{"id":41,"date":"2018-07-11T09:32:09","date_gmt":"2018-07-11T09:32:09","guid":{"rendered":"http:\/\/itp4.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=41"},"modified":"2019-05-13T11:29:56","modified_gmt":"2019-05-13T11:29:56","slug":"hill-cipher","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/itp4\/chapter\/hill-cipher\/","title":{"rendered":"Hill cipher"},"content":{"raw":"<div><span style=\"float: right;\"><a href=\"https:\/\/youtu.be\/hQR_IHxXUOw\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n\r\n<strong>Multiletter cipher \u2013 Hill Cipher:<\/strong>\r\n\r\n&nbsp;\r\n<ul>\r\n \t<li>M \u2013 Square Matrix<\/li>\r\n \t<li>M-1 \u2013 Inverse square matrix<\/li>\r\n \t<li>M(M-1 ) = M-1 M = I \u2013 I is the identity matrix where only diagonal elements are 1 from upper left to lower right and all other elements are zero.<\/li>\r\n \t<li>Every time inverse of the matrix does not exist.<\/li>\r\n<\/ul>\r\n&nbsp;\r\n\r\n<strong>M(M<\/strong><strong>-1<\/strong><strong> ) = I:<\/strong>\r\n<ul>\r\n \t<li><strong>[1] <\/strong>Cryptography and Network Security By William Stallings<\/li>\r\n<\/ul>\r\n<img class=\"size-full wp-image-42 aligncenter\" src=\"http:\/\/itp4.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-16.png\" alt=\"\" width=\"720\" height=\"707\" \/>\r\n\r\n<img class=\"size-full wp-image-43 aligncenter\" src=\"http:\/\/itp4.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-17.png\" alt=\"\" width=\"835\" height=\"201\" \/>\r\n\r\n<strong>Calculation of inverse of matrix:<\/strong>\r\n\r\n&nbsp;\r\n<ul>\r\n \t<li>If determinant of a square matrix is nonzero, then the inverse of matrix is computed as [A-1]ij = (det A)-1 (-1)i+j (Dji) where (Dji) is the subdeterminant obtained by deleting the jth row and the ith column of A. det(A) is the determinant of A and (det A)-1 is multiplicative inverse of (det A) mod 26.<\/li>\r\n<\/ul>\r\n<img class=\"size-full wp-image-45 aligncenter\" src=\"http:\/\/itp4.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-19.png\" alt=\"\" width=\"865\" height=\"303\" \/>\r\n\r\n<strong>Hill Algorithm:<\/strong>\r\n\r\n&nbsp;\r\n<ul>\r\n \t<li>C = PK mod 26<\/li>\r\n \t<li>C \u2013 ciphertext row vector of length 3<\/li>\r\n \t<li>P \u2013 plaintext row vector of length 3<\/li>\r\n \t<li>K is 3x3 matrix of encryption key.<\/li>\r\n<\/ul>\r\n&nbsp;\r\n\r\n<strong>Hill algorithm example:<\/strong>\r\n\r\n<img class=\"size-full wp-image-46 aligncenter\" src=\"http:\/\/itp4.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-20.png\" alt=\"\" width=\"386\" height=\"202\" \/>\r\n\r\n<img class=\"size-full wp-image-47 aligncenter\" src=\"http:\/\/itp4.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-21.png\" alt=\"\" width=\"847\" height=\"788\" \/>\r\n\r\n<strong>Strength of Hill cipher:<\/strong>\r\n\r\n&nbsp;\r\n<ul>\r\n \t<li>Completely hides single \u2013 letter frequency<\/li>\r\n \t<li>3x3 Hill cipher hides two-letter frequecy.<\/li>\r\n \t<li>Protect against ciphertext only attack.<\/li>\r\n \t<li>Weak against known plaintext attack.<\/li>\r\n \t<li>Given m Plaintext-ciphertext pairs of length m.<\/li>\r\n \t<li>C=PK. P and C are known hence K can be obtained.<\/li>\r\n<\/ul>\r\n<strong>Evaluation of Known plaintext attack:<\/strong>\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-48 aligncenter\" src=\"http:\/\/itp4.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-22.png\" alt=\"\" width=\"497\" height=\"691\" \/>\r\n\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Hill Cipher<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/hQR_IHxXUOw\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n<strong>Suggested Reading:<\/strong>\r\n\r\n&nbsp;\r\n<ol>\r\n \t<li>Cryptography and Network Security Principles and Practice by William Stallings, sixth Edition, PEARSON.<\/li>\r\n \t<li>Security in Computing by Charles Pfleeger &amp; Shari Lawrence Pfleeger, fourth Edition, PEARSON.<\/li>\r\n \t<li>Network Security by Charlie Kaufman, Radia Perlman, Mike Speciner, second Edition, PHI.