Demonstrate how to use Excel to encrypt or code. The message to be encoded is "SEPTEMBER IS HERE" message using matrices and their inverse. The encoded message to be formed using triplets of numbers and the JxJ matrix A = √2, whose inverse is A-1. Use the following association of letters and divide the message into triplets of letters: SEP TEM BER ISH ERE 13 16 17 19 20 21 22 23 24 To decode the message, form 3x1 column vectors of the numbers in the coded message and multiply on the left by the inverse matrix.
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First, we need to associate each letter with a number. We can use the following associations: A=1, B=2, C=3, ..., Z=26 Show more…
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Encryption Use the methods presented in Example 7 along with the given matrix $B$ to do the following. $$B=\left[\begin{array}{rrr}{2} & {4} & {6} \\ {-1} & {-4} & {-3} \\ {0} & {1} & {-1}\end{array}\right]$$ a. Encode the message, To be or not to be b. Find the inverse of $B$ . c. Use the inverse of $B$ to decode the message $116,-60,-15,$ $294,-197,-2,148,-92,-9,96,-64,4,264,-182,-2$
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One method of encryption is to use a matrix to encrypt the message and then use the corresponding inverse matrix to decode the message. The encrypted matrix, $E,$ is obtained by multiplying the message matrix, $M$ by a key matrix, $K .$ The original message can be retrieved by multiplying the encrypted matrix by the inverse of the key matrix. That is, $E=M \cdot K$ and $M=E \cdot K^{-1}$ (a) Given the key matrix $K=\left[\begin{array}{ccc}{2} & {1} & {1} \\ {1} & {1} & {0} \\ {1} & {1} & {1}\end{array}\right],$ find its inverse, $K^{-1} .$ [Note: This key matrix is known as the $Q_{2}^{3}$ Fibonacci encryption matrix. (b) Use your result from part (a) to decode the encrypted matrix $E=\left[\begin{array}{lll}{47} & {34} & {33} \\ {44} & {36} & {27} \\ {47} & {41} & {20}\end{array}\right]$ (c) Each entry in your result for part (b) represents the position of a letter in the English alphabet $(A=1, B=2$, $C=3, \text { and so on }) .$ What is the original message?
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Decoding a Message by Finding An Inverse Internet sites often ask for a secret phrase to recover lost passwords Jason encoded a secret phrase using matrix multiplication He multiplied the clear text code for each letter by the matrix c-[3 3 The matrix representing the encoded text iS. [-2 13 -33 -19 -32 -24 ~9 12 Ls ~12 53 38 50 45 21 ~12 Clear text encoding: E H 2 3 4 | 5 6 7 | 8 10 K M N 12 13 14 15 16 17 18 19 20 Jason $ secret phrase iS w XY 2 SPACE DONE 21 22 23 24 25 26
Madhur L.
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