{"id":"https://openalex.org/W3173766149","doi":"https://doi.org/10.1142/s1793830921501445","title":"Exploiting the security of N = prqs through approximation of \u03d5(N)","display_name":"Exploiting the security of N = prqs through approximation of \u03d5(N)","publication_year":2021,"publication_date":"2021-06-21","ids":{"openalex":"https://openalex.org/W3173766149","doi":"https://doi.org/10.1142/s1793830921501445","mag":"3173766149"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830921501445","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830921501445","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"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":"Discrete Mathematics, Algorithms and Applications","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/A5029415697","display_name":"Saidu Isah Abubakar","orcid":"https://orcid.org/0000-0002-0201-0064"},"institutions":[{"id":"https://openalex.org/I3129379329","display_name":"Sokoto State University","ror":"https://ror.org/00zgr4s34","country_code":"NG","type":"education","lineage":["https://openalex.org/I3129379329"]}],"countries":["NG"],"is_corresponding":true,"raw_author_name":"Saidu Isah Abubakar","raw_affiliation_strings":["Department of Mathematics, Sokoto State University, Airport Road Sokoto, PMB 2134, Nigeria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sokoto State University, Airport Road Sokoto, PMB 2134, Nigeria","institution_ids":["https://openalex.org/I3129379329"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064887933","display_name":"Sadiq Shehu","orcid":"https://orcid.org/0000-0001-5908-7452"},"institutions":[{"id":"https://openalex.org/I3129379329","display_name":"Sokoto State University","ror":"https://ror.org/00zgr4s34","country_code":"NG","type":"education","lineage":["https://openalex.org/I3129379329"]}],"countries":["NG"],"is_corresponding":false,"raw_author_name":"Sadiq Shehu","raw_affiliation_strings":["Department of Mathematics, Sokoto State University, Airport Road Sokoto, PMB 2134, Nigeria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sokoto State University, Airport Road Sokoto, PMB 2134, Nigeria","institution_ids":["https://openalex.org/I3129379329"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029415697"],"corresponding_institution_ids":["https://openalex.org/I3129379329"],"apc_list":null,"apc_paid":null,"fwci":0.2754,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.59772052,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"14","issue":"04","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9993000030517578,"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/T11130","display_name":"Coding theory and cryptography","score":0.998199999332428,"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":0.5944671034812927},{"id":"https://openalex.org/keywords/moduli","display_name":"Moduli","score":0.5821345448493958},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5366062521934509},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5329827666282654},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5228400826454163},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.47264450788497925},{"id":"https://openalex.org/keywords/prime-power","display_name":"Prime power","score":0.4704799950122833},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33072131872177124},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3227955102920532},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14931988716125488},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13664132356643677},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12999466061592102},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06192964315414429}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5944671034812927},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.5821345448493958},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5366062521934509},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5329827666282654},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5228400826454163},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.47264450788497925},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.4704799950122833},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33072131872177124},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3227955102920532},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14931988716125488},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13664132356643677},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12999466061592102},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06192964315414429},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830921501445","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830921501445","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"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":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.4000000059604645}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W93179768","https://openalex.org/W1484022276","https://openalex.org/W1598552949","https://openalex.org/W1827261485","https://openalex.org/W1865276762","https://openalex.org/W1985273268","https://openalex.org/W2141040012","https://openalex.org/W2156666175","https://openalex.org/W2164238143","https://openalex.org/W2166780626","https://openalex.org/W2167900818","https://openalex.org/W2410582300","https://openalex.org/W2617356521","https://openalex.org/W2905138110","https://openalex.org/W4232836212","https://openalex.org/W4322095736"],"related_works":["https://openalex.org/W2369076105","https://openalex.org/W2382409946","https://openalex.org/W2374471856","https://openalex.org/W2390036829","https://openalex.org/W2348092648","https://openalex.org/W2543275399","https://openalex.org/W1998402533","https://openalex.org/W2069443110","https://openalex.org/W2292792029","https://openalex.org/W860790991"],"abstract_inverted_index":{"This":[0,45],"paper":[1],"reports":[2],"new":[3],"techniques":[4,133],"that":[5,24,96],"exploit":[6],"the":[7,10,25,54,57,66,69,79,84,92,99,102,116],"security":[8,100],"of":[9,41,56,61,68,83,101,113,115],"prime":[11,104],"power":[12,105],"moduli":[13,85,106],"[Formula:":[14,28,35,42,50,62,73,86,107,118,122,135,139],"see":[15,29,36,43,51,63,74,87,108,119,123,136,140],"text]":[16,30,37,52,64,75,109,120,124,137],"using":[17,34,110],"continued":[18,58],"fraction":[19],"method.":[20],"Our":[21],"study":[22],"shows":[23],"key":[26],"equation":[27,114],"can":[31,97],"be":[32],"exploited":[33],"as":[38],"good":[39],"approximation":[40],"text].":[44,88,141],"enables":[46],"us":[47],"to":[48,78],"get":[49],"from":[53],"convergents":[55],"fractions":[59],"expansion":[60],"where":[65,134],"bound":[67],"private":[70],"exponent":[71],"is":[72],"which":[76],"leads":[77],"polynomial":[80,93],"time":[81,94],"factorization":[82],"We":[89],"further":[90],"report":[91],"attacks":[95],"break":[98],"generalized":[103,111],"system":[112],"form":[117],"and":[121,130,138],"by":[125],"applying":[126],"simultaneous":[127],"Diophantine":[128],"approximations":[129],"LLL":[131],"algorithm":[132]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}