Cryptography 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 ⋅ K and M = E ⋅ K − 1 (a) Given the key matrix K = [ 2 1 1 1 1 0 1 1 1 ] , find its inverse, K − 1 . [ Note: This key matrix is known as the Q 3 2 Fibonacci encryption matrix.] (b) Use your result from part (a) to decode the encrypted matrix E = [ 47 34 33 44 36 27 47 41 20 ] (c) Each entry in your result for part (b) represents the position of a letter in the English alphabet K ( A = 1 , B = 2 , C = 3 , a n d s o o n ) . What is the original message? Source: goldenmuseum.com
Cryptography 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 ⋅ K and M = E ⋅ K − 1 (a) Given the key matrix K = [ 2 1 1 1 1 0 1 1 1 ] , find its inverse, K − 1 . [ Note: This key matrix is known as the Q 3 2 Fibonacci encryption matrix.] (b) Use your result from part (a) to decode the encrypted matrix E = [ 47 34 33 44 36 27 47 41 20 ] (c) Each entry in your result for part (b) represents the position of a letter in the English alphabet K ( A = 1 , B = 2 , C = 3 , a n d s o o n ) . What is the original message? Source: goldenmuseum.com
Solution Summary: The author explains how to find the key matrix K and encrypted matrix E, where K is the Key matrix.
Cryptography 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,
, is obtained by multiplying the message matrix,
, by a key matrix,
. The original message can be retrieved by multiplying the encrypted matrix by the inverse of the key matrix.That is,
and
(a) Given the key matrix
, find its inverse,
. [Note: This key matrix is known as the
Fibonacci encryption matrix.]
(b) Use your result from part (a) to decode the encrypted matrix
(c) Each entry in your result for part (b) represents the position of a letter in the English alphabet
. What is the original message?
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