# Question Solved1 AnswerAn Affine-Hill Cipher is the following modification of a Hill Cipher. Let m be a positive integer, and define P = C = (Z26)". In this cryptosystem, a key K consists of a pair (L,b), where L is an m x m invertible matrix over Z26, and be (Z26). For r (x1, ..., Xm) E P and K = (L,b) E K, we compute y = eK(x) = (y1, ... , Ym) by means of the formula y = xL + b. Hence, if L = (li,j) and b = (b1, ..., bm), then 11,7 12,m (y1, ..., Ym) = (x1, ..., Im) 11,1 11,2 12,1 12,2 : lim,1 lm, 2 + (b1, ..., bm). Im,m) Suppose Oscar has learned that the plaintext adisplayedequation is encrypted to give the ciphertext DSRMSIOPLXLJBZULLM and Oscar also knows that m = 3. Determine the key, showing all computations.

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Transcribed Image Text: An Affine-Hill Cipher is the following modification of a Hill Cipher. Let m be a positive integer, and define P = C = (Z26)". In this cryptosystem, a key K consists of a pair (L,b), where L is an m x m invertible matrix over Z26, and be (Z26). For r (x1, ..., Xm) E P and K = (L,b) E K, we compute y = eK(x) = (y1, ... , Ym) by means of the formula y = xL + b. Hence, if L = (li,j) and b = (b1, ..., bm), then 11,7 12,m (y1, ..., Ym) = (x1, ..., Im) 11,1 11,2 12,1 12,2 : lim,1 lm, 2 + (b1, ..., bm). Im,m) Suppose Oscar has learned that the plaintext adisplayedequation is encrypted to give the ciphertext DSRMSIOPLXLJBZULLM and Oscar also knows that m = 3. Determine the key, showing all computations.
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Transcribed Image Text: An Affine-Hill Cipher is the following modification of a Hill Cipher. Let m be a positive integer, and define P = C = (Z26)". In this cryptosystem, a key K consists of a pair (L,b), where L is an m x m invertible matrix over Z26, and be (Z26). For r (x1, ..., Xm) E P and K = (L,b) E K, we compute y = eK(x) = (y1, ... , Ym) by means of the formula y = xL + b. Hence, if L = (li,j) and b = (b1, ..., bm), then 11,7 12,m (y1, ..., Ym) = (x1, ..., Im) 11,1 11,2 12,1 12,2 : lim,1 lm, 2 + (b1, ..., bm). Im,m) Suppose Oscar has learned that the plaintext adisplayedequation is encrypted to give the ciphertext DSRMSIOPLXLJBZULLM and Oscar also knows that m = 3. Determine the key, showing all computations.