[169],"correctness":[171],"requirements":[172,189],"signatures.":[176,193],"In":[177],"terms":[178],"security,":[180],"satisfies":[183],"anonymity,":[185],"unforgeability,":[186],"linkability":[188],"process":[197],"does":[198],"not":[199],"leak":[200],"information":[201],"about":[202],"members,":[205,221],"ensuring":[206],"strong":[207],"protection.":[209],"Experimental":[210],"results":[211],"demonstrate":[212],"that,":[213],"when":[214],"size":[217],"scales":[218],"1024":[220],"our":[222],"outperforms":[224],"Dilithium-based":[227],"logarithmic":[228],"scheme,":[232],"with":[233],"nearly":[234],"98.25%":[235],"lower":[236,240],"98.90%":[239],"99.81%":[244],"smaller":[245],"size.":[247]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2026-01-24T00:00:00"}