Without drilling down to the maths, how Faber college knows it is dealing with the real Alice and real Bob should be again another proof process.
Case 1: It can be simply that Faber have met Alice and Bob physically, and they have presented photoed IDs that make Faber college convinced. This is what we see in today's world.
Case 2: It can be proof presented by Alice and Bob using verifiable credential issued by say another org like Government. As far as Government, Faber College are in the same system/platform, and Faber trusts that the government has done its best for checking before issuing the verifiable credential to Alice and Bob, Faber should be comfortable it's speaking to the real Alice and Bob.
I think maths provides a tool to enable this trust system. The trust system participants must trust it before using this system to implement anything. That's the reason that this type of trust system must be driven by some authority such that every participant can trust and use it.
Just my 2 cents.