{"id":"https://openalex.org/W4416999561","doi":"https://doi.org/10.48550/arxiv.2512.02087","title":"A survey about Hidden Subgroup Problem from a mathematical and cryptographic perspective","display_name":"A survey about Hidden Subgroup Problem from a mathematical and cryptographic perspective","publication_year":2025,"publication_date":"2025-12-01","ids":{"openalex":"https://openalex.org/W4416999561","doi":"https://doi.org/10.48550/arxiv.2512.02087"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2512.02087","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.02087","pdf_url":"https://arxiv.org/pdf/2512.02087","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2512.02087","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026538952","display_name":"Simone Dutto","orcid":"https://orcid.org/0000-0002-6508-7843"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dutto, Simone","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022443092","display_name":"Pietro Mercuri","orcid":"https://orcid.org/0000-0003-4402-6432"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mercuri, Pietro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031579561","display_name":"Nadir Murru","orcid":"https://orcid.org/0000-0003-0509-6278"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Murru, Nadir","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5077000743","display_name":"Lorenzo Romano","orcid":"https://orcid.org/0000-0001-7574-2592"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Romano, Lorenzo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.26750001311302185,"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":0.26750001311302185,"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/T10849","display_name":"Finite Group Theory Research","score":0.2606000006198883,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.12160000205039978,"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/semidirect-product","display_name":"Semidirect product","score":0.7124000191688538},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.6317999958992004},{"id":"https://openalex.org/keywords/graph-isomorphism","display_name":"Graph isomorphism","score":0.5867000222206116},{"id":"https://openalex.org/keywords/dihedral-group","display_name":"Dihedral group","score":0.5852000117301941},{"id":"https://openalex.org/keywords/non-abelian-group","display_name":"Non-abelian group","score":0.545199990272522},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.43389999866485596},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4133000075817108},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.39430001378059387},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37880000472068787}],"concepts":[{"id":"https://openalex.org/C75066664","wikidata":"https://www.wikidata.org/wiki/Q291126","display_name":"Semidirect product","level":3,"score":0.7124000191688538},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6317999958992004},{"id":"https://openalex.org/C61665672","wikidata":"https://www.wikidata.org/wiki/Q303100","display_name":"Graph isomorphism","level":4,"score":0.5867000222206116},{"id":"https://openalex.org/C72409365","wikidata":"https://www.wikidata.org/wiki/Q558339","display_name":"Dihedral group","level":3,"score":0.5852000117301941},{"id":"https://openalex.org/C170124329","wikidata":"https://www.wikidata.org/wiki/Q592651","display_name":"Non-abelian group","level":4,"score":0.545199990272522},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5070000290870667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47279998660087585},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.43389999866485596},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4133000075817108},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39480000734329224},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.39430001378059387},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37290000915527344},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.3727000057697296},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.37209999561309814},{"id":"https://openalex.org/C81008192","wikidata":"https://www.wikidata.org/wiki/Q1017231","display_name":"Elementary abelian group","level":3,"score":0.36039999127388},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3472000062465668},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C14669601","wikidata":"https://www.wikidata.org/wiki/Q2293759","display_name":"Torsion subgroup","level":4,"score":0.2971000075340271},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.2639000117778778},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.25929999351501465},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2574000060558319},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2547000050544739},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.25429999828338623},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.25060001015663147},{"id":"https://openalex.org/C181149355","wikidata":"https://www.wikidata.org/wiki/Q897511","display_name":"Cryptanalysis","level":3,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2512.02087","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.02087","pdf_url":"https://arxiv.org/pdf/2512.02087","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2512.02087","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.02087","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2512.02087","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.02087","pdf_url":"https://arxiv.org/pdf/2512.02087","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,22,59,115],"provide":[1],"a":[2,107,150],"survey":[3],"on":[4,80],"the":[5,17,25,37,62,66,89,97,111,118,123,132,136,140],"Hidden":[6],"Subgroup":[7],"Problem":[8],"(HSP),":[9],"which":[10],"plays":[11],"an":[12,32],"important":[13],"role":[14],"in":[15,106,125,146],"studying":[16],"security":[18],"of":[19,65],"public-key":[20],"cryptosystems.":[21],"first":[23],"review":[24],"abelian":[26,56],"case,":[27,109],"where":[28,71],"Kitaev's":[29],"algorithm":[30],"yields":[31],"efficient":[33,74],"quantum":[34,75],"solution":[35,76],"to":[36,88,96,110],"HSP,":[38,70],"recalling":[39],"how":[40],"classical":[41],"problems":[42],"(such":[43],"as":[44,55],"order":[45],"finding,":[46],"integer":[47],"factorization,":[48],"and":[49,101,131,144],"discrete":[50],"logarithm)":[51],"can":[52],"be":[53],"formulated":[54],"HSP":[57,124],"instances.":[58],"then":[60],"examine":[61],"current":[63],"state":[64],"art":[67],"for":[68,121],"non-abelian":[69,126],"no":[72],"general":[73],"is":[77],"known,":[78],"focusing":[79],"some":[81],"relevant":[82],"groups":[83,94],"including":[84],"dihedral":[85],"group":[86],"(connected":[87,95],"shortest":[90],"vector":[91],"problem),":[92,100],"symmetric":[93],"graph":[98],"isomorphism":[99],"semidirect":[102],"product":[103],"constructions":[104],"(connected,":[105],"special":[108],"code":[112],"equivalence":[113],"problem).":[114],"also":[116],"describe":[117],"main":[119],"techniques":[120],"addressing":[122],"cases,":[127],"namely":[128],"Fourier":[129],"sampling":[130],"black-box":[133],"approach.":[134],"Throughout":[135],"paper,":[137],"we":[138],"highlight":[139],"mathematical":[141],"notions":[142],"required":[143],"exploited":[145],"this":[147],"context,":[148],"providing":[149],"cryptography-oriented":[151],"perspective.":[152]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-12-04T00:00:00"}