{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44956,"title":"Determine RSA keys (public and private) given two prime number character strings (p and q)","description":"Given two prime number character strings (p and q), generate the RSA public and private keys (n and d) with e = 65537. The more difficult part is doing this without the use of symbolic numbers.\r\nExample: p = '3355335697481001330501721', q = '5955344080483688912855719'\r\nn='19982178584029090861856118769095354822153154192399'\r\nd='3270348772331599380262578849367006078599068947553'\r\n\r\n\u003chttps://simple.wikipedia.org/wiki/RSA_algorithm\u003e\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eGiven two prime number character strings (p and q), generate the RSA public and private keys (n and d) with e = 65537. The more difficult part is doing this without the use of symbolic numbers.\r\nExample: p = '3355335697481001330501721', q = '5955344080483688912855719'\r\nn='19982178584029090861856118769095354822153154192399'\r\nd='3270348772331599380262578849367006078599068947553'\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://simple.wikipedia.org/wiki/RSA_algorithm\"\u003ehttps://simple.wikipedia.org/wiki/RSA_algorithm\u003c/a\u003e\u003c/p\u003e","function_template":"function [n,d] = keyGeneration(p,q)\r\n  n = p;\r\n  d = q;\r\nend","test_suite":"%%\r\np = '3355335697481001330501721';\r\nq = '5955344080483688912855719';\r\nn='19982178584029090861856118769095354822153154192399';\r\nd='3270348772331599380262578849367006078599068947553';\r\n[a,b]=keyGeneration(p,q);\r\nassert(isequal(a,n))\r\nassert(isequal(b,d))\r\n%%\r\np = '813610636673';\r\nq = '1605983302589';\r\nn='1306645097305643499246397';\r\nd='355984378478555057894913';\r\n[a,b]=keyGeneration(p,q);\r\nassert(isequal(a,n))\r\nassert(isequal(b,d))\r\n%%\r\np = '67979691391330950855242581938207942707483223433259';\r\nq = '6153843674264879356192291854148321819411378704398479';\r\nn='418336393847020647250825879743341651032293545176800777981294580200903315345456262337972725306797613061';\r\nd='8444986024072025211908427894173383040354675378319105204646840203847580180874615752845913488969020869';\r\n[a,b]=keyGeneration(p,q);\r\nassert(isequal(a,n))\r\nassert(isequal(b,d))\r\n%%\r\np = '9889977922600049892469466917642800243744956526655686322206918503863571743809023708648966023469645149';\r\nq = '2476454822450020555811121392457617785385805217059253393679351596046272567110905233495088857069108236299';\r\nn = '24492083520347129695334786995557239882540750861618765872694983337614252441655470479409598244691513160097634784088025768219041142794039842531021683737585081956313858395523050254392582005967309810771063551';\r\nd = '7043758337908398316945695794623843894382227935971901356005844728128437829322707899292187736941661046350269216062193211515498221491327821445579367736374708711769362662280124297131956999441862850977388289';\r\n[a,b]=keyGeneration(p,q);\r\nassert(isequal(a,n))\r\nassert(isequal(b,d))\r\n%%\r\np = '26892754546730837119898059580995437039544399594421875855251066246511044160199048288603963625982639028058714345196159764252398791569637860905138287322706679328840515337572608690956308136959236074835599';\r\nq = '76019400184540822543696224086250845563040709795227937154720461468348727220343229834542918037619525984430713380822472295398107810565069813256377730791194881206750953165713183208458761595898204049235781';\r\nn='2044371069952561243871813747701535503388267616657953475148898181142012590397809234167373308955772082860082985954286137615597515257087506574051530104475374974920093127841789408014496870693507622812332673504654584870100580476794800708440785082437228308551107726064054828640053321250498545183042994878498928173976370185712833904492317580152665428272199317847097773542066059565512439224992672101163367819';\r\nd='131358569595346680469722564224349085322306406056832660693226883146757023027681686453130430199929142940992255578581548217026735077095312421736286269892515739496597527524021166625708322359741224036234988705082882699895245449017415856831226734459122764117157172961113990706104659539690141481103935528273973382371183154438463086325519326121228923730136467766036183357672350586091588640276470994058874793';\r\n[a,b]=keyGeneration(p,q);\r\nassert(isequal(a,n))\r\nassert(isequal(b,d))","published":true,"deleted":false,"likes_count":3,"comments_count":10,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2019-08-28T22:45:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-08-26T02:38:07.000Z","updated_at":"2026-03-04T16:55:19.000Z","published_at":"2019-08-26T02:45:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven two prime number character strings (p and q), generate the RSA public and private keys (n and d) with e = 65537. The more difficult part is doing this without the use of symbolic numbers. Example: p = '3355335697481001330501721', q = '5955344080483688912855719' n='19982178584029090861856118769095354822153154192399' d='3270348772331599380262578849367006078599068947553'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://simple.wikipedia.org/wiki/RSA_algorithm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://simple.wikipedia.org/wiki/RSA_algorithm\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":44956,"title":"Determine RSA keys (public and private) given two prime number character strings (p and q)","description":"Given two prime number character strings (p and q), generate the RSA public and private keys (n and d) with e = 65537. The more difficult part is doing this without the use of symbolic numbers.