{"id":"https://openalex.org/W1745295339","doi":"https://doi.org/10.1007/978-3-642-39059-3_14","title":"Injective Encodings to Elliptic Curves","display_name":"Injective Encodings to Elliptic Curves","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1745295339","doi":"https://doi.org/10.1007/978-3-642-39059-3_14","mag":"1745295339"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-39059-3_14","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-39059-3_14","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-01094294","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016755346","display_name":"Pierre-Alain Fouque","orcid":"https://orcid.org/0000-0003-4997-2276"},"institutions":[{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]},{"id":"https://openalex.org/I185839726","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266","country_code":"FR","type":"education","lineage":["https://openalex.org/I185839726"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Pierre-Alain Fouque","raw_affiliation_strings":["University of Rennes, France","IUF - Institut Universitaire de France (Maison des Universit\u00e9s 103 Boulevard Saint-Michel 75005 Paris - France)","UR - Universit\u00e9 de Rennes (Campus de Beaulieu, 263 avenue G\u00e9n\u00e9ral Leclerc, CS 74205, 35042 RENNES CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"University of Rennes, France","institution_ids":["https://openalex.org/I56067802"]},{"raw_affiliation_string":"IUF - Institut Universitaire de France (Maison des Universit\u00e9s 103 Boulevard Saint-Michel 75005 Paris - France)","institution_ids":["https://openalex.org/I185839726"]},{"raw_affiliation_string":"UR - Universit\u00e9 de Rennes (Campus de Beaulieu, 263 avenue G\u00e9n\u00e9ral Leclerc, CS 74205, 35042 RENNES CEDEX - France)","institution_ids":["https://openalex.org/I56067802"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009219098","display_name":"Antoine Joux","orcid":"https://orcid.org/0000-0003-2682-6508"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210086502","display_name":"CryptoExperts (France)","ror":"https://ror.org/0030xrh72","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210086502"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Antoine Joux","raw_affiliation_strings":["CryptoExperts and Universit\u00e9 de Versailles\u2013Saint-Quentin, France","UPMC - Universit\u00e9 Pierre et Marie Curie - Paris 6 (4 place Jussieu - 75005 Paris - France)"],"affiliations":[{"raw_affiliation_string":"CryptoExperts and Universit\u00e9 de Versailles\u2013Saint-Quentin, France","institution_ids":["https://openalex.org/I4210086502"]},{"raw_affiliation_string":"UPMC - Universit\u00e9 Pierre et Marie Curie - Paris 6 (4 place Jussieu - 75005 Paris - France)","institution_ids":["https://openalex.org/I39804081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082427466","display_name":"Mehdi Tibouchi","orcid":"https://orcid.org/0000-0002-2736-2963"},"institutions":[{"id":"https://openalex.org/I2251713219","display_name":"NTT (Japan)","ror":"https://ror.org/00berct97","country_code":"JP","type":"company","lineage":["https://openalex.org/I2251713219"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Mehdi Tibouchi","raw_affiliation_strings":["NTT Secure Platform Laboratories, Japan","NTT Secure Platform Laboratories [Tokyo] (Tokyo - Japon)"],"affiliations":[{"raw_affiliation_string":"NTT Secure Platform Laboratories, Japan","institution_ids":["https://openalex.org/I2251713219"]},{"raw_affiliation_string":"NTT Secure Platform Laboratories [Tokyo] (Tokyo - Japon)","institution_ids":["https://openalex.org/I2251713219"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016755346"],"corresponding_institution_ids":["https://openalex.org/I185839726","https://openalex.org/I56067802"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":9.068,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.98417722,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"203","last_page":"218"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9929999709129333,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9916999936103821,"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/elliptic-curve","display_name":"Elliptic curve","score":0.7023370862007141},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.6771852970123291},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.6135384440422058},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.573342502117157},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5162501335144043},{"id":"https://openalex.org/keywords/edwards-curve","display_name":"Edwards curve","score":0.5138342976570129},{"id":"https://openalex.org/keywords/hessian-form-of-an-elliptic-curve","display_name":"Hessian form of an elliptic curve","score":0.49507513642311096},{"id":"https://openalex.org/keywords/jacobian-curve","display_name":"Jacobian curve","score":0.4924941956996918},{"id":"https://openalex.org/keywords/elliptic-curve-point-multiplication","display_name":"Elliptic