{"id":"https://openalex.org/W1964311183","doi":"https://doi.org/10.1007/s13389-011-0012-0","title":"Scalar multiplication on Weierstra\u00df elliptic curves from Co-Z arithmetic","display_name":"Scalar multiplication on Weierstra\u00df elliptic curves from Co-Z arithmetic","publication_year":2011,"publication_date":"2011-08-01","ids":{"openalex":"https://openalex.org/W1964311183","doi":"https://doi.org/10.1007/s13389-011-0012-0","mag":"1964311183"},"language":"en","primary_location":{"id":"doi:10.1007/s13389-011-0012-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s13389-011-0012-0","pdf_url":null,"source":{"id":"https://openalex.org/S2764800400","display_name":"Journal of Cryptographic Engineering","issn_l":"2190-8508","issn":["2190-8508","2190-8516"],"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 Cryptographic Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061937142","display_name":"Raveen R. Goundar","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Raveen R. Goundar","raw_affiliation_strings":["P.O. Box 794, Ba, Fiji Islands","Ba, Fiji Islands"],"affiliations":[{"raw_affiliation_string":"P.O. Box 794, Ba, Fiji Islands","institution_ids":[]},{"raw_affiliation_string":"Ba, Fiji Islands","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074996766","display_name":"Marc J\u00f3ye","orcid":"https://orcid.org/0000-0003-4433-2333"},"institutions":[{"id":"https://openalex.org/I2929663463","display_name":"Technicolor (Germany)","ror":"https://ror.org/00besvm65","country_code":"DE","type":"company","lineage":["https://openalex.org/I2929663463","https://openalex.org/I4210121266"]},{"id":"https://openalex.org/I4210121266","display_name":"Technicolor (France)","ror":"https://ror.org/02ya5n776","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210121266"]}],"countries":["DE","FR"],"is_corresponding":false,"raw_author_name":"Marc Joye","raw_affiliation_strings":["Technicolor, Security and Content Protection Labs, 1 av. de Belle Fontaine, 35576, Cesson-S\u00e9vign\u00e9 Cedex, France","Technicolor, Security and Content Protection Labs"],"affiliations":[{"raw_affiliation_string":"Technicolor, Security and Content Protection Labs, 1 av. de Belle Fontaine, 35576, Cesson-S\u00e9vign\u00e9 Cedex, France","institution_ids":["https://openalex.org/I4210121266"]},{"raw_affiliation_string":"Technicolor, Security and Content Protection Labs","institution_ids":["https://openalex.org/I2929663463"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010929606","display_name":"Atsuko Miyaji","orcid":"https://orcid.org/0000-0001-8822-5287"},"institutions":[{"id":"https://openalex.org/I177738480","display_name":"Japan Advanced Institute of Science and Technology","ror":"https://ror.org/03frj4r98","country_code":"JP","type":"education","lineage":["https://openalex.org/I177738480"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Atsuko Miyaji","raw_affiliation_strings":["Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan","Japan Advanced Inst. of Science and Technology"],"affiliations":[{"raw_affiliation_string":"Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan","institution_ids":["https://openalex.org/I177738480"]},{"raw_affiliation_string":"Japan Advanced Inst. of Science and Technology","institution_ids":["https://openalex.org/I177738480"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075769848","display_name":"Matthieu Rivain","orcid":"https://orcid.org/0000-0002-9855-4161"},"institutions":[{"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":"Matthieu Rivain","raw_affiliation_strings":["CryptoExperts, 41 Boulevard des Capucines, 75002, Paris, France","CryptoExperts"],"affiliations":[{"raw_affiliation_string":"CryptoExperts, 41 Boulevard des Capucines, 75002, Paris, France","institution_ids":["https://openalex.org/I4210086502"]},{"raw_affiliation_string":"CryptoExperts","institution_ids":["https://openalex.org/I4210086502"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074492497","display_name":"Alexandre Venelli","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexandre Venelli","raw_affiliation_strings":["Inside Secure, Avenue Victoire, 13790, Rousset, France","Inside Secure"],"affiliations":[{"raw_affiliation_string":"Inside Secure, Avenue Victoire, 13790, Rousset, France","institution_ids":[]},{"raw_affiliation_string":"Inside Secure","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5061937142"],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":18.3466,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.98952155,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"1","issue":"2","first_page":"161","last_page":"176"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"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":0.9998999834060669,"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/T11130","display_name":"Coding theory and