Revision as of 17:46, 17 September 2008

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.

$ \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} $

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

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

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

(2,23,5) --> BWE