{"id":"https://openalex.org/W4417423500","doi":"https://doi.org/10.1186/s42400-025-00515-w","title":"Quantum algorithm for solving binary hyperelliptic curve discrete logarithm problem","display_name":"Quantum algorithm for solving binary hyperelliptic curve discrete logarithm problem","publication_year":2025,"publication_date":"2025-12-17","ids":{"openalex":"https://openalex.org/W4417423500","doi":"https://doi.org/10.1186/s42400-025-00515-w"},"language":"en","primary_location":{"id":"doi:10.1186/s42400-025-00515-w","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s42400-025-00515-w","pdf_url":"https://link.springer.com/content/pdf/10.1186/s42400-025-00515-w.pdf","source":{"id":"https://openalex.org/S3035238565","display_name":"Cybersecurity","issn_l":"2523-3246","issn":["2523-3246"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cybersecurity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1186/s42400-025-00515-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088020021","display_name":"Yan Huang","orcid":"https://orcid.org/0000-0002-6685-0142"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]},{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yan Huang","raw_affiliation_strings":["College of Science, National University of Defense Technology, Changsha, 410083, China","School of Mathematics and Statistics, Hunan University of Science and Technology, Xiangtan, 411201, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, National University of Defense Technology, Changsha, 410083, China","institution_ids":["https://openalex.org/I170215575"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Hunan University of Science and Technology, Xiangtan, 411201, China","institution_ids":["https://openalex.org/I121296143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005533554","display_name":"De Zeng","orcid":"https://orcid.org/0000-0002-9141-5505"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Du Zeng","raw_affiliation_strings":["School of Mathematics and Statistics, Hunan University of Science and Technology, Xiangtan, 411201, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Hunan University of Science and Technology, Xiangtan, 411201, China","institution_ids":["https://openalex.org/I121296143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100408418","display_name":"Chao Chen","orcid":"https://orcid.org/0009-0006-9113-7994"},"institutions":[{"id":"https://openalex.org/I4210110849","display_name":"Sichuan Tourism University","ror":"https://ror.org/018rwb805","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210110849"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chao Chen","raw_affiliation_strings":["College of Big Data and Statistics, Sichuan Tourism University, Chengdu, 610100, Sichuan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Big Data and Statistics, Sichuan Tourism University, Chengdu, 610100, Sichuan, China","institution_ids":["https://openalex.org/I4210110849"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016400836","display_name":"Zijian Zhou","orcid":"https://orcid.org/0000-0001-5728-2908"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zijian Zhou","raw_affiliation_strings":["College of Science, National University of Defense Technology, Changsha, 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, National University of Defense Technology, Changsha, 410083, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005731945","display_name":"Fangguo Zhang","orcid":"https://orcid.org/0000-0002-0486-6413"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]},{"id":"https://openalex.org/I4210098034","display_name":"Key Laboratory of Guangdong Province","ror":"https://ror.org/00swtqp09","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210098034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fangguo Zhang","raw_affiliation_strings":["Guangdong Province Key Laboratory of Information Security Technology, Guangzhou, 510006, China","School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, 510006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangdong Province Key Laboratory of Information Security Technology, Guangzhou, 510006, China","institution_ids":["https://openalex.org/I4210098034"]},{"raw_affiliation_string":"School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, 510006, China","institution_ids":["https://openalex.org/I157773358"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5088020021"],"corresponding_institution_ids":["https://openalex.org/I121296143","https://openalex.org/I170215575"],"apc_list":{"value":1230,"currency":"USD","value_usd":1230},"apc_paid":{"value":1230,"currency":"USD","value_usd":1230},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.48297465,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.7547000050544739,"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"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.7547000050544739,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.18479999899864197,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.03579999879002571,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.7208999991416931},{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.6931999921798706},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.5771999955177307},{"id":"https://openalex.org/keywords/post-quantum-cryptography","display_name":"Post-quantum cryptography","score":0.5723999738693237},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.46369999647140503},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.428600013256073},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.42410001158714294},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.41100001335144043},{"id":"https://openalex.org/keywords/quantum-phase-estimation-algorithm","display_name":"Quantum phase estimation algorithm","score":0.4043999910354614}],"concepts":[{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.7208999991416931},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.6931999921798706},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.599399983882904},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.5771999955177307},{"id":"https://openalex.org/C108277079","wikidata":"https://www.wikidata.org/wiki/Q7233576","display_name":"Post-quantum