Question

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 2 matrix [2 4; 1 3]. 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. Encrypted Matrix = [2 4; 1 3][1 15 20 13 19 9 14; 2 18 0 9 19 15 0] = [10 102 40 62 114 78 28; 7 69 20 40 76 54 14], which we can also write as [10 7 102 69 40 20 62 40 114 76 78 54 28 14]. To decipher the encoded message, multiply the encrypted matrix by A^-1. The following exercise uses the above matrix A for encoding and decoding. Use the matrix A to encode the phrase "GO TO PLAN B".

          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   2 matrix [2 4; 1 3].
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.
Encrypted Matrix = [2 4; 1 3][1 15 20 13 19 9 14; 2 18 0 9 19 15 0]
= [10 102 40 62 114 78 28; 7 69 20 40 76 54 14],
which we can also write as
[10 7 102 69 40 20 62 40 114 76 78 54 28 14].
To decipher the encoded message, multiply the encrypted matrix by A^-1. The following exercise uses the above matrix A for encoding and decoding.
Use the matrix A to encode the phrase "GO TO PLAN B".

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 2 matrix [2 4; 1 3].
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.
Encrypted Matrix = [2 4; 1 3][1 15 20 13 19 9 14; 2 18 0 9 19 15 0]
= [10 102 40 62 114 78 28; 7 69 20 40 76 54 14],
which we can also write as
[10 7 102 69 40 20 62 40 114 76 78 54 28 14].
To decipher the encoded message, multiply the encrypted matrix by A^-1. The following exercise uses the above matrix A for encoding and decoding.
Use the matrix A to encode the phrase "GO TO PLAN B".

Added by Michele M.

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