Table 2 LFT computation table.
From: A study of text-theoretical approach to S-box construction with image encryption applications
Alphabets | Adjacency Matrices \(\left[{M}_{i,j}\right]\) | Graph | \(xI+\left[{M}_{i,j}\right]=[{a}_{i,j}]\) | \(\sum_{i,j}{a}_{i,j}\) |
|---|---|---|---|---|
U | \(\left[\begin{array}{cc}\begin{array}{cc}0& 1\\ 1& 0\\ 0& 1\end{array}& \begin{array}{ccc}0& 0& 1\\ 1& 0& 0\\ 0& 2& 0\end{array}\\ \begin{array}{cc}0& 0\\ 1& 0\end{array}& \begin{array}{ccc}2& 0& 2\\ 0& 2& 0\end{array}\end{array}\right]\) |
| \(\left[\begin{array}{cc}\begin{array}{cc}x& 1\\ 1& x\\ 0& 1\end{array}& \begin{array}{ccc}0& 0& 1\\ 1& 0& 0\\ x& 2& 0\end{array}\\ \begin{array}{cc}0& 0\\ 1& 0\end{array}& \begin{array}{ccc}2& x& 2\\ 0& 2& x\end{array}\end{array}\right]\) | \(5x+14\) |
N | \(\left[\begin{array}{cc}\begin{array}{cc}0& 1\\ 1& 0\\ 0& 2\end{array}& \begin{array}{ccc}0& 0& 2\\ 2& 0& 0\\ 0& 1& 0\end{array}\\ \begin{array}{cc}0& 0\\ 2& 0\end{array}& \begin{array}{ccc}1& 0& 1\\ 0& 1& 0\end{array}\end{array}\right]\) |
| \(\left[\begin{array}{cc}\begin{array}{cc}x& 1\\ 1& x\\ 0& 2\end{array}& \begin{array}{ccc}0& 0& 2\\ 2& 0& 0\\ x& 1& 0\end{array}\\ \begin{array}{cc}0& 0\\ 2& 0\end{array}& \begin{array}{ccc}1& x& 1\\ 0& 1& x\end{array}\end{array}\right]\) | \(5x+14\) |
I | \(\left[\begin{array}{cc}\begin{array}{cc}0& 1\\ 1& 0\end{array}& \begin{array}{cc}0& 1\\ 2& 0\end{array}\\ \begin{array}{cc}0& 2\\ 1& 0\end{array}& \begin{array}{cc}0& 3\\ 3& 0\end{array}\end{array}\right]\) |
| \(\left[\begin{array}{cc}\begin{array}{cc}x& 1\\ 1& x\end{array}& \begin{array}{cc}0& 1\\ 2& 0\end{array}\\ \begin{array}{cc}0& 2\\ 1& 0\end{array}& \begin{array}{cc}x& 3\\ 3& x\end{array}\end{array}\right]\) | \(4x+14\) |
T | \(\left[\begin{array}{cc}\begin{array}{cc}0& 1\\ 1& 0\end{array}& \begin{array}{cc}0& 3\\ 1& 0\end{array}\\ \begin{array}{cc}0& 1\\ 3& 0\end{array}& \begin{array}{cc}0& 2\\ 2& 0\end{array}\end{array}\right]\) |
| \(\left[\begin{array}{cc}\begin{array}{cc}x& 1\\ 1& x\end{array}& \begin{array}{cc}0& 3\\ 1& 0\end{array}\\ \begin{array}{cc}0& 1\\ 3& 0\end{array}& \begin{array}{cc}x& 2\\ 2& x\end{array}\end{array}\right]\) | \(4x+14\) |
Y | \(\left[\begin{array}{cc}\begin{array}{cc}0& 1\\ 1& 0\\ 0& 1\end{array}& \begin{array}{ccc}0& 0& 1\\ 1& 0& 0\\ 0& 1& 0\end{array}\\ \begin{array}{cc}0& 0\\ 1& 0\end{array}& \begin{array}{ccc}1& 0& 3\\ 0& 3& 0\end{array}\end{array}\right]\) |
| \(\left[\begin{array}{cc}\begin{array}{cc}x& 1\\ 1& x\\ 0& 1\end{array}& \begin{array}{ccc}0& 0& 1\\ 1& 0& 0\\ x& 1& 0\end{array}\\ \begin{array}{cc}0& 0\\ 1& 0\end{array}& \begin{array}{ccc}1& x& 3\\ 0& 3& x\end{array}\end{array}\right]\) | \(5x+14\) |
