Common input precomputing for selectors

The selector polynomials q_L, q_R, q_O, q_M, q_C are common public inputs and specific to a particular circuit. In this case, the verifier needs to calculate these 5 polynomials as well.

My question is that what the computation cost for verifier, we need to use FFT to evaluate degree n polynomials. How fast it compares to MSM?

These can be precomputed in commitment form during setup (so not part of the public input), so you could see this as free.

If I remember correctly the verifier does not evaluate these and keep them in commitment form.

So basically, we still have to setup them every time for a new circuit.

However, if the verifier doesn’t evaluate/setup it as you said, how can the verifier trust it’s calculated correctly?

Yeah they’ll be different for every circuits.

If the verifier doesn’t perform this setup themselves, they have to trust the person who give them the precomputed stuff.

Yeah, that makes sense. Thanks!