curve point multiplication","score":0.465246319770813},{"id":"https://openalex.org/keywords/counting-points-on-elliptic-curves","display_name":"Counting points on elliptic curves","score":0.43902429938316345},{"id":"https://openalex.org/keywords/twists-of-curves","display_name":"Twists of curves","score":0.4390026926994324},{"id":"https://openalex.org/keywords/tripling-oriented-doche\u2013icart\u2013kohel-curve","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","score":0.42892026901245117},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.4221951961517334},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39183878898620605},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.362374484539032},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.2832546830177307},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.257598340511322},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.10876521468162537}],"concepts":[{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.7023370862007141},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.6771852970123291},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.6135384440422058},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.573342502117157},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5162501335144043},{"id":"https://openalex.org/C92727272","wikidata":"https://www.wikidata.org/wiki/Q3001190","display_name":"Edwards curve","level":5,"score":0.5138342976570129},{"id":"https://openalex.org/C104993295","wikidata":"https://www.wikidata.org/wiki/Q17023345","display_name":"Hessian form of an elliptic curve","level":5,"score":0.49507513642311096},{"id":"https://openalex.org/C79993320","wikidata":"https://www.wikidata.org/wiki/Q6119657","display_name":"Jacobian curve","level":5,"score":0.4924941956996918},{"id":"https://openalex.org/C117121985","wikidata":"https://www.wikidata.org/wiki/Q78380999","display_name":"Elliptic curve point multiplication","level":3,"score":0.465246319770813},{"id":"https://openalex.org/C68782407","wikidata":"https://www.wikidata.org/wiki/Q5177153","display_name":"Counting points on elliptic curves","level":5,"score":0.43902429938316345},{"id":"https://openalex.org/C131182338","wikidata":"https://www.wikidata.org/wiki/Q7858596","display_name":"Twists of curves","level":5,"score":0.4390026926994324},{"id":"https://openalex.org/C37055786","wikidata":"https://www.wikidata.org/wiki/Q7843607","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","level":5,"score":0.42892026901245117},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.4221951961517334},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39183878898620605},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.362374484539032},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.2832546830177307},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.257598340511322},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.10876521468162537},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"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":2,"locations":[{"id":"doi:10.1007/978-3-642-39059-3_14","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-39059-3_14","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:HAL:hal-01094294v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01094294","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Information Security and Privacy - 18th Australasian Conference, Jul 2013, Brisbane, Australia. pp.16, ⟨10.1007/978-3-642-39059-3_14⟩","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01094294v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01094294","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Information Security and Privacy - 18th Australasian Conference, Jul 2013, Brisbane, Australia. pp.16, ⟨10.1007/978-3-642-39059-3_14⟩","raw_type":"Conference papers"},"sustainable_development_goals":[{"score":0.47999998927116394,"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W77681064","https://openalex.org/W645185567","https://openalex.org/W1487143383","https://openalex.org/W1488467418","https://openalex.org/W1490394993","https://openalex.org/W1527414074","https://openalex.org/W1537838966","https://openalex.org/W1860928555","https://openalex.org/W2005836292","https://openalex.org/W2080206293","https://openalex.org/W2108834246","https://openalex.org/W2126484007","https://openalex.org/W2131559681","https://openalex.org/W2152924492","https://openalex.org/W2154290215","https://openalex.org/W2164988972","https://openalex.org/W2211728331","https://openalex.org/W4212933304"],"related_works":["https://openalex.org/W28923676","https://openalex.org/W2548082687","https://openalex.org/W2188057592","https://openalex.org/W3211097549","https://openalex.org/W2953939619","https://openalex.org/W3138493780","https://openalex.org/W1175355266","https://openalex.org/W3172172454","https://openalex.org/W2374178740","https://openalex.org/W2084836129"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}