Should not be to hard.
Make it simple:
Store the first touch as the center of the spiral. Store every other point in an array. Calculate the distance between the origin and each point.
Idealy every point has a slightly bigger distance to the center of the spiral. (work with some form of tolerance (even if some points are of it still counts as a spiral))
You can also calculate the angle between the touch and the center point, idealy again: all angles should increase (or decrease) steadily with some amount. 0 to 30 to 60 to 90 … to 360%360, to 390%360…
If the user actually starts from the outer edge, you have to get the last point and apply the same rules starting from the last point, ending at the first point.