following the previous posts about spartan: 1 and 2
Chapter 5, A family of NIZKs with succinct interactive argument of knowledge
from post 1 we get a goal to check
\(\mathcal{Q}_{io}(\tau)=\sum\limits_{x\in \{0,1\}^s}\mathcal{G}_{io,\tau}(x)=\sum\limits_{x\in \{0,1\}^s}\widetilde{F}_{io}(x)\cdot \widetilde{eq}(\tau,x)=0\)
where \(\tau\) is a random checking point.
recall we have:
\(\widetilde{F}_{io}(x)=\left(\sum\limits_{y\in\{0,1\}^s}\widetilde{A}(x,y)\cdot Z(y)\right)\cdot \left(\sum\limits_{y\in\{0,1\}^s}\widetilde{B}(x,y)\cdot Z(y)\right)\)
let’s start …