\r\nExample: p = '3355335697481001330501721', q = '5955344080483688912855719'\r\nn='19982178584029090861856118769095354822153154192399'\r\nd='3270348772331599380262578849367006078599068947553'\r\n\r\n\u003chttps://simple.wikipedia.org/wiki/RSA_algorithm\u003e\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eGiven two prime number character strings (p and q), generate the RSA public and private keys (n and d) with e = 65537. The more difficult part is doing this without the use of symbolic numbers.\r\nExample: p = '3355335697481001330501721', q = '5955344080483688912855719'\r\nn='19982178584029090861856118769095354822153154192399'\r\nd='3270348772331599380262578849367006078599068947553'\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://simple.wikipedia.org/wiki/RSA_algorithm\"\u003ehttps://simple.wikipedia.org/wiki/RSA_algorithm\u003c/a\u003e\u003c/p\u003e","function_template":"function [n,d] = keyGeneration(p,q)\r\n  n = p;\r\n  d = q;\r\nend","test_suite":"%%\r\np = '3355335697481001330501721';\r\nq = '5955344080483688912855719';\r\nn='19982178584029090861856118769095354822153154192399';\r\nd='3270348772331599380262578849367006078599068947553';\r\n[a,b]=keyGeneration(p,q);\r\nassert(isequal(a,n))\r\nassert(isequal(b,d))\r\n%%\r\np = '813610636673';\r\nq = '1605983302589';\r\nn='1306645097305643499246397';\r\nd='355984378478555057894913';\r\n[a,b]=keyGeneration(p,q);\r\nassert(isequal(a,n))\r\nassert(isequal(b,d))\r\n%%\r\np = '67979691391330950855242581938207942707483223433259';\r\nq = '6153843674264879356192291854148321819411378704398479';\r\nn='418336393847020647250825879743341651032293545176800777981294580200903315345456262337972725306797613061';\r\nd='8444986024072025211908427894173383040354675378319105204646840203847580180874615752845913488969020869';\r\n[a,b]=keyGeneration(p,q);\r\nassert(isequal(a,n))\r\nassert(isequal(b,d))\r\n%%\r\np = '9889977922600049892469466917642800243744956526655686322206918503863571743809023708648966023469645149';\r\nq = '2476454822450020555811121392457617785385805217059253393679351596046272567110905233495088857069108236299';\r\nn = '24492083520347129695334786995557239882540750861618765872694983337614252441655470479409598244691513160097634784088025768219041142794039842531021683737585081956313858395523050254392582005967309810771063551';\r\nd = '7043758337908398316945695794623843894382227935971901356005844728128437829322707899292187736941661046350269216062193211515498221491327821445579367736374708711769362662280124297131956999441862850977388289';\r\n[a,b]=keyGeneration(p,q);\r\nassert(isequal(a,n))\r\nassert(isequal(b,d))\r\n%%\r\np = '26892754546730837119898059580995437039544399594421875855251066246511044160199048288603963625982639028058714345196159764252398791569637860905138287322706679328840515337572608690956308136959236074835599';\r\nq = '76019400184540822543696224086250845563040709795227937154720461468348727220343229834542918037619525984430713380822472295398107810565069813256377730791194881206750953165713183208458761595898204049235781';\r\nn='2044371069952561243871813747701535503388267616657953475148898181142012590397809234167373308955772082860082985954286137615597515257087506574051530104475374974920093127841789408014496870693507622812332673504654584870100580476794800708440785082437228308551107726064054828640053321250498545183042994878498928173976370185712833904492317580152665428272199317847097773542066059565512439224992672101163367819';\r\nd='131358569595346680469722564224349085322306406056832660693226883146757023027681686453130430199929142940992255578581548217026735077095312421736286269892515739496597527524021166625708322359741224036234988705082882699895245449017415856831226734459122764117157172961113990706104659539690141481103935528273973382371183154438463086325519326121228923730136467766036183357672350586091588640276470994058874793';\r\n[a,b]=keyGeneration(p,q);\r\nassert(isequal(a,n))\r\nassert(isequal(b,d))","published":true,"deleted":false,"likes_count":3,"comments_count":10,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2019-08-28T22:45:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-08-26T02:38:07.000Z","updated_at":"2026-03-04T16:55:19.000Z","published_at":"2019-08-26T02:45:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven two prime number character strings (p and q), generate the RSA public and private keys (n and d) with e = 65537. The more difficult part is doing this without the use of symbolic numbers. Example: p = '3355335697481001330501721', q = '5955344080483688912855719' n='19982178584029090861856118769095354822153154192399' d='3270348772331599380262578849367006078599068947553'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://simple.wikipedia.org/wiki/RSA_algorithm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://simple.wikipedia.org/wiki/RSA_algorithm\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" 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