Q. In an RSA cryptosystem, the value of the public modulus parameter \ud835\udc5b is 3007. If it is also known that \u03c6(\ud835\udc5b) = 2880, where \u03c6() denotes Euler\u2019s Totient Function, then the prime factor of \ud835\udc5b which is greater than 50 is<\/p>\n\n\n\n
Ans:<\/p>\n\n\n\n
Given,<\/p>\n\n\n\n
n = p * q = 3007 … … (1)<\/p>\n\n\n\n
And,<\/p>\n\n\n\n
\u03c6(n) = (p – 1) * (q – 1) = 2880 … … (2)<\/p>\n\n\n\n
\u2192 pq – p – q + 1 = 2880<\/p>\n\n\n\n
\u2192 3007 – p – q + 1 = 2880<\/p>\n\n\n\n
\u2192 p + q = 128 ……(2)<\/p>\n\n\n\n
Using equation (1) and (2),<\/p>\n\n\n\n
\u2192 (3007 \/ q) + q = 128<\/p>\n\n\n\n
\u2192 q2 – (128*q) + 3007 = 0<\/p>\n\n\n\n
On solving the above equation:<\/p>\n\n\n\n
q = 31, 97 <\/p>\n\n\n\n
97 is greater than 50.<\/p>\n","protected":false},"excerpt":{"rendered":"
Q. In an RSA cryptosystem, the value of the public modulus parameter \ud835\udc5b is 3007. If it is also known that \u03c6(\ud835\udc5b) = 2880, where \u03c6() denotes Euler\u2019s Totient Function, then the prime factor of \ud835\udc5b which is greater than 50 is Ans: Given, n = p * q = 3007 … … (1) And, […]<\/p>\n","protected":false},"author":419,"featured_media":154183,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-154182","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154182","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=154182"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154182\/revisions"}],"predecessor-version":[{"id":154184,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154182\/revisions\/154184"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/154183"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=154182"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=154182"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=154182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}