<\/li>\r\n \t<li>The Complete Reference \u2013 Network Security by Roberta Bragg, Mark Rhodes-Ousley &amp; Keith Strassberg, Tata McGraw Hill<\/li>\r\n \t<li>Network Security Bible by Eric Cole, Ronald Krutz, James Conley, Wiley<\/li>\r\n \t<li>Hacking 6 Exposed by Stuart McClure, Joel Scambray &amp; George Kurtz , Tata McGraw Hill .<\/li>\r\n \t<li><a href=\"http:\/\/www.snort.org\/\">www.snort.org<\/a><\/li>\r\n \t<li><a href=\"https:\/\/nmap.org\/\">https:\/\/nmap.org<\/a><\/li>\r\n<\/ol>","rendered":"<div><span style=\"float: right;\"><a href=\"https:\/\/youtu.be\/hQR_IHxXUOw\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p><strong>Multiletter cipher \u2013 Hill Cipher:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li>M \u2013 Square Matrix<\/li>\n<li>M-1 \u2013 Inverse square matrix<\/li>\n<li>M(M-1 ) = M-1 M = I \u2013 I is the identity matrix where only diagonal elements are 1 from upper left to lower right and all other elements are zero.<\/li>\n<li>Every time inverse of the matrix does not exist.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><strong>M(M<\/strong><strong>-1<\/strong><strong> ) = I:<\/strong><\/p>\n<ul>\n<li><strong>[1] <\/strong>Cryptography and Network Security By William Stallings<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-42 aligncenter\" src=\"http:\/\/itp4.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-16.png\" alt=\"\" width=\"720\" height=\"707\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-16.png 720w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-16-300x295.png 300w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-16-65x64.png 65w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-16-225x221.png 225w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-16-350x344.png 350w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-43 aligncenter\" src=\"http:\/\/itp4.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-17.png\" alt=\"\" width=\"835\" height=\"201\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-17.png 835w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-17-300x72.png 300w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-17-768x185.png 768w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-17-65x16.png 65w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-17-225x54.png 225w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-17-350x84.png 350w\" sizes=\"auto, (max-width: 835px) 100vw, 835px\" \/><\/p>\n<p><strong>Calculation of inverse of matrix:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li>If determinant of a square matrix is nonzero, then the inverse of matrix is computed as [A-1]ij = (det A)-1 (-1)i+j (Dji) where (Dji) is the subdeterminant obtained by deleting the jth row and the ith column of A. det(A) is the determinant of A and (det A)-1 is multiplicative inverse of (det A) mod 26.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-45 aligncenter\" src=\"http:\/\/itp4.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-19.png\" alt=\"\" width=\"865\" height=\"303\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-19.png 865w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-19-300x105.png 300w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-19-768x269.png 768w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-19-65x23.png 65w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-19-225x79.png 225w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-19-350x123.png 350w\" sizes=\"auto, (max-width: 865px) 100vw, 865px\" \/><\/p>\n<p><strong>Hill Algorithm:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li>C = PK mod 26<\/li>\n<li>C \u2013 ciphertext row vector of length 3<\/li>\n<li>P \u2013 plaintext row vector of length 3<\/li>\n<li>K is 3&#215;3 matrix of encryption key.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><strong>Hill algorithm example:<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-46 aligncenter\" src=\"http:\/\/itp4.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-20.png\" alt=\"\" width=\"386\" height=\"202\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-20.png 386w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-20-300x157.png 300w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-20-65x34.png 65w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-20-225x118.png 225w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-20-350x183.png 350w\" sizes=\"auto, (max-width: 386px) 100vw, 386px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-47 aligncenter\" src=\"http:\/\/itp4.