cryptography","score":0.9842000007629395,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9708999991416931,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/scalar-multiplication","display_name":"Scalar multiplication","score":0.8090509176254272},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.700427770614624},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6975459456443787},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.6577670574188232},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4967692494392395},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.4583112895488739},{"id":"https://openalex.org/keywords/supersingular-elliptic-curve","display_name":"Supersingular elliptic curve","score":0.45633429288864136},{"id":"https://openalex.org/keywords/elliptic-curve-point-multiplication","display_name":"Elliptic curve point multiplication","score":0.41986677050590515},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39827960729599},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3204490542411804},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26958227157592773},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18650564551353455},{"id":"https://openalex.org/keywords/quarter-period","display_name":"Quarter period","score":0.08632194995880127}],"concepts":[{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.8090509176254272},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.700427770614624},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6975459456443787},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6577670574188232},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4967692494392395},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.4583112895488739},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.45633429288864136},{"id":"https://openalex.org/C117121985","wikidata":"https://www.wikidata.org/wiki/Q78380999","display_name":"Elliptic curve point multiplication","level":3,"score":0.41986677050590515},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39827960729599},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3204490542411804},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26958227157592773},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18650564551353455},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.08632194995880127}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s13389-011-0012-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s13389-011-0012-0","pdf_url":null,"source":{"id":"https://openalex.org/S2764800400","display_name":"Journal of Cryptographic Engineering","issn_l":"2190-8508","issn":["2190-8508","2190-8516"],"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 Cryptographic Engineering","raw_type":"journal-article"},{"id":"pmh:oai:dspace.jaist.ac.jp:10119/10293","is_oa":false,"landing_page_url":"http://hdl.handle.net/10119/10293","pdf_url":null,"source":{"id":"https://openalex.org/S4406922663","display_name":"JAIST Repository","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.5199999809265137,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W47178525","https://openalex.org/W239595814","https://openalex.org/W1500693694","https://openalex.org/W1511843316","https://openalex.org/W1519539754","https://openalex.org/W1522228241","https://openalex.org/W1523814493","https://openalex.org/W1531102506","https://openalex.org/W1539482743","https://openalex.org/W1543173858","https://openalex.org/W1562630396","https://openalex.org/W1565369953","https://openalex.org/W1574299633","https://openalex.org/W1584722274","https://openalex.org/W1592482282","https://openalex.org/W1603321026","https://openalex.org/W1747031273","https://openalex.org/W1786490218","https://openalex.org/W1935672779","https://openalex.org/W1971605365","https://openalex.org/W2003736153","https://openalex.org/W2009129512","https://openalex.org/W2036378739","https://openalex.org/W2038233446","https://openalex.org/W2066425771","https://openalex.org/W2096133993","https://openalex.org/W2125272473","https://openalex.org/W2144952508","https://openalex.org/W2151279347","https://openalex.org/W2154909745","https://openalex.org/W2246315406","https://openalex.org/W2267101561","https://openalex.org/W2394969257","https://openalex.org/W2478327424","https://openalex.org/W2480510614","https://openalex.org/W2484860292","https://openalex.org/W2496045601","https://openalex.org/W2498906313","https://openalex.org/W2499605333","https://openalex.org/W2506013821","https://openalex.org/W2580496263","https://openalex.org/W2607990001","https://openalex.org/W2787221650","https://openalex.org/W3031837899"],"related_works":["https://openalex.org/W2408633203","https://openalex.org/W2348491713","https://openalex.org/W1763830924","https://openalex.org/W2951901236","https://openalex.org/W2390491088","https://openalex.org/W192355887","https://openalex.org/W2385005755","https://openalex.org/W1966557000","https://openalex.org/W2898308840","https://openalex.org/W2143306991"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
