Why can we reverse the tempering function?

There are to kinds of operations in the tempering function of the MT:

	1) Right shift
	2) Left shift with an AND

To undo the first operation, a simple shift is straight forward. Let's consider
the following example of a 24-bit number

	0010 1010 1011 1101 1111 0111					y
	0000 0000 0000 0000 0000 1010 1010 1111 0111 1101 11		y >> 18 := N
			      ^
			      orginal string
	0010 1010 1011 1101 1111 1101					y ^ (y>>18) := M


On can see, that the first  18 bits of M are the same than y. That's clear,
because we have shifted 18 new 0 into it. But now we also now N completly, since
the last 6 bits are the first 6 of M (N is a shifted version of M).
If you shift less than 24/2 = 12 bits, you have to do the above steps in a
loop, because you cannot determin N completly one step.

To understand why one can undo the second operation was a bit harder for me.
For me it was the easiest to understand it with the feistel network.


	y			y << 15
	|			  |
	|			  |
       XOR<--------- F <-----------
        |			  |
	 \_______________________ /
	 /\______________________