{"id":"https://openalex.org/W2999104950","doi":"https://doi.org/10.1007/s13389-019-00221-7","title":"Efficient modular operations using the adapted modular number system","display_name":"Efficient modular operations using the adapted modular number system","publication_year":2020,"publication_date":"2020-01-06","ids":{"openalex":"https://openalex.org/W2999104950","doi":"https://doi.org/10.1007/s13389-019-00221-7","mag":"2999104950"},"language":"en","primary_location":{"id":"doi:10.1007/s13389-019-00221-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s13389-019-00221-7","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":true,"oa_status":"green","oa_url":"https://hal.science/hal-02486345","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073280168","display_name":"Laurent-St\u00e9phane Didier","orcid":null},"institutions":[{"id":"https://openalex.org/I143002897","display_name":"Universit\u00e9 de Toulon","ror":"https://ror.org/02m9kbe37","country_code":"FR","type":"education","lineage":["https://openalex.org/I143002897"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Laurent-St\u00e9phane Didier","raw_affiliation_strings":["Institut de Math\u00e9matiques de Toulon, Universit\u00e9 de Toulon, Toulon, France","IMATH - Institut de Math\u00e9matiques de Toulon - EA 2134 (Universit\u00e9 de Toulon - B\u00e2timent M - B.P. 20132 - 83957 La Garde Cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Toulon, Universit\u00e9 de Toulon, Toulon, France","institution_ids":["https://openalex.org/I143002897"]},{"raw_affiliation_string":"IMATH - Institut de Math\u00e9matiques de Toulon - EA 2134 (Universit\u00e9 de Toulon - B\u00e2timent M - B.P. 20132 - 83957 La Garde Cedex - France)","institution_ids":["https://openalex.org/I143002897"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031742444","display_name":"Fangan-Yssouf Dosso","orcid":null},"institutions":[{"id":"https://openalex.org/I143002897","display_name":"Universit\u00e9 de Toulon","ror":"https://ror.org/02m9kbe37","country_code":"FR","type":"education","lineage":["https://openalex.org/I143002897"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fangan-Yssouf Dosso","raw_affiliation_strings":["Institut de Math\u00e9matiques de Toulon, Universit\u00e9 de Toulon, Toulon, France","IMATH - Institut de Math\u00e9matiques de Toulon - EA 2134 (Universit\u00e9 de Toulon - B\u00e2timent M - B.P. 20132 - 83957 La Garde Cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Toulon, Universit\u00e9 de Toulon, Toulon, France","institution_ids":["https://openalex.org/I143002897"]},{"raw_affiliation_string":"IMATH - Institut de Math\u00e9matiques de Toulon - EA 2134 (Universit\u00e9 de Toulon - B\u00e2timent M - B.P. 20132 - 83957 La Garde Cedex - France)","institution_ids":["https://openalex.org/I143002897"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023817947","display_name":"Pascal V\u00e9ron","orcid":"https://orcid.org/0000-0001-7610-6870"},"institutions":[{"id":"https://openalex.org/I143002897","display_name":"Universit\u00e9 de Toulon","ror":"https://ror.org/02m9kbe37","country_code":"FR","type":"education","lineage":["https://openalex.org/I143002897"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Pascal V\u00e9ron","raw_affiliation_strings":["Institut de Math\u00e9matiques de Toulon, Universit\u00e9 de Toulon, Toulon, France","IMATH - Institut de Math\u00e9matiques de Toulon - EA 2134 (Universit\u00e9 de Toulon - B\u00e2timent M - B.P. 20132 - 83957 La Garde Cedex - France)"],"raw_orcid":"https://orcid.org/0000-0001-7610-6870","affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Toulon, Universit\u00e9 de Toulon, Toulon, France","institution_ids":["https://openalex.org/I143002897"]},{"raw_affiliation_string":"IMATH - Institut de Math\u00e9matiques de Toulon - EA 2134 (Universit\u00e9 de Toulon - B\u00e2timent M - B.P. 20132 - 83957 La Garde Cedex - France)","institution_ids":["https://openalex.org/I143002897"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023817947"],"corresponding_institution_ids":["https://openalex.org/I143002897"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":3.0766,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.92947383,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"10","issue":"2","first_page":"111","last_page":"133"},"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tuple","display_name":"Tuple","score":0.7435571551322937},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.6397525072097778},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.6346454620361328},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.6164015531539917},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4996800422668457},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4551955461502075},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.44546711444854736},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4219851493835449},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41050195693969727},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4068428874015808},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3852224349975586},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3348795771598816},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27568888664245605},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.22693517804145813}],"concepts":[{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.7435571551322937},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6397525072097778},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.6346454620361328},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.6164015531539917},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4996800422668457},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4551955461502075},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.44546711444854736},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4219851493835449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41050195693969727},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4068428874015808},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3852224349975586},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3348795771598816},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27568888664245605},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.22693517804145813}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s13389-019-00221-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s13389-019-00221-7","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:HAL:hal-02486345v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02486345","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":"Journal of Cryptographic Engineering, 2020, &#x27E8;10.1007/s13389-019-00221-7&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-02486345v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02486345","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":"Journal of Cryptographic Engineering, 2020, &#x27E8;10.1007/s13389-019-00221-7&#x27E9;","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7281448862","display_name":"Randomized Arithmetics","funder_award_id":"ANR-15-CE39-0002","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W70752072","https://openalex.org/W263238470","https://openalex.org/W1498685334","https://openalex.org/W1504599740","https://openalex.org/W1506134992","https://openalex.org/W1509468219","https://openalex.org/W1529207657","https://openalex.org/W1576555092","https://openalex.org/W1613874182","https://openalex.org/W1757804052","https://openalex.org/W2004814164","https://openalex.org/W2024250625","https://openalex.org/W2100264217","https://openalex.org/W2100891661","https://openalex.org/W2104841597","https://openalex.org/W2141040012","https://openalex.org/W2154909745","https://openalex.org/W2155095649","https://openalex.org/W2157999631","https://openalex.org/W2172184773","https://openalex.org/W2264040999","https://openalex.org/W2408211519","https://openalex.org/W2527617455","https://openalex.org/W2612686320","https://openalex.org/W2920685123","https://openalex.org/W2982006139","https://openalex.org/W3091983754","https://openalex.org/W3163191147","https://openalex.org/W4234682643"],"related_works":["https://openalex.org/W2177966018","https://openalex.org/W2964242841","https://openalex.org/W4302423208","https://openalex.org/W2196131019","https://openalex.org/W2112041331","https://openalex.org/W3087194925","https://openalex.org/W2467357782","https://openalex.org/W3152691454","https://openalex.org/W4288118777","https://openalex.org/W3104344759"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