cryptography","level":4,"score":0.5723999738693237},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47189998626708984},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.46369999647140503},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.428600013256073},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.42410001158714294},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41749998927116394},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.41100001335144043},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.4043999910354614},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.39739999175071716},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.39010000228881836},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.38960000872612},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.38269999623298645},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.38109999895095825},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.37880000472068787},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.3653999865055084},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.35589998960494995},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.326200008392334},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.30169999599456787},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.296999990940094},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.28769999742507935},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26100000739097595},{"id":"https://openalex.org/C144901912","wikidata":"https://www.wikidata.org/wiki/Q471906","display_name":"Quantum cryptography","level":4,"score":0.2567000091075897},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C11074058","wikidata":"https://www.wikidata.org/wiki/Q850110","display_name":"Hyperelliptic curve","level":3,"score":0.2524000108242035}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1186/s42400-025-00515-w","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s42400-025-00515-w","pdf_url":"https://link.springer.com/content/pdf/10.1186/s42400-025-00515-w.pdf","source":{"id":"https://openalex.org/S3035238565","display_name":"Cybersecurity","issn_l":"2523-3246","issn":["2523-3246"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cybersecurity","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:2d26589377d344f7b3dc2954a033be7b","is_oa":true,"landing_page_url":"https://doaj.org/article/2d26589377d344f7b3dc2954a033be7b","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":"Cybersecurity, Vol 8, Iss 1, Pp 1-15 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1186/s42400-025-00515-w","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s42400-025-00515-w","pdf_url":"https://link.springer.com/content/pdf/10.1186/s42400-025-00515-w.pdf","source":{"id":"https://openalex.org/S3035238565","display_name":"Cybersecurity","issn_l":"2523-3246","issn":["2523-3246"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cybersecurity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4303523871","display_name":null,"funder_award_id":"62202475","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6744699187","display_name":null,"funder_award_id":"62272491","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7122009151","display_name":null,"funder_award_id":"62204275","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8424688696","display_name":null,"funder_award_id":"12401696","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4417423500.pdf"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1552628852","https://openalex.org/W2135273380","https://openalex.org/W2146532505","https://openalex.org/W2168676717","https://openalex.org/W2330347957","https://openalex.org/W2951773754","https://openalex.org/W2998412871","https://openalex.org/W3022840541","https://openalex.org/W3172928694","https://openalex.org/W4242597152","https://openalex.org/W4319158786","https://openalex.org/W4383216716","https://openalex.org/W4393155886","https://openalex.org/W4402994415","https://openalex.org/W4412748949"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"It":[1],"is":[2,222],"well-established":[3],"that":[4],"Shor\u2019s":[5,64],"algorithm":[6,43],"can":[7],"solve":[8],"the":[9,78,112,117,133,154,189,218,228],"discrete":[10],"logarithm":[11],"problem":[12],"(DLP)":[13],"in":[14,71],"polynomial":[15,86],"time.":[16],"The":[17,67],"hyperelliptic":[18],"curve":[19],"DLP":[20],"(HCDLP)":[21],"of":[22,81,119,156,203,224],"genus":[23],"2":[24],"has":[25],"found":[26],"widespread":[27],"industrial":[28],"applications":[29],"and":[30,126,152,176,216],"remains":[31],"an":[32],"active":[33],"research":[34],"domain.":[35],"In":[36],"this":[37],"work,":[38],"we":[39,110,131],"develop":[40],"a":[41],"quantum":[42,114,128,134,160,174,178,192,219],"for":[44,137,145,194,212,239],"solving":[45,138,146,167,182],"HCDLP":[46,139,147,168,195],"over":[47,140,148,169,184],"binary":[48,141,170],"fields":[49,142,151,171],"$$\\mathbb":[50],"{F}_{2^n}$$":[51],"<mml:math":[52,97,205,230],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[53,98,206,231],"<mml:msub>":[54],"<mml:mi>F</mml:mi>":[55],"<mml:msup>":[56,207,232],"<mml:mn>2</mml:mn>":[57,208,233],"<mml:mi>n</mml:mi>":[58,100],"</mml:msup>":[59,210,235],"</mml:msub>":[60],"</mml:math>":[61,108,211,236],"by":[62],"adapting":[63],"algorithmic":[65],"framework.":[66],"core":[68],"innovation":[69],"lies":[70],"our":[72],"divisor":[73,82],"addition":[74],"implementation,":[75],"which":[76],"combines":[77],"geometric":[79],"interpretation":[80],"operations":[83],"with":[84,143],"symmetric":[85],"techniques.":[87],"Using":[88],"representative":[89],"parameters":[90],"(":[91],"$$n":[92],"=":[93],"163,":[94],"283,":[95],"571$$":[96],"<mml:mrow>":[99],"<mml:mo>=</mml:mo>":[101],"<mml:mn>163</mml:mn>":[102],"<mml:mo>,</mml:mo>":[103,105],"<mml:mn>283</mml:mn>":[104],"<mml:mn>571</mml:mn>":[106],"</mml:mrow>":[107],"),":[109],"quantify":[111],"required":[113,136],"resources":[115,135,237],"from":[116],"perspective":[118],"minimal":[120,123,127],"qubit":[121],"count,":[122],"T-gate":[124],"usage,":[125],"depth.":[129],"Furthermore,":[130],"compare":[132],"those":[144],"general":[149,185],"prime":[150,186],"demonstrate":[153],"vulnerability":[155],"HCDLP-based":[157],"cryptosystems":[158],"to":[159,181],"attacks.":[161,241],"Our":[162],"analysis":[163],"reveals":[164],"that:":[165],"(1)":[166],"requires":[172],"fewer":[173],"gates":[175],"less":[177],"depth":[179,193],"compared":[180],"it":[183],"fields;":[187],"(2)":[188],"maximum":[190],"achievable":[191],"attacks":[196],"falls":[197],"below":[198],"NIST\u2019s":[199],"minimum":[200],"security":[201],"threshold":[202],"$$2^{40}$$":[204],"<mml:mn>40</mml:mn>":[209],"comparable":[213],"protection":[214],"levels,":[215],"(3)":[217],"computational":[220],"cost":[221],"orders":[223],"magnitude":[225],"lower":[226],"than":[227],"$$2^{157}$$":[229],"<mml:mn>157</mml:mn>":[234],"needed":[238],"AES-128":[240]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-12-17T00:00:00"}