Homework3 Part C

How can Bob decode the message?

Bob can decode the message by breaking the message into segments of three,
and then multiplying each 3 bit segment by the inverse of the encryption vector.

Can Eve decrypt it without finding the inverse of the encryption matrix?

No, Eve would have to find the inverse of the matrix in order to decode the messages.
However, She does have enough information to determine the encryption vector.

$ \begin{bmatrix} 1 & 0 & 4 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix} \cdot \begin{bmatrix} A & B & C \\ D & E & F \\ G & H & I \end{bmatrix} = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 3 \end{bmatrix} $

Solving for the alphabet characters matrix, she will find:

$ \begin{bmatrix} -\frac{2}{3} & 0 & \frac{2}{3} \\ 0 & 1 & 0 \\ 4 & 0 & -1 \end{bmatrix} $

What is the decrypted message corresponding to (2,23,3)? (Write it as a text)

(2,23,5) --> BWE