Sumcheck Protocol - Educational Rust Implementation

An educational implementation of the sumcheck protocol in Rust, using the arkworks ecosystem for finite fields and multivariate polynomials.

The sumcheck protocol is a fundamental