(→Problem #3) |
(→Problem #3) |
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4 & 0 & -1 | 4 & 0 & -1 | ||
\end{bmatrix}</math> | \end{bmatrix}</math> | ||
| + | |||
| + | <math> \begin{bmatrix} | ||
| + | \frac{-2}{3} & 0 & \frac{2}{3} \\ | ||
| + | 0 & 1 & 0 \\ | ||
| + | 4 & 0 & -1 | ||
| + | \end{bmatrix}^{-1} | ||
| + | = \begin{bmatrix} | ||
| + | \frac{1}{2} & 0 & \frac{1}{3} \\ | ||
| + | 0 & 1 & 0 \\ | ||
| + | 2 & 0 & \frac{1}{3} | ||
| + | \end{bmatrix}</math> | ||
| + | |||
| + | Now that you have the decrypting matrix, you will be able to decrypt any secret message. | ||
| + | |||
| + | Example: | ||
| + | |||
| + | Decrypting matrix * secret message = decrypted secret message | ||
| + | |||
| + | <math> \begin{bmatrix} | ||
| + | \frac{1}{2} & 0 & \frac{1}{3} \\ | ||
| + | 0 & 1 & 0 \\ | ||
| + | 2 & 0 & \frac{1}{3} | ||
| + | \end{bmatrix} | ||
| + | x \begin{bmatrix} | ||
| + | 2 \\ | ||
| + | 23 \\ | ||
| + | 3 | ||
| + | \end{bmatrix} | ||
| + | = \begin{bmatrix} | ||
| + | 2 \\ | ||
| + | 23 \\ | ||
| + | 5 | ||
| + | \end{bmatrix}</math> | ||
| + | |||
| + | The decrypted code is BWE. | ||
Latest revision as of 21:46, 17 September 2008
Problem #1
Bob can decrypt the message by splitting the encrypted text into a 3x3 matrix, then multiplying the encrypted by the inverse of the secret message matrix. The secret message is also a 3x3 matrix.
Problem #2
No she cannot figure out the secret message without finding the inverse of the secret matrix. As of right now, I cannot think of another way to decrypt the message without using the inverse of the matrix.
Problem #3
Step by Step equations to finding the ecrypted message:
$ \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} x \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} $
$ \begin{bmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 3 \end{bmatrix} x \begin{bmatrix} 1 & 0 & 4 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix}^{-1} = \begin{bmatrix} \frac{-2}{3} & 0 & \frac{2}{3} \\ 0 & 1 & 0 \\ 4 & 0 & -1 \end{bmatrix} $
$ \begin{bmatrix} \frac{-2}{3} & 0 & \frac{2}{3} \\ 0 & 1 & 0 \\ 4 & 0 & -1 \end{bmatrix}^{-1} = \begin{bmatrix} \frac{1}{2} & 0 & \frac{1}{3} \\ 0 & 1 & 0 \\ 2 & 0 & \frac{1}{3} \end{bmatrix} $
Now that you have the decrypting matrix, you will be able to decrypt any secret message.
Example:
Decrypting matrix * secret message = decrypted secret message
$ \begin{bmatrix} \frac{1}{2} & 0 & \frac{1}{3} \\ 0 & 1 & 0 \\ 2 & 0 & \frac{1}{3} \end{bmatrix} x \begin{bmatrix} 2 \\ 23 \\ 3 \end{bmatrix} = \begin{bmatrix} 2 \\ 23 \\ 5 \end{bmatrix} $
The decrypted code is BWE.
