{"id":"https://openalex.org/W4386557143","doi":"https://doi.org/10.62056/an2isgsfg","title":"On the success probability of the quantum algorithm for the short DLP","display_name":"On the success probability of the quantum algorithm for the short DLP","publication_year":2026,"publication_date":"2026-05-04","ids":{"openalex":"https://openalex.org/W4386557143","doi":"https://doi.org/10.62056/an2isgsfg"},"language":"en","primary_location":{"id":"doi:10.62056/an2isgsfg","is_oa":true,"landing_page_url":"https://doi.org/10.62056/an2isgsfg","pdf_url":"https://cic.iacr.org/p/3/1/10/pdf","source":{"id":"https://openalex.org/S4394708374","display_name":"IACR Communications in Cryptology","issn_l":"3006-5496","issn":["3006-5496"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320989","host_organization_name":"International Association for Cryptologic Research","host_organization_lineage":["https://openalex.org/P4310320989"],"host_organization_lineage_names":["International Association for Cryptologic Research"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Communications in Cryptology","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://cic.iacr.org/p/3/1/10/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046120717","display_name":"Martin Eker\u00e5","orcid":"https://orcid.org/0000-0002-7061-2374"},"institutions":[{"id":"https://openalex.org/I1289187217","display_name":"Swedish Armed Forces","ror":"https://ror.org/04qn5a624","country_code":"SE","type":"government","lineage":["https://openalex.org/I1289187217"]},{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Martin Eker\u00e5","raw_affiliation_strings":["KTH Royal Institute of Technology","Swedish NCSA, Swedish Armed Forces"],"raw_orcid":"https://orcid.org/0000-0002-7061-2374","affiliations":[{"raw_affiliation_string":"KTH Royal Institute of Technology","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"Swedish NCSA, Swedish Armed Forces","institution_ids":["https://openalex.org/I1289187217"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046120717"],"corresponding_institution_ids":["https://openalex.org/I1289187217","https://openalex.org/I86987016"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.00105281,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"3","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","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/T10682","display_name":"Quantum Computing Algorithms and Architecture","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/T10237","display_name":"Cryptography and Data Security","score":0.994700014591217,"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/T11130","display_name":"Coding theory and cryptography","score":0.9751999974250793,"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/parameterized-complexity","display_name":"Parameterized complexity","score":0.6474693417549133},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.623889684677124},{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.6172990798950195},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5475883483886719},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5148988962173462},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4905669093132019},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4503447413444519},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4386771619319916},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32688283920288086},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2948494851589203},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.09604984521865845}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6474693417549133},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.623889684677124},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.6172990798950195},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5475883483886719},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5148988962173462},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4905669093132019},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4503447413444519},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4386771619319916},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32688283920288086},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2948494851589203},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.09604984521865845},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.62056/an2isgsfg","is_oa":true,"landing_page_url":"https://doi.org/10.62056/an2isgsfg","pdf_url":"https://cic.iacr.org/p/3/1/10/pdf","source":{"id":"https://openalex.org/S4394708374","display_name":"IACR Communications in Cryptology","issn_l":"3006-5496","issn":["3006-5496"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320989","host_organization_name":"International