{"id":"https://openalex.org/W3011125593","doi":"https://doi.org/10.1142/s0129054120500045","title":"A Unified Method for Private Exponent Attacks on RSA Using Lattices","display_name":"A Unified Method for Private Exponent Attacks on RSA Using Lattices","publication_year":2020,"publication_date":"2020-02-01","ids":{"openalex":"https://openalex.org/W3011125593","doi":"https://doi.org/10.1142/s0129054120500045","mag":"3011125593"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054120500045","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054120500045","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://normandie-univ.hal.science/hal-02320914","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037170867","display_name":"Hatem M. Bahig","orcid":"https://orcid.org/0000-0002-8137-7939"},"institutions":[{"id":"https://openalex.org/I107720978","display_name":"Ain Shams University","ror":"https://ror.org/00cb9w016","country_code":"EG","type":"education","lineage":["https://openalex.org/I107720978"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Hatem M. Bahig","raw_affiliation_strings":["Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt"],"affiliations":[{"raw_affiliation_string":"Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt","institution_ids":["https://openalex.org/I107720978"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006723199","display_name":"Dieaa I. Nassr","orcid":"https://orcid.org/0000-0002-5550-3372"},"institutions":[{"id":"https://openalex.org/I107720978","display_name":"Ain Shams University","ror":"https://ror.org/00cb9w016","country_code":"EG","type":"education","lineage":["https://openalex.org/I107720978"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Dieaa I. Nassr","raw_affiliation_strings":["Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt"],"affiliations":[{"raw_affiliation_string":"Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt","institution_ids":["https://openalex.org/I107720978"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006005380","display_name":"Ashraf Bhery","orcid":"https://orcid.org/0000-0001-9016-2705"},"institutions":[{"id":"https://openalex.org/I107720978","display_name":"Ain Shams University","ror":"https://ror.org/00cb9w016","country_code":"EG","type":"education","lineage":["https://openalex.org/I107720978"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Ashraf Bhery","raw_affiliation_strings":["Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt"],"affiliations":[{"raw_affiliation_string":"Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt","institution_ids":["https://openalex.org/I107720978"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083370009","display_name":"Abderrahmane Nitaj","orcid":"https://orcid.org/0000-0002-0372-1757"},"institutions":[{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]},{"id":"https://openalex.org/I4387155825","display_name":"Laboratoire de Math\u00e9matiques Nicolas Oresme","ror":"https://ror.org/03jm2hc44","country_code":null,"type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210105918","https://openalex.org/I4387155825","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Abderrahmane Nitaj","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques Nicolas Oresme, Universit\u00e9 de Caen, Basse Normandie, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Nicolas Oresme, Universit\u00e9 de Caen, Basse Normandie, France","institution_ids":["https://openalex.org/I4210155549","https://openalex.org/I4387155825"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5037170867"],"corresponding_institution_ids":["https://openalex.org/I107720978"],"apc_list":null,"apc_paid":null,"fwci":0.7954,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.7758669,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"31","issue":"02","first_page":"207","last_page":"231"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9998000264167786,"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":0.9998000264167786,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9961000084877014,"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":0.9944000244140625,"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/mathematics","display_name":"Mathematics","score":0.6796420812606812},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.6039965748786926},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.5758672952651978},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.547838032245636},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4962230324745178},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.48488956689834595},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4606601595878601},{"id":"https://openalex.org/keywords/key-size","display_name":"Key size","score":0.44509467482566833},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4398794174194336},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4355352520942688},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.41405802965164185},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3565983176231384},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19580078125},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.19124197959899902},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17604640126228333},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09951463341712952}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6796420812606812},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.6039965748786926},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.5758672952651978},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.547838032245636},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4962230324745178},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.48488956689834595},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4606601595878601},{"id":"https://openalex.org/C47750902","wikidata":"https://www.wikidata.org/wiki/Q1557574","display_name":"Key size","level":4,"score":0.44509467482566833},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4398794174194336},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4355352520942688},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.41405802965164185},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3565983176231384},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19580078125},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.19124197959899902},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17604640126228333},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09951463341712952},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0129054120500045","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054120500045","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02320914v1","is_oa":true,"landing_page_url":"https://normandie-univ.hal.science/hal-02320914","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":"International Journal of Foundations of Computer Science, In press, &#x27E8;10.1142/s0129054120500045&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-02320914v1","is_oa":true,"landing_page_url":"https://normandie-univ.hal.science/hal-02320914","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":"International Journal of Foundations of Computer Science, In press, &#x27E8;10.1142/s0129054120500045&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W93179768","https://openalex.org/W95797130","https://openalex.org/W180417168","https://openalex.org/W1550863203","https://openalex.org/W1558666880","https://openalex.org/W1599227824","https://openalex.org/W1865276762","https://openalex.org/W1961022628","https://openalex.org/W2019689629","https://openalex.org/W2062099180","https://openalex.org/W2085667065","https://openalex.org/W2101040389","https://openalex.org/W2105418754","https://openalex.org/W2116178359","https://openalex.org/W2141040012","https://openalex.org/W2149180563","https://openalex.org/W2156666175","https://openalex.org/W2166780626","https://openalex.org/W4232836212"],"related_works":["https://openalex.org/W2369076105","https://openalex.org/W2382409946","https://openalex.org/W2374471856","https://openalex.org/W2390036829","https://openalex.org/W2010306471","https://openalex.org/W2348092648","https://openalex.org/W2149477863","https://openalex.org/W3007745699","https://openalex.org/W4377234699","https://openalex.org/W2912829606"],"abstract_inverted_index":{"Let":[0],"[Formula:":[1,12,16,20,69,112,141,149,153,157,160],"see":[2,13,17,21,70,113,142,150,154,158,161],"text]":[3,14,18,22,71,114,143,151,155,159,162],"be":[4,88],"an":[5,166],"RSA":[6,57,73,109,137],"public":[7,110],"key":[8,67,111,131],"with":[9,156],"private":[10],"exponent":[11],"where":[15],"and":[19,51],"are":[23],"large":[24],"primes":[25],"of":[26,43,63,72,84,122,152,168],"the":[27,56,66,130],"same":[28],"bit":[29],"size.":[30],"At":[31],"Eurocrypt":[32],"96,":[33],"Coppersmith":[34],"presented":[35],"a":[36,61,91,95,103,107],"polynomial-time":[37],"algorithm":[38],"for":[39,106,119],"finding":[40],"small":[41],"roots":[42],"univariate":[44],"modular":[45],"equations":[46],"based":[47],"on":[48,65],"lattice":[49],"reduction":[50],"then":[52],"succussed":[53],"to":[54],"factorize":[55],"modulus.":[58],"Since":[59],"then,":[60],"series":[62],"attacks":[64,86],"equation":[68],"have":[74,147],"been":[75],"presented.":[76],"In":[77],"this":[78],"paper,":[79],"we":[80,134,146],"show":[81,135],"that":[82,128,136,145],"many":[83],"such":[85,124],"can":[87],"unified":[89],"in":[90],"single":[92],"attack":[93,164],"using":[94],"new":[96],"notion":[97],"called":[98],"Coppersmith\u2019s":[99,104,169],"interval.":[100],"We":[101],"determine":[102],"interval":[105,116],"given":[108],"The":[115,163],"is":[117,138,165],"valid":[118],"any":[120],"variant":[121],"RSA,":[123,127],"as":[125],"Multi-Prime":[126],"uses":[129],"equation.":[132],"Then":[133],"insecure":[139],"if":[140],"provided":[144],"approximation":[148],"extension":[167],"result.":[170]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
