Hey @vladyslavmunin, great to see that this is of interest to you.
Indeed, if one has a way of subverting some combination of the parameters in the setup phase, then then potentially fake proofs could be generated.
Specifically, if a malicious prover gets hold of the \gamma or of the \delta, then they could generate fake proofs. This is because they would be able to change the values of the v_i, w_i, u_i to make the expression divisible, where the verifier would not know what is the relation being proven on.
There are a couple of interesting works around this:
- https://eprint.iacr.org/2017/599
- https://eprint.iacr.org/2017/587.pdf
- https://par.nsf.gov/servlets/purl/10055717 , which has a great talk https://www.youtube.com/watch?v=DP8xSEM9bd8
I can also recommend two blog posts:
Hope this helps and good luck!