halo2 VS halo2-tutorial

Circuits were written with Circom and that’s what we’re going to change. We’ll rewrite those circuits with Halo2, the PSE implementation (the KZG one, i’ll tell you more about it in the next section).

When starting with Halo2, keep in mind that there are two flavors of the framework out there: the vanilla one maintained by ZCash, and the fork by Ethereum's Privacy and Scaling Explorations team which uses a different polynomial commitment (KZG instead of IPA) that's more friendly for Ethereum.

As another example, you could define a circuit for proving the N-th Fibonacci number, where row i of the matrix has the values x[i-2], x[i-1], x[i]. This means you'd need three advice columns to begin with, let's call them a, b, c. Then, you'd constrain c to be equal to a + b in the same row using a gate, which requires adding a selector column for controlling it. And you'd have to set up equality constraints so that a and b are equal to b and c from the previous row. Last, in order to expose the N-th number as a public value, you'd need an instance column, constrained to equal the value of c at the last row.