The main scenario of a ZKP – the digital cave

Imagine this fantastic scenario: Peggy has to demonstrate to Victor that she is able to open a locked door in the middle of Ali Baba’s cave, an annular cave with only one entrance/exit that can be reached from two directions, as you can see in the following figure. I suppose you have noticed that I have changed the names of the two actors, Peggy and Victor, from the usual Alice and Bob, just because here a verification is due, and the names Peggy and Victor match better with the first letters of prover (P) and verifier (V).

Figure 5.1 – Ali Baba's cave

This example involves Ali Baba's cave revisited in modern times, in which the door in the middle of the cave is locked through a secret electronic combination that's strong enough to prevent the entry of anyone who doesn't know the secret combination.

Now, suppose that Peggy must prove to Victor that she knows the...