by Guest » Sun Dec 19, 2021 12:08 pm
We are not told HOW to use the key but since it is a 2 by 2 matrix and the coded message consists of pairs of integers, I would try matrix multiplication.
[tex]\begin{pmatrix} 2 & 1 \\ -2 & 0 \end{pmatrix}\begin{pmatrix}21 \\ -9\end{pmatrix}=\begin{pmatrix} 33 \\ -42\end{pmatrix}[/tex].
Now, how do we interpret THAT? Well, at a guess, 33- 42= -9 and the 9th letter in the alphabet is I.
[tex]\begin{pmatrix} 2 & 1 \\ -2 & 0 \end{pmatrix}\begin{pmatrix}59 \\ -22\end{pmatrix}=\begin{pmatrix} 96 \\ -118\end{pmatrix}[/tex].
96- 118= -26 and the 26th letter is z.
[tex]\begin{pmatrix} 2 & 1 \\ -2 & 0 \end{pmatrix}\begin{pmatrix}48 \\ -15\end{pmatrix}=\begin{pmatrix} 81 \\ -96\end{pmatrix}[/tex].
81- 96= -15 and the 15th letter is o.
[tex]\begin{pmatrix} 2 & 1 \\ -2 & 0 \end{pmatrix}\begin{pmatrix}42 \\ -20\end{pmatrix}=\begin{pmatrix} 64 \\ -84\end{pmatrix}[/tex].
64- 84= -20 and the 20th letter is t.
[tex]\begin{pmatrix} 2 & 1 \\ -2 & 0 \end{pmatrix}\begin{pmatrix}35 \\ -5\end{pmatrix}=\begin{pmatrix} 65 \\ -70\end{pmatrix}[/tex].
65- 70= -5 and the 5th letter is e.
[tex]\begin{pmatrix} 2 & 1 \\ -2 & 0 \end{pmatrix}\begin{pmatrix}22 \\ -4\end{pmatrix}=\begin{pmatrix} 40 \\ -44\end{pmatrix}[/tex].
40- 44= -4 and the 4 letter is d.
Was there a candidate named "Izoted"?
I suspect that I screwed up on the second letter and she simply wrote "I voted"!