Learning new things!
This module contains different evaluation domains used for polynomial arithmetic, especially those friendly to fast Fourier transforms (FFTs).
Contains the GeneralEvaluationDomain for FFT-friendly fields.
Contains the MixedRadixEvaluationDomain for fields that do not …
Docker is an open-source platform designed to automate the deployment, scaling, and management of applications. It uses container technology to package applications and their dependencies into lightweight, portable containers. These containers ensure that your application runs consistently regardless of where it’s deployed.
Docker offers …
This blog is the learning note for Brainfuck VM
Using the following example to go through GKR protocol
this blogs follows the example in Spartan 预备知识：GKR with ZK Argument
zero knowledge version of GKR, Hyrax approach.
Using an example of 3 variants multilinear polynomial to explain the design idea of sum-check protocol.
A 3 variants multilinear polynomial can be generally represented as
$$g(X,Y,Z)=a_0+a_xX+a_yY+a_zZ+a_{xy}XY+a_{xz}XZ+a_{yz}YZ+a_{xyz}XYZ$$
In the final round of sumcheck protocol, assuming the verifier gets a one degree polynomial
$$h(z)=g(r_1,r_2,\ldots,z )=\alpha_n z …
Following the definition from Justin Thaler
Let \(\mathbb{F}\) be any finite field, and let \( f : \{0,1\}^v \rightarrow \mathbb{F} \) be any function mapping the \( v \)-dimensional Boolean hypercube to \(\mathbb{F}\). A \( v \)-variate polynomial \( g \) over \(\mathbb{F}\) is said to be an …
These will be a series post about FFT and the math structure behind it. My goal are:
However, …
Take example circuit in figure 1, following the Arithmetization described in post, a step by step description of GKR arithmetication of a concrete example.
\(q’\in \{0,1\}^{b_N}\): The index of one of the \(N\) identical copies of the base circuit \(C_0\) within \(C\).…