History of ZKP

Let’s start with classical proofs. So when we think of a classical proof, we think about these various esteemed provers, Gauss, Euclid, Emmy Noether, Alan Turing, and our own, Steve Cook. And we think about theorems, the kind of theorems that you learn perhaps in geometry in class where there’s a bunch of axioms, there’s a claim that you’re trying to prove or theorem,you make a sequence of derivations from the axioms and then eventually you declare the theorem as proved. It could be the prime number theorem, the Pythagorean theorem, and so forth. But today, we’re going to think of proofas an interactive process where there is the prover. But maybe more importantly for our study, there is a verifier. So there is an explicit referenceto whoever it is that’s reading the proof and verifying it is correct. And we think about this as follows. There’s a claim, which is an input to both prover and the verifier. Both of the prover and the verifier are actually algorithms.