(a) Encrypt the message "GROWTH" using a Hill cipher with encryption matrix A = [4 1 3; 0 2 4; 2 1 2] Ciphertext: QWYTKK (b) What is the decryption matrix? A^-1 = [0 -1/4 1/2; -2 -1/2 4; 1 1/2 -2] (c) Decrypt the message "KFNYWA". Plaintext:
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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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Obtain the Hill cipher of the message $$\text {DARK NIGHT}$$ for each of the following enciphering matrices: (a) $\left[\begin{array}{ll}1 & 3 \\ 2 & 1\end{array}\right]$ (b) $\left[\begin{array}{ll}4 & 3 \\ 1 & 2\end{array}\right]$
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