Association for Cryptologic Research","host_organization_lineage":["https://openalex.org/P4310320989"],"host_organization_lineage_names":["International Association for Cryptologic Research"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Communications in Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2309.01754","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.01754","pdf_url":"https://arxiv.org/pdf/2309.01754","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:arXiv.org:2309.01754","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2309.01754","pdf_url":"https://arxiv.org/pdf/2309.01754","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.2309.01754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2309.01754","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":"doi:10.62056/an2isgsfg","is_oa":true,"landing_page_url":"https://doi.org/10.62056/an2isgsfg","pdf_url":"https://cic.iacr.org/p/3/1/10/pdf","source":{"id":"https://openalex.org/S4394708374","display_name":"IACR Communications in Cryptology","issn_l":"3006-5496","issn":["3006-5496"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320989","host_organization_name":"International Association for Cryptologic Research","host_organization_lineage":["https://openalex.org/P4310320989"],"host_organization_lineage_names":["International Association for Cryptologic Research"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Communications in Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[{"id":"https://openalex.org/G8869864247","display_name":null,"funder_award_id":"2022-06725","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"}],"funders":[{"id":"https://openalex.org/F4320312143","display_name":"National Centre for Supercomputing Applications","ror":"https://ror.org/03r10zj06"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"},{"id":"https://openalex.org/F4320325664","display_name":"F\u00f6rsvarsmakten","ror":"https://ror.org/04qn5a624"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386557143.pdf","grobid_xml":"https://content.openalex.org/works/W4386557143.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1555245969","https://openalex.org/W2321282558","https://openalex.org/W2299507895","https://openalex.org/W1900540279","https://openalex.org/W4300200155","https://openalex.org/W4300498183","https://openalex.org/W2577600644","https://openalex.org/W1544736259","https://openalex.org/W2012392278","https://openalex.org/W2656095712"],"abstract_inverted_index":{"Eker\u00e5":[0],"and":[1,195],"H\u00e5stad":[2],"have":[3],"introduced":[4],"a":[5,36,56,101,109,199],"variation":[6],"of":[7,28,42,149],"Shor's":[8,17],"algorithm":[9,21,44],"for":[10,86],"the":[11,23,40,46,62,113,137,140,159,166,169,202,209],"discrete":[12],"logarithm":[13,48],"problem":[14,206],"(DLP).":[15],"Unlike":[16],"original":[18],"algorithm,":[19],"Eker\u00e5\u2013H\u00e5stad's":[20,43],"solves":[22],"short":[24,47,88,193,210],"DLP":[25],"in":[26,55,112,136,174,189],"groups":[27,191],"unknown":[29],"order.":[30],"In":[31],"this":[32],"work,":[33],"we":[34],"prove":[35],"lower":[37],"bound":[38],"on":[39,168],"probability":[41,64,104,161],"recovering":[45],"<mml:math":[49,72,89,143,150,175],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[50,73,90,144,151,176],"<mml:mrow>":[51,74,79,91,145,152,177],"<mml:mi>d</mml:mi>":[52,92,153],"</mml:mrow>":[53,82,84,93,147,154,179],"</mml:math>":[54,85,94,148,155,180],"single":[57],"run.":[58],"By":[59],"our":[60],"bound,":[61],"success":[63,103,160],"can":[65],"easily":[66],"be":[67,125],"pushed":[68],"as":[69,71,139],"high":[70,102],"<mml:mn>1</mml:mn>":[75],"<mml:mo>\u2212</mml:mo>":[76,80],"<mml:msup>":[77],"<mml:mn>10</mml:mn>":[78,81],"</mml:msup>":[83],"any":[87],".":[95,181],"A":[96],"key":[97],"to":[98,106,127,157,163,187,196,208],"achieving":[99],"such":[100],"is":[105],"efficiently":[107],"perform":[108],"limited":[110],"search":[111,170],"classical":[114,132],"post-processing":[115,133],"by":[116],"leveraging":[117],"meet-in-the-middle":[118],"or":[119],"random-walk":[120],"techniques.":[121],"These":[122],"techniques":[123],"may":[124],"generalized":[126],"speed":[128],"up":[129],"other":[130],"related":[131],"algorithms.":[134],"Asymptotically,":[135],"limit":[138],"bit":[141],"length":[142],"<mml:mi>m</mml:mi>":[146,178],"tends":[156,162],"infinity,":[158],"one":[164],"if":[165],"limits":[167],"space":[171],"are":[172,184],"parameterized":[173],"Our":[182],"results":[183],"directly":[185],"applicable":[186],"Diffie\u2013Hellman":[188],"safe-prime":[190],"with":[192],"exponents,":[194],"RSA":[197,203],"via":[198],"reduction":[200],"from":[201],"integer":[204],"factoring":[205],"(IFP)":[207],"DLP.":[211]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2023-09-09T00:00:00"}
