{"id":"https://openalex.org/W2911446493","doi":"https://doi.org/10.1007/s00145-019-09311-5","title":"On Tight Security Proofs for Schnorr Signatures","display_name":"On Tight Security Proofs for Schnorr Signatures","publication_year":2019,"publication_date":"2019-02-06","ids":{"openalex":"https://openalex.org/W2911446493","doi":"https://doi.org/10.1007/s00145-019-09311-5","mag":"2911446493"},"language":"en","primary_location":{"id":"doi:10.1007/s00145-019-09311-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00145-019-09311-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00145-019-09311-5.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/s00145-019-09311-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000634122","display_name":"Nils Fleischhacker","orcid":"https://orcid.org/0000-0002-2770-5444"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Nils Fleischhacker","raw_affiliation_strings":["Ruhr University Bochum, Bochum, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ruhr University Bochum, Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090157645","display_name":"Tibor Jager","orcid":"https://orcid.org/0000-0002-3205-7699"},"institutions":[{"id":"https://openalex.org/I206945453","display_name":"Paderborn University","ror":"https://ror.org/058kzsd48","country_code":"DE","type":"education","lineage":["https://openalex.org/I206945453"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tibor Jager","raw_affiliation_strings":["Paderborn University, Paderborn, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Paderborn University, Paderborn, Germany","institution_ids":["https://openalex.org/I206945453"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053197848","display_name":"Dominique Schr\u00f6der","orcid":"https://orcid.org/0000-0001-6943-8914"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dominique Schr\u00f6der","raw_affiliation_strings":["Friedrich-Alexander-University Erlangen-N\u00fcrnberg, N\u00fcrnberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Friedrich-Alexander-University Erlangen-N\u00fcrnberg, N\u00fcrnberg, Germany","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000634122"],"corresponding_institution_ids":["https://openalex.org/I904495901"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.7421,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.88373269,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"32","issue":"2","first_page":"566","last_page":"599"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":1.0,"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":1.0,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9833999872207642,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9824000000953674,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/random-oracle","display_name":"Random oracle","score":0.86141037940979},{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.7076050043106079},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6931730508804321},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6925270557403564},{"id":"https://openalex.org/keywords/schnorr-signature","display_name":"Schnorr signature","score":0.6599100232124329},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5405672192573547},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.5191358923912048},{"id":"https://openalex.org/keywords/concrete-security","display_name":"Concrete security","score":0.49895787239074707},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47772762179374695},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44741666316986084},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.43538662791252136},{"id":"https://openalex.org/keywords/signature","display_name":"Signature (topology)","score":0.4172673225402832},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38829225301742554},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.27622392773628235},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2678605318069458},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.23592829704284668},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.10942435264587402},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.07060149312019348}],"concepts":[{"id":"https://openalex.org/C94284585","wikidata":"https://www.wikidata.org/wiki/Q228184","display_name":"Random oracle","level":4,"score":0.86141037940979},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.7076050043106079},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6931730508804321},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6925270557403564},{"id":"https://openalex.org/C124968333","wikidata":"https://www.wikidata.org/wiki/Q1465057","display_name":"Schnorr signature","level":5,"score":0.6599100232124329},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5405672192573547},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5191358923912048},{"id":"https://openalex.org/C147343967","wikidata":"https://www.wikidata.org/wiki/Q5159078","display_name":"Concrete security","level":3,"score":0.49895787239074707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47772762179374695},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44741666316986084},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43538662791252136},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.4172673225402832},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38829225301742554},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.27622392773628235},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2678605318069458},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.23592829704284668},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.10942435264587402},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.07060149312019348},{"id":"https://openalex.org/C18899389","wikidata":"https://www.wikidata.org/wiki/Q2736593","display_name":"Blind signature","level":4,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00145-019-09311-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00145-019-09311-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00145-019-09311-5.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/s00145-019-09311-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00145-019-09311-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00145-019-09311-5.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":[{"id":"https://openalex.org/F4320320873","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2911446493.pdf","grobid_xml":"https://content.openalex.org/works/W2911446493.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W258602522","https://openalex.org/W1508759756","https://openalex.org/W1529156313","https://openalex.org/W1559365371","https://openalex.org/W1574186939","https://openalex.org/W1589034595","https://openalex.org/W1592092778","https://openalex.org/W1601106539","https://openalex.org/W1604930642","https://openalex.org/W1625658248","https://openalex.org/W1646354800","https://openalex.org/W1704483751","https://openalex.org/W1805549252","https://openalex.org/W1848025830","https://openalex.org/W2019213727","https://openalex.org/W2052267638","https://openalex.org/W2054482077","https://openalex.org/W2088548892","https://openalex.org/W2095708839","https://openalex.org/W2114296987","https://openalex.org/W2135222307","https://openalex.org/W2149093588","https://openalex.org/W2149096890","https://openalex.org/W2151413173","https://openalex.org/W2158276883","https://openalex.org/W2162653919","https://openalex.org/W2164988972","https://openalex.org/W2166462813","https://openalex.org/W2171480079","https://openalex.org/W2224364690","https://openalex.org/W2280984960","https://openalex.org/W2293448892","https://openalex.org/W2492190064","https://openalex.org/W6668345831"],"related_works":["https://openalex.org/W2038033376","https://openalex.org/W2089800851","https://openalex.org/W110748487","https://openalex.org/W1526844866","https://openalex.org/W2492190064","https://openalex.org/W2354840055","https://openalex.org/W2610688825","https://openalex.org/W2025342333","https://openalex.org/W1606603454","https://openalex.org/W2911446493"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}