Chapter 15 gave a signature functionality and proved two properties of it. This chapter asks the three questions that leaves open. What does a scheme have to satisfy for a protocol built on it to inherit those properties — and what does the protocol look like, drawn in this framework’s own terms, with its randomness and its state held where Section 3.2 says they must be? Does the converse hold: are the two properties enough to characterize \(\Fsig \), so that anything with its interfaces satisfying them realizes it? And is \(\Fsig \) the strongest object of its shape, or does a realization of it satisfy something it does not?
The answers are: yes with a scheme’s own security as the bound; no, and instructively so; and no — a realization can be strictly stronger, which is worth knowing about ideal functionalities in general.