Question Solved1 Answer 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 x = (21, ..., 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 = (bi, ...,bm), then l1, m 11,2 11,1 12,1 12,2 l2, m (41, ... , Ym) = (x1, ..., 8m) + (61, ...,bm). : : : lm, 1 lm, 2 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 x = (21, ..., 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 = (bi, ...,bm), then l1, m 11,2 11,1 12,1 12,2 l2, m (41, ... , Ym) = (x1, ..., 8m) + (61, ...,bm). : : : lm, 1 lm, 2 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 x = (21, ..., 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 = (bi, ...,bm), then l1, m 11,2 11,1 12,1 12,2 l2, m (41, ... , Ym) = (x1, ..., 8m) + (61, ...,bm). : : : lm, 1 lm, 2 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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Here, m is a positive integer which is given as 3 Y is computed by using the formula y= xl+ b, where l is a matrix of (3*3) and y,x and b is a matrix of (1*3) Here m=3{:[(y_(1,)y_(2),y_(3))=(x_(1),x_(2),x_(3))([l_(13)",",l_(1,2),l_(1,3)],[d_(2,),l_(2,2),l_(2,3)],[l_(3,2)",",l_(3,2)",",l_(3,3)])_(3,3)],[{:[=x_(1)l_(31)+x_(2)l_(2,1)+x_(3)l_(3,1)],[([x_(1)l_(1,1)+,x_(1)l_(1,2),x_(1)l_(1,3)],[x_(2)l_(2,1)+,x ... See the full answer