{"id":185698,"date":"2025-01-22T20:30:11","date_gmt":"2025-01-22T20:30:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=185698"},"modified":"2025-01-22T20:30:13","modified_gmt":"2025-01-22T20:30:13","slug":"what-is-the-decryption-function-for-an-affine-cipher-if-the-encryption-function-is-c-15p-13-mod-26","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/22\/what-is-the-decryption-function-for-an-affine-cipher-if-the-encryption-function-is-c-15p-13-mod-26\/","title":{"rendered":"What is the decryption function for an affine cipher if the encryption function is c = (15p + 13) mod 26"},"content":{"rendered":"\n<p>What is the decryption function for an affine cipher if the encryption function is c = (15p + 13) mod 26?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The Affine cipher encryption function is typically written as: c=(ap+b)mod\u2009\u2009mc = (ap + b) \\mod m<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>cc is the ciphertext character,<\/li>\n\n\n\n<li>pp is the plaintext character,<\/li>\n\n\n\n<li>aa and bb are keys for the cipher (with aa being coprime to mm, which is the number of letters in the alphabet, usually 26 for the English alphabet),<\/li>\n\n\n\n<li>mm is the modulus (in this case, m=26m = 26 for the English alphabet).<\/li>\n<\/ul>\n\n\n\n<p>Given that the encryption function is: c=(15p+13)mod\u2009\u200926c = (15p + 13) \\mod 26<\/p>\n\n\n\n<p>we can identify that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=15a = 15,<\/li>\n\n\n\n<li>b=13b = 13,<\/li>\n\n\n\n<li>m=26m = 26.<\/li>\n<\/ul>\n\n\n\n<p>To decrypt the message, we need to reverse the encryption process. The decryption function for the Affine cipher is: p=a\u22121(c\u2212b)mod\u2009\u2009mp = a^{-1}(c &#8211; b) \\mod m<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>pp is the plaintext character,<\/li>\n\n\n\n<li>a\u22121a^{-1} is the modular multiplicative inverse of aa modulo mm.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-Step Decryption Process<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Find the modular inverse of a=15a = 15 modulo 26<\/strong>: We need to find an integer a\u22121a^{-1} such that: 15a\u22121\u22611mod\u2009\u20092615a^{-1} \\equiv 1 \\mod 26 To find the inverse, we can use the Extended Euclidean Algorithm.<\/li>\n\n\n\n<li><strong>Solve for pp<\/strong>: Once we have a\u22121a^{-1}, we can substitute it, along with b=13b = 13 and the ciphertext cc, into the decryption formula.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Calculating the Modular Inverse of 15 Modulo 26<\/h3>\n\n\n\n<p>Using the Extended Euclidean Algorithm: 15\u22c5a\u22121\u22611mod\u2009\u20092615 \\cdot a^{-1} \\equiv 1 \\mod 26<\/p>\n\n\n\n<p>The modular inverse of 15 modulo 26 is 7. (This is because 15\u00d77=105\u22611mod\u2009\u20092615 \\times 7 = 105 \\equiv 1 \\mod 26).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Decryption Formula:<\/h3>\n\n\n\n<p>Now that we know the modular inverse of 15 is 7, we can substitute this value into the decryption formula: p=7(c\u221213)mod\u2009\u200926p = 7(c &#8211; 13) \\mod 26<\/p>\n\n\n\n<p>This function will decrypt any ciphertext generated using the encryption function c=(15p+13)mod\u2009\u200926c = (15p + 13) \\mod 26.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the decryption function for an affine cipher if the encryption function is c = (15p + 13) mod 26? The Correct Answer and Explanation is : The Affine cipher encryption function is typically written as: c=(ap+b)mod\u2009\u2009mc = (ap + b) \\mod m where: Given that the encryption function is: c=(15p+13)mod\u2009\u200926c = (15p + [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","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-5)","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-5)","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-5)","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":[25],"tags":[],"class_list":["post-185698","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185698","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=185698"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185698\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=185698"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=185698"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=185698"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}