{"id":"https://openalex.org/W2905143760","doi":"https://doi.org/10.3390/cryptography3010002","title":"New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method","display_name":"New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method","publication_year":2018,"publication_date":"2018-12-20","ids":{"openalex":"https://openalex.org/W2905143760","doi":"https://doi.org/10.3390/cryptography3010002","mag":"2905143760"},"language":"en","primary_location":{"id":"doi:10.3390/cryptography3010002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography3010002","pdf_url":"https://www.mdpi.com/2410-387X/3/1/2/pdf?version=1545389543","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2410-387X/3/1/2/pdf?version=1545389543","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071414544","display_name":"Muhammad Rezal Kamel Ariffin","orcid":"https://orcid.org/0000-0001-5000-354X"},"institutions":[{"id":"https://openalex.org/I130343225","display_name":"Universiti Putra Malaysia","ror":"https://ror.org/02e91jd64","country_code":"MY","type":"education","lineage":["https://openalex.org/I130343225"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Muhammad Rezal Kamel Ariffin","raw_affiliation_strings":["Al-Kindi Cryptography Research Laboratory, Institute for Mathematical Research, Universiti Putra Malaysia, Selangor 43400, Malaysia","Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor 43400, Malaysia"],"affiliations":[{"raw_affiliation_string":"Al-Kindi Cryptography Research Laboratory, Institute for Mathematical Research, Universiti Putra Malaysia, Selangor 43400, Malaysia","institution_ids":["https://openalex.org/I130343225"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor 43400, Malaysia","institution_ids":["https://openalex.org/I130343225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029415697","display_name":"Saidu Isah Abubakar","orcid":"https://orcid.org/0000-0002-0201-0064"},"institutions":[{"id":"https://openalex.org/I130343225","display_name":"Universiti Putra Malaysia","ror":"https://ror.org/02e91jd64","country_code":"MY","type":"education","lineage":["https://openalex.org/I130343225"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Saidu Isah Abubakar","raw_affiliation_strings":["Al-Kindi Cryptography Research Laboratory, Institute for Mathematical Research, Universiti Putra Malaysia, Selangor 43400, Malaysia"],"affiliations":[{"raw_affiliation_string":"Al-Kindi Cryptography Research Laboratory, Institute for Mathematical Research, Universiti Putra Malaysia, Selangor 43400, Malaysia","institution_ids":["https://openalex.org/I130343225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003441438","display_name":"Faridah Yunos","orcid":"https://orcid.org/0000-0002-1197-0972"},"institutions":[{"id":"https://openalex.org/I130343225","display_name":"Universiti Putra Malaysia","ror":"https://ror.org/02e91jd64","country_code":"MY","type":"education","lineage":["https://openalex.org/I130343225"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Faridah Yunos","raw_affiliation_strings":["Al-Kindi Cryptography Research Laboratory, Institute for Mathematical Research, Universiti Putra Malaysia, Selangor 43400, Malaysia","Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor 43400, Malaysia"],"affiliations":[{"raw_affiliation_string":"Al-Kindi Cryptography Research Laboratory, Institute for Mathematical Research, Universiti Putra Malaysia, Selangor 43400, Malaysia","institution_ids":["https://openalex.org/I130343225"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor 43400, Malaysia","institution_ids":["https://openalex.org/I130343225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011968072","display_name":"Muhammad Asyraf Asbullah","orcid":"https://orcid.org/0000-0002-0778-4456"},"institutions":[{"id":"https://openalex.org/I130343225","display_name":"Universiti Putra Malaysia","ror":"https://ror.org/02e91jd64","country_code":"MY","type":"education","lineage":["https://openalex.org/I130343225"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Muhammad Asyraf Asbullah","raw_affiliation_strings":["Al-Kindi Cryptography Research Laboratory, Institute for Mathematical Research, Universiti Putra Malaysia, Selangor 43400, Malaysia","Centre of Foundation Studies for Agriculture Science, Universiti Putra Malaysia, Selangor 43400, Malaysia"],"affiliations":[{"raw_affiliation_string":"Al-Kindi Cryptography Research Laboratory, Institute for Mathematical Research, Universiti Putra Malaysia, Selangor 43400, Malaysia","institution_ids":["https://openalex.org/I130343225"]},{"raw_affiliation_string":"Centre of Foundation Studies for Agriculture Science, Universiti Putra Malaysia, Selangor 43400, Malaysia","institution_ids":["https://openalex.org/I130343225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5029415697"],"corresponding_institution_ids":["https://openalex.org/I130343225"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1732},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1732},"fwci":1.523,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.87501609,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"3","issue":"1","first_page":"2","last_page":"2"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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/T10237","display_name":"Cryptography and Data