Contents
Part C: Application of Linearity
How can Bob decrypt the message?
Since Alice tells Bob what the secret Matrix is going to be, he can easily decrypt the message. First he'll need to take the inverse of the Secret Matrix. Once Bob has the inverse of the secret Matrix, he will take the message three entries at a time, turn it into a 1x3 matrix and multiply it by the inverse of the Secret matrix. From this multiplication, Bob will get the decrypted number and then can easily find what letter of the Alphabet it corresponds to since the number is the order in the Alphabet (and 0 counts as a space).
Can Eve decrypt the message without finding the inverse of the secret matrix?
Since Eve knows the initial message and what it yields after it passes through the encrypter, then she can easily determine the Secret Matrix (especially if she has Matlab).
The Secret Matrix ends up being (using Christen Juzeszyn's answer to determine how to have a matrix in Latex):
$ \begin{matrix} - \frac{2}{3} & 0 & \frac{2}{3} \\ 0 & 1 & 0 \\ 4 &0 & -1 \end{matrix} $
What is the decrypted message corresponding to (2, 23, 3)?
Using my previous entry on "How can Bob decrypt the message?" we find that:
$ (2,23,3) \rightarrow (Secret Matrix)^{-1} \rightarrow (2, 23, 5) \rightarrow\! $ BWE
