ypelok 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 numE so let us take = 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 We can first arrange the coded sequence of numbers in the form of a matrix with two rows (using zero in the last place if we have an odd number of characters) and ther multiply on the left by A. 3 1 [1 15 20 13 19 9 14 Encrypted Matrix = 2 4 2 18 0 9 19 150 5 63 60 48 76 42 42 10 102 40 62 114 78 28 which we can also write as [5 10 63 102 60 40 48 62 76 114 42 78 42 28]. To decipher the encoded message, multiply the encrypted matrix by A. The following exercise uses the above matrix A for encoding and decoding. Use the matrix A to encode the phrase "GO TO PLAN B".
ypelok 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 numE so let us take = 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 We can first arrange the coded sequence of numbers in the form of a matrix with two rows (using zero in the last place if we have an odd number of characters) and ther multiply on the left by A. 3 1 [1 15 20 13 19 9 14 Encrypted Matrix = 2 4 2 18 0 9 19 150 5 63 60 48 76 42 42 10 102 40 62 114 78 28 which we can also write as [5 10 63 102 60 40 48 62 76 114 42 78 42 28]. To decipher the encoded message, multiply the encrypted matrix by A. The following exercise uses the above matrix A for encoding and decoding. Use the matrix A to encode the phrase "GO TO PLAN B".
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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![Encryption 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
We can first arrange the coded sequence of numbers in the form 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.
3 1
1 15 20 13 19 9 14
Encrypted Matrix =
2 4
2 18
19 15 0
5
63
60 48 76 42 42
10 102 40 62 114 78 28
which we can also write as
[5 10 63 102 60 40 48 62 76 114 42 78 42 28].
To decipher the encoded message, multiply the encrypted matrix by A-. The following exercise uses the above matrix A for encoding and decoding.
Use the matrix A to encode the phrase "GO TO PLAN B".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9bc8794-1faf-4b80-9c12-acf824da0430%2Ff4cde575-09c2-46cc-bcc3-fa25bf3c76b2%2Fqe2vx0d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Encryption 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
We can first arrange the coded sequence of numbers in the form 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.
3 1
1 15 20 13 19 9 14
Encrypted Matrix =
2 4
2 18
19 15 0
5
63
60 48 76 42 42
10 102 40 62 114 78 28
which we can also write as
[5 10 63 102 60 40 48 62 76 114 42 78 42 28].
To decipher the encoded message, multiply the encrypted matrix by A-. The following exercise uses the above matrix A for encoding and decoding.
Use the matrix A to encode the phrase "GO TO PLAN B".
Expert Solution
Step 1
Take <space>=0
Now the position of alphabets are
Now, GO TO PLAN B becomes
Arrange the coded sequence of numbers in the form of a matrix with two rows
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