Symmetry of input and output.

In a hostile environment, a symmetry exists between the customer and the smart card. (The principal differences are that the smart card has more memory and more computational ability.) Input from the customer's point of view is equivalent to output from the smart card's point of view, and vice versa. Suppose a rule exists of the form

Then by this symmetry, we also have:

Applying this rule to the above equivalences, we obtain the following: