1.Image array disturbed algorithm has been improved to implement multiple permute better.The algorithm shortens its encryption time, so it fits image encryption well.
3.It turns out though, if you think about the group which permutes the roots of such a polynomial, there's something about the nature of this group that reveals that no quintic formula can exist.
4.This particular isomorphism between cube rotations and permutations of four objects is a bit subtle, but for the curious among you, you may enjoy taking a moment to think hard about how the rotations of a cube permute its four diagonals.