My question is related to information security, in particular data integrity.
Consider a client has a fixed value $y$ and two uniformly random values $a$ and $b$. It computes $v=a\cdot y+b$. Note the value $a,y,v\neq 0$ and all the values are defined over a finite field $\mathbb{F}^*_p$, for a large prime number $p$ (512-bit).
The client sends $v$ to the server. The server can apply ANY change to $v$. In fact it computes any function of $v$, $f(v)$. The client downloads $f(v)$ and then computes $y'=(a)^{-1}(f(v)-b)$
Question 1: Would this make $y'$ a uniformly random?
Or
Question 2: How does this change affect the distribution of $y'$?
I need to mention that a very close question was asked here. I do appreciate the answerer effort to answer that question; but I'm still not convinced with the answer: How To prove Any Change to $v=a\cdot y + b$ maks $y=(a)^{-1}(v-b)$ Uni. random value