Sumcheck Protocol Implementation This repository contains scripts for implementing the Sumcheck Protocol based on the description in Section 4.1 of the book "Proofs, Arguments, and Zero-Knowledge" by Justin Thaler.

Scripts

1. Sumcheck Protocol File: sumcheck_protocol.py Description: This script implements the Sumcheck Protocol, a fundamental concept in interactive proof systems. It follows the methodology described in Section 4.1 of the book.
2. Univariate Polynomial File: univariate_polynomial.py Description: This script assists the prover in computing the univariate polynomial corresponding to each round of the Sumcheck Protocol. It plays a crucial role in the protocol's execution. Constants The constants.py file contains essential functions and constants that are configurable by the user. char: Characteristic of the finite field. poly: Definition of the hidden polynomial in terms of coefficients and degrees of variables. dimension: Maximal degree of each variable. Users can modify these constants to tailor the protocol to specific scenarios or field characteristics.

Functions boolean_matrix(n): Description: Generates a matrix of size n x 2^n with all possible boolean combinations. Used within the protocol computation. Usage: matrix = boolean_matrix(n)

evaluate_polynomial(coefficients, x) Description: Computes the value of the univariate polynomial with given coefficients at the specified value x. Usage: result = evaluate_polynomial(coefficients, x) Constants

Usage Clone the repository to your local machine using git clone https://github.com/nestordc97/sumcheck-protocol.git. Navigate to the repository directory using cd sumcheck-protocol. Explore and modify the scripts and constants as needed. Run the scripts using python sumcheck_protocol.py and python univariate_polynomial.py. Acknowledgments Justin Thaler's book "Proofs, Arguments, and Zero-Knowledge" for providing the foundation for this implementation.