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Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.) [63 39 90 90 17 21 20 60 57 31 111 103 77 51]

Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.) [63 39 90 90 17 21 20 60 57 31 111 103 77 51]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Matrices are commonly used to encrypt data. Here is a simple form such an encryption can take. First, we represent each letter in the alphabet by a number, so let us take <space> = 0, A = 1, B= 2, and so on. Thus, for example, "ABORT MISSION" becomes [1 2 15 18 20 0 13 9 19 19 9 15 14]. To encrypt this coded phrase, we use an invertible matrix of any size with integer entries. For instance, let us take A to be the 2 x 2 matrix of a matrix with two rows (using zero in the last place if we have an odd number of characters) and then multiply on the left by A. 14 1 ][ 32 2 [ - [2 = Encrypted Matrix = which we can also write as 9 87 20 15 20 13 19 9 14 18 0 9 19 15 0 49 95 69 14 7 81 60 57 95 57 42 14 32 Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.) [63 39 90 90 17 21 20 60 57 31 111 103 77 51] We can first arrange the coded sequence of numbers in the form [9 7 87 81 20 60 49 57 95 95 69 57 14 42]. To decipher the encoded message, multiply the encrypted matrix by A-1. The following question uses the above matrix A for encoding and decoding.
Transcribed Image Text:Matrices are commonly used to encrypt data. Here is a simple form such an encryption can take. First, we represent each letter in the alphabet by a number, so let us take <space> = 0, A = 1, B= 2, and so on. Thus, for example, "ABORT MISSION" becomes [1 2 15 18 20 0 13 9 19 19 9 15 14]. To encrypt this coded phrase, we use an invertible matrix of any size with integer entries. For instance, let us take A to be the 2 x 2 matrix of a matrix with two rows (using zero in the last place if we have an odd number of characters) and then multiply on the left by A. 14 1 ][ 32 2 [ - [2 = Encrypted Matrix = which we can also write as 9 87 20 15 20 13 19 9 14 18 0 9 19 15 0 49 95 69 14 7 81 60 57 95 57 42 14 32 Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.) [63 39 90 90 17 21 20 60 57 31 111 103 77 51] We can first arrange the coded sequence of numbers in the form [9 7 87 81 20 60 49 57 95 95 69 57 14 42]. To decipher the encoded message, multiply the encrypted matrix by A-1. The following question uses the above matrix A for encoding and decoding.
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