Spartan 3

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 …

Spartan 2 some basic terminologies

Follow my first post for Spartan

Closed-form expression for evaluating a polynomial

The closed-form expression for evaluating a polynomial \(\mathcal{G}(\cdot)\) at \((r_1,…,r_m)\in \mathbb{F}^m\) is

$$\mathcal{G}(r_1,…,r_m)=\sum\limits_{x\in\{0,1\}^m}\mathcal{G}(x)\prod\limits^{m}_{i=1}\underbrace{(r_i\cdot …

Circle STARK: Understanding Circle Group’s Operation as Rotation

The goal of this blog is to explain circle group without complex mathematical definitions. However, this approach is not rigorous, it serves more like a intuition of understanding the geometry of a circle group. Before diving into the blog, may you need some pre-readings like Exploring circle STARKs or Yet