Introduction To Linear Algebra 5th Edition Johnson Solutions
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In the design of the Polyalphabetic Locking Key, any integer between 0 and 63 is assigned as a 'key' for the alphabet substitution. A simple substitution would be assigning the lower case letters a through z to 12 in place of 9 cipher alphabets thus making a simple substitution cipher. In the Polyalphabetic Locking Key, the letters a, b, c,..., z will be assigned to respective integers by decimal separator rule. It is assumed that the Catholic monastic communities that are the inventors of the Polyalphabetic Locking Key had a decimal equivalent value (384) in their script. This integer was chosen because it is the sum of the cyclical phi, which is 1+2+... + 63 = 128, and the cyclical phi squared which is the sum of the square of i=1+2+3+...+63=2^5=32. Note
The Polyalphabetic Locking Key (118 in number) is a generalization of the Cyclic Locking Key which is composed of 2 alpha-based transposition subkeys. The Polyalphabetic Locking Key has a dictionary of 119 letters that are modified by the A, B, C,..., Z, a, b, c,... z keys of the 118 cipher alphabets. The Polyalphabetic Locking Key – like other Polyalphabetic Locking Key – has a sub cipher alphabet and more than 10 different sub cipher alphabets for substitution in pairs with the 118 general cipher alphabets. The single general cipher alphabet of the Polyalphabetic Locking Key is assigned a number between 1 and 25 (inclusive).
To stay in line with the Caesar cipher, unscramble the plain text using all available letter substitutions of the Polyalphabetic Locking Key. If the alphabet substitution profile has 7 alphabets assigned to Z, then the resultant scrambled letter is Z. The letter 'Z' is then assigned a key of 2(119+0) and a substitution value of 2(0+2+0+0+3+1+0+0). d2c66b5586