View source for HW3.C Xujun Huang ECE301Fall2008mboutin - Rhea

1. Bob needs to calculate the inverse of the secret matrix, and multiply it by the code given by Alice to get a vector.
Then replaces each three entries by its corresponding letter in the alphabet.

2.Eve can get the secret matrix through calculation.
<br>

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

</math>
<br>
Thus we have
A+C=2 <br>
B=0 <br>
4A+C=0 <br>
D+F=0 <br>
E=1 <br>
4D+F=0 <br>
G+I=0 <br>
H=0 <br>
4G+I=3 <br>
and so
D=0 <br>
E=1 <br>
F=0 <br>
A=B=-2/3 <br>
G=H=2/3 <br>
I=-1 <br>
C=4 <br>
i.e.


:<math>
\begin{bmatrix}
     -\frac{2}{3} & -\frac{2}{3} & 4 \\ 
     0 & 1 & 0 \\
     \frac{2}{3} & \frac{2}{3} & -1
  \end{bmatrix}
</math>

3. The inverse matrix is <br>
:<math>
\begin{bmatrix}
     \frac{1}{2} & -1 & 2 \\ 
     0 & 1 & 0 \\
     \frac{1}{3} & 0 & \frac{1}{3}
  \end{bmatrix}
</math><br>
So(2,23,3) --> (1,23,1) --> AWE