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-21.png\" alt=\"\" width=\"847\" height=\"788\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-21.png 847w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-21-300x279.png 300w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-21-768x715.png 768w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-21-65x60.png 65w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-21-225x209.png 225w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-21-350x326.png 350w\" sizes=\"auto, (max-width: 847px) 100vw, 847px\" \/><\/p>\n<p><strong>Strength of Hill cipher:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li>Completely hides single \u2013 letter frequency<\/li>\n<li>3&#215;3 Hill cipher hides two-letter frequecy.<\/li>\n<li>Protect against ciphertext only attack.<\/li>\n<li>Weak against known plaintext attack.<\/li>\n<li>Given m Plaintext-ciphertext pairs of length m.<\/li>\n<li>C=PK. P and C are known hence K can be obtained.<\/li>\n<\/ul>\n<p><strong>Evaluation of Known plaintext attack:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-48 aligncenter\" src=\"http:\/\/itp4.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-22.png\" alt=\"\" width=\"497\" height=\"691\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-22.png 497w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-22-216x300.png 216w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-22-65x90.png 65w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-22-225x313.png 225w, https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-content\/uploads\/sites\/25\/2018\/07\/Untitled-22-350x487.png 350w\" sizes=\"auto, (max-width: 497px) 100vw, 497px\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Hill Cipher<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/hQR_IHxXUOw\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Suggested Reading:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<ol>\n<li>Cryptography and Network Security Principles and Practice by William Stallings, sixth Edition, PEARSON.<\/li>\n<li>Security in Computing by Charles Pfleeger &amp; Shari Lawrence Pfleeger, fourth Edition, PEARSON.<\/li>\n<li>Network Security by Charlie Kaufman, Radia Perlman, Mike Speciner, second Edition, PHI.<\/li>\n<li>The Complete Reference \u2013 Network Security by Roberta Bragg, Mark Rhodes-Ousley &amp; Keith Strassberg, Tata McGraw Hill<\/li>\n<li>Network Security Bible by Eric Cole, Ronald Krutz, James Conley, Wiley<\/li>\n<li>Hacking 6 Exposed by Stuart McClure, Joel Scambray &amp; George Kurtz , Tata McGraw Hill .<\/li>\n<li><a href=\"http:\/\/www.snort.org\/\">www.snort.org<\/a><\/li>\n<li><a href=\"https:\/\/nmap.org\/\">https:\/\/nmap.org<\/a><\/li>\n<\/ol>\n","protected":false},"author":4,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["miss-hiteishi-diwanji"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-41","chapter","type-chapter","status-publish","hentry","contributor-miss-hiteishi-diwanji"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-json\/pressbooks\/v2\/chapters\/41","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-json\/wp\/v2\/users\/4"}],"version-history":[{"count":3,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-json\/pressbooks\/v2\/chapters\/41\/revisions"}],"predecessor-version":[{"id":425,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-json\/pressbooks\/v2\/chapters\/41\/revisions\/425"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-json\/pressbooks\/v2\/chapters\/41\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-json\/wp\/v2\/media?parent=41"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-json\/pressbooks\/v2\/chapter-type?post=41"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-json\/wp\/v2\/contributor?post=41"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp4\/wp-json\/wp\/v2\/license?post=41"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}