Security","score":0.9994999766349792,"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":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6207444071769714},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4772769808769226},{"id":"https://openalex.org/keywords/modulus","display_name":"Modulus","score":0.46268999576568604},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.36513739824295044},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34698352217674255},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33614033460617065},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15839719772338867},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.085589200258255}],"concepts":[{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6207444071769714},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4772769808769226},{"id":"https://openalex.org/C193867417","wikidata":"https://www.wikidata.org/wiki/Q6889814","display_name":"Modulus","level":2,"score":0.46268999576568604},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.36513739824295044},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34698352217674255},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33614033460617065},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15839719772338867},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.085589200258255}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/cryptography3010002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography3010002","pdf_url":"https://www.mdpi.com/2410-387X/3/1/2/pdf?version=1545389543","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6e6be974c7b74e97b1fc09efa1befe04","is_oa":true,"landing_page_url":"https://doaj.org/article/6e6be974c7b74e97b1fc09efa1befe04","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cryptography, Vol 3, Iss 1, p 2 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2410-387X/3/1/2/","is_oa":true,"landing_page_url":"http://doi.org/10.3390/cryptography3010002","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cryptography","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/cryptography3010002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/cryptography3010002","pdf_url":"https://www.mdpi.com/2410-387X/3/1/2/pdf?version=1545389543","source":{"id":"https://openalex.org/S4210223320","display_name":"Cryptography","issn_l":"2410-387X","issn":["2410-387X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2905143760.pdf","grobid_xml":"https://content.openalex.org/works/W2905143760.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W93179768","https://openalex.org/W633449635","https://openalex.org/W1484022276","https://openalex.org/W1557608351","https://openalex.org/W1865276762","https://openalex.org/W1980291956","https://openalex.org/W2019689629","https://openalex.org/W2141040012","https://openalex.org/W2156666175","https://openalex.org/W2166780626","https://openalex.org/W2167900818","https://openalex.org/W2335977982","https://openalex.org/W2410582300","https://openalex.org/W4232836212"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793"],"abstract_inverted_index":{"This":[0],"paper":[1,27,117],"presents":[2],"new":[3],"short":[4,289],"decryption":[5],"exponent":[6,291],"attacks":[7,121],"on":[8,122],"RSA,":[9],"which":[10,74,293],"successfully":[11],"leads":[12],"to":[13,68,296],"the":[14,32,37,40,46,61,88,91,116,175,281,305],"factorization":[15],"of":[16,39,45,63,90,95,115,125,165,174,270],"RSA":[17,126,259],"modulus":[18],"N":[19,58,82,97,107,128,148,158,168,185,199,213,229],"=":[20,130,137,188,202,216,232],"p":[21,51,65,131],"q":[22,55,64,133],"in":[23,265,304],"polynomial":[24,266],"time.":[25],"The":[26,112],"has":[28],"two":[29],"parts.":[30],"In":[31,279],"first":[33],"part,":[34],"we":[35,146,255,284],"report":[36],"usage":[38],"small":[41],"prime":[42],"difference":[43],"method":[44],"form":[47],"|":[48,56],"b":[49,69,103,106,154,157],"2":[50,54,70,72,81,101,104,140,152,155],"\u2212":[52,85,98,149,180,195,208,225],"a":[53,71,76,100,105,151,156],"&lt;":[57,79],"\u03b3":[59,86],"where":[60,145,254],"ratio":[62],"is":[66,294],"close":[67],",":[73,139,141,143,190,204,219,240,243,246,249,253],"yields":[75],"bound":[77],"d":[78,179,193,207,223,239,244],"3":[80,83],"4":[84],"from":[87],"convergents":[89],"continued":[92],"fraction":[93],"expansion":[94],"e":[96,177,191,205,221],"\u2308":[99,150],"+":[102,109,153,160],"\u2309":[108,159],"1":[110,138,161,189,203],".":[111],"second":[113],"part":[114],"reports":[118],"four":[119],"cryptanalytic":[120],"t":[123,144,258],"instances":[124],"moduli":[127,260],"s":[129,132,134,136,178,182,186,192,194,200,206,210,214,218,222,224,230,234,242,245,248,252],"for":[135,235],"\u2026":[142],"use":[147],"as":[162,302],"an":[163,287],"approximation":[164],"\u03d5":[166,183,197,211,227],"(":[167,184,198,212,228],")":[169,187,201,215,231],"satisfying":[170],"generalized":[171],"key":[172],"equations":[173],"shape":[176],"k":[181,196,209,226,241,247],"z":[217,233,251],"and":[220,250,274],"unknown":[236],"positive":[237],"integers":[238],"establish":[256],"that":[257],"can":[261],"be":[262,297],"simultaneously":[263],"factored":[264],"time":[267],"using":[268],"combinations":[269],"simultaneous":[271],"Diophantine":[272],"approximations":[273],"lattice":[275],"basis":[276],"reduction":[277],"methods.":[278],"all":[280],"reported":[282,303],"attacks,":[283],"have":[285],"found":[286],"improved":[288],"secret":[290],"bound,":[292],"considered":[295],"better":[298],"than":[299],"some":[300],"bounds":[301],"literature.":[306]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
