Do I have a point in this endless wittering? :) Well, I've always thought that engineers, and sometimes the most brilliant ones are the most guilty of this, have a tendency to over-optimise and over-engineer, and simplicity is absolutely key for robustness. There is nothing simpler than a group with NO structure - a cyclic group of prime order.

And as a counterpoint, building a system which is so cool in its sophistication that you don't need to check whether external inputs are adversarial, just lacks common sense.