When you tap a shift register, instead of taking bit 1 as bit 1 it is changed for bit 5 for example, and so on. There are many methods but wireing your ADC to your PISO register through a switch array is the most common, and easiest. Then on the other side you wire up your SIPO register to the DAC in the oposite way.
Scrambling is not a very good way of encrypting data though, it can be pseudo cracked by brute force, and completely or effecively cracked just by listening or using an oscilloscope.