{"id":"https://openalex.org/W2071680489","doi":"https://doi.org/10.1007/s001459900040","title":"The Improbability That an Elliptic Curve Has Subexponential Discrete Log Problem under the Menezes\u2014Okamoto\u2014Vanstone Algorithm","display_name":"The Improbability That an Elliptic Curve Has Subexponential Discrete Log Problem under the Menezes\u2014Okamoto\u2014Vanstone Algorithm","publication_year":1998,"publication_date":"1998-03-01","ids":{"openalex":"https://openalex.org/W2071680489","doi":"https://doi.org/10.1007/s001459900040","mag":"2071680489"},"language":"en","primary_location":{"id":"doi:10.1007/s001459900040","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s001459900040","pdf_url":"https://link.springer.com/content/pdf/10.1007/s001459900040.pdf","source":{"id":"https://openalex.org/S190936789","display_name":"Journal of Cryptology","issn_l":"0933-2790","issn":["0933-2790","1432-1378"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s001459900040.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103258382","display_name":"R. Balasubramanian","orcid":null},"institutions":[{"id":"https://openalex.org/I59611059","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05078rg59","country_code":"IN","type":"facility","lineage":["https://openalex.org/I59611059"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"R. Balasubramanian","raw_affiliation_strings":["Institute of Mathematical Sciences, Taramani, 600 013, Madras, India","Institute of Mathematical Sciences, Madras, India#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences, Taramani, 600 013, Madras, India","institution_ids":["https://openalex.org/I59611059"]},{"raw_affiliation_string":"Institute of Mathematical Sciences, Madras, India#TAB#","institution_ids":["https://openalex.org/I59611059"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077509996","display_name":"Neal Koblitz","orcid":"https://orcid.org/0000-0003-3309-7366"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Neal Koblitz","raw_affiliation_strings":["Department of Mathematics, University of Washington, Box 354350, 98195, Seattle, WA, U.S.A","Department of Mathematics, University of Washington, Seattle, U.S.A. 98195#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Washington, Box 354350, 98195, Seattle, WA, U.S.A","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, University of Washington, Seattle, U.S.A. 98195#TAB#","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103258382"],"corresponding_institution_ids":["https://openalex.org/I59611059"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":18.6972,"has_fulltext":true,"cited_by_count":206,"citation_normalized_percentile":{"value":0.99215317,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"11","issue":"2","first_page":"141","last_page":"145"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9993000030517578,"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":0.9993000030517578,"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/T10237","display_name":"Cryptography and Data Security","score":0.9961000084877014,"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":0.9797999858856201,"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/discrete-logarithm","display_name":"Discrete logarithm","score":0.8687011003494263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7130748629570007},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6909964084625244},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.6578192710876465},{"id":"https://openalex.org/keywords/multiplicative-group","display_name":"Multiplicative group","score":0.5803771018981934},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5628695487976074},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5478066205978394},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5070967674255371},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.48291799426078796},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.46212196350097656},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4417405128479004},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.4363342225551605},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.42792171239852905},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.42129606008529663},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3871460258960724},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.351019024848938},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2234002649784088},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19961956143379211},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.145643949508667},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1322307288646698},{"id":"https://openalex.org/keywords/quarter-period","display_name":"Quarter period","score":0.11166411638259888},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06296691298484802}],"concepts":[{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.8687011003494263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7130748629570007},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6909964084625244},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6578192710876465},{"id":"https://openalex.org/C92788228","wikidata":"https://www.wikidata.org/wiki/Q3777923","display_name":"Multiplicative group","level":3,"score":0.5803771018981934},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5628695487976074},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5478066205978394},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5070967674255371},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.48291799426078796},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.46212196350097656},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4417405128479004},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.4363342225551605},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.42792171239852905},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.42129606008529663},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3871460258960724},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.351019024848938},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2234002649784088},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19961956143379211},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.145643949508667},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1322307288646698},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.11166411638259888},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06296691298484802},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s001459900040","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s001459900040","pdf_url":"https://link.springer.com/content/pdf/10.1007/s001459900040.pdf","source":{"id":"https://openalex.org/S190936789","display_name":"Journal of Cryptology","issn_l":"0933-2790","issn":["0933-2790","1432-1378"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptology","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s001459900040","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s001459900040","pdf_url":"https://link.springer.com/content/pdf/10.1007/s001459900040.pdf","source":{"id":"https://openalex.org/S190936789","display_name":"Journal of Cryptology","issn_l":"0933-2790","issn":["0933-2790","1432-1378"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2071680489.pdf","grobid_xml":"https://content.openalex.org/works/W2071680489.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1486898453","https://openalex.org/W1508193711","https://openalex.org/W1830587842","https://openalex.org/W1969728959","https://openalex.org/W2005317356","https://openalex.org/W2036378739","https://openalex.org/W2043926312","https://openalex.org/W2084360184","https://openalex.org/W2094556471","https://openalex.org/W2098377074","https://openalex.org/W2111310412","https://openalex.org/W2128718974","https://openalex.org/W4245047333","https://openalex.org/W4253109663","https://openalex.org/W4292027090","https://openalex.org/W6600380672","https://openalex.org/W6610284376","https://openalex.org/W6637792554","https://openalex.org/W6640346001","https://openalex.org/W6805608002","https://openalex.org/W6818990792"],"related_works":["https://openalex.org/W4380051813","https://openalex.org/W2548082687","https://openalex.org/W3172172454","https://openalex.org/W4221139454","https://openalex.org/W2149528579","https://openalex.org/W2915223967","https://openalex.org/W2794946234","https://openalex.org/W1835682632","https://openalex.org/W2158553589","https://openalex.org/W2071680489"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":10}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
