{"id":"https://openalex.org/W2615279577","doi":"https://doi.org/10.1515/jmc-2016-0025","title":"Cryptanalysis of an RSA variant with moduli <i>N</i> = <i> p <sup>r</sup> q <sup>l</sup> </i>","display_name":"Cryptanalysis of an RSA variant with moduli <i>N</i> = <i> p <sup>r</sup> q <sup>l</sup> </i>","publication_year":2017,"publication_date":"2017-05-16","ids":{"openalex":"https://openalex.org/W2615279577","doi":"https://doi.org/10.1515/jmc-2016-0025","mag":"2615279577"},"language":"en","primary_location":{"id":"doi:10.1515/jmc-2016-0025","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jmc-2016-0025","pdf_url":null,"source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"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/A5101983112","display_name":"Yao Lu","orcid":"https://orcid.org/0000-0001-9824-6348"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yao Lu","raw_affiliation_strings":["The University of Tokyo , Tokyo , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Tokyo , Tokyo , Japan","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077538627","display_name":"Liqiang Peng","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liqiang Peng","raw_affiliation_strings":["Institute of Information Engineering , Chinese Academy of Sciences , Beijing , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Information Engineering , Chinese Academy of Sciences , Beijing , P. R. China","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058432784","display_name":"Santanu Sarkar","orcid":"https://orcid.org/0000-0001-6821-920X"},"institutions":[{"id":"https://openalex.org/I24676775","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49","country_code":"IN","type":"facility","lineage":["https://openalex.org/I24676775"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Santanu Sarkar","raw_affiliation_strings":["Indian Institute of Technology , Madras , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology , Madras , India","institution_ids":["https://openalex.org/I24676775"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058432784"],"corresponding_institution_ids":["https://openalex.org/I24676775"],"apc_list":{"value":1000,"currency":"EUR","value_usd":1078},"apc_paid":null,"fwci":1.2485,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.84868552,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"11","issue":"2","first_page":"117","last_page":"130"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9979000091552734,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9975000023841858,"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/exponent","display_name":"Exponent","score":0.5517487525939941},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5104671716690063},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5071392059326172},{"id":"https://openalex.org/keywords/moduli","display_name":"Moduli","score":0.45642563700675964},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.40488287806510925},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3143104910850525},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.09669163823127747},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08836895227432251}],"concepts":[{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5517487525939941},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5104671716690063},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5071392059326172},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.45642563700675964},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.40488287806510925},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3143104910850525},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.09669163823127747},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08836895227432251},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/jmc-2016-0025","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jmc-2016-0025","pdf_url":null,"source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1a901e8d0f99419590b2c97af2fa016f","is_oa":false,"landing_page_url":"https://doaj.org/article/1a901e8d0f99419590b2c97af2fa016f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"Journal of Mathematical Cryptology, Vol 11, Iss 2, Pp 117-130 (2017)","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G676629878","display_name":null,"funder_award_id":"61472417","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W6111282","https://openalex.org/W83014205","https://openalex.org/W211145104","https://openalex.org/W1483793314","https://openalex.org/W1490771242","https://openalex.org/W1503520699","https://openalex.org/W1529862094","https://openalex.org/W1544369918","https://openalex.org/W1550863203","https://openalex.org/W1598552949","https://openalex.org/W1602764130","https://openalex.org/W2010504984","https://openalex.org/W2019689629","https://openalex.org/W2101040389","https://openalex.org/W2117948393","https://openalex.org/W2141040012","https://openalex.org/W2166780626","https://openalex.org/W2225440610","https://openalex.org/W2296540018","https://openalex.org/W3123233317"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"In":[1,110],"this":[2,66],"paper":[3],"we":[4],"study":[5],"an":[6],"RSA":[7,74,87],"variant":[8,48,67],"with":[9],"moduli":[10,75],"of":[11,79,86],"the":[12,72,77,111,114,119,184,230],"form":[13],"<m:math":[14,34,90,124,187,234],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[15,35,91,125,188,235],"<m:mrow>":[16,19,36,92,95,126,127,133,136,139,148,155,157,165,167,189,190,196,199,200,202,210,212,236,241,244,245,247,248,260,262],"<m:mi>N</m:mi>":[17,93,240],"<m:mo>=</m:mo>":[18,94],"<m:msup>":[20,25,96,101,137,146,239,259],"<m:mi>p</m:mi>":[21,97,138,158,203],"<m:mi>r</m:mi>":[22,37,98,140,251,263],"</m:msup>":[23,28,99,104,144,153],"<m:mo>\u2062</m:mo>":[24,100,129,145,154,164,192,209,250,258],"<m:mi>q</m:mi>":[26,102,147,168,213],"<m:mi>l</m:mi>":[27,39,103,149,254,265],"</m:mrow>":[29,30,42,105,106,131,143,152,161,163,171,173,174,175,176,194,206,208,216,218,219,220,221,252,255,257,266],"</m:math>":[31,43,107,177,222],"{N=p^{r}q^{l}}":[32,108],"(":[33],"<m:mo>&gt;</m:mo>":[38],"<m:mo>\u2265</m:mo>":[40],"<m:mn>2</m:mn>":[41],"{r&gt;l\\geq":[44],"2}":[45],").":[46],"This":[47],"was":[49],"mentioned":[50],"by":[51],"Boneh,":[52],"Durfee":[53],"and":[54,61,118],"Howgrave-Graham":[55],"[2].":[56],"Later":[57],"Lim,":[58],"Kim,":[59],"Yie":[60],"Lee":[62],"[11]":[63],"showed":[64],"that":[65,228],"is":[68],"much":[69],"faster":[70],"than":[71],"standard":[73],"in":[76,183],"step":[78],"decryption":[80,120],"procedure.":[81],"There":[82],"are":[83],"two":[84],"proposals":[85],"variants":[88],"when":[89],".":[109,225],"first":[112,231],"proposal,":[113],"encryption":[115],"exponent":[116,121],"e":[117],"d":[122],"satisfy":[123],"<m:mi>e</m:mi>":[128,191],"<m:mi>d</m:mi>":[130,193,237],"<m:mo>\u2261</m:mo>":[132,195],"<m:mn>1</m:mn>":[134,142,151,160,170,197,205,215,242],"<m:mo>mod</m:mo>":[135,198],"<m:mo>-</m:mo>":[141,150,159,169,204,214,243],"<m:mo>(</m:mo>":[156,166,201,211,246,261],"<m:mo>)</m:mo>":[162,172,207,217,256,267],"ed\\equiv":[178,223],"1\\bmod":[179],"p^{r-1}q^{l-1}(p-1)(q-1)":[180],",":[181],"whereas":[182],"second":[185],"proposal":[186],"1\\bmod(p-1)(q-1)":[224],"We":[226],"prove":[227],"for":[229],"case":[232],"if":[233],"<m:mo>&lt;</m:mo>":[238],"<m:mn>3</m:mn>":[249],"<m:mo>+</m:mo>":[253,264],"</m":[268]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2017-05-26T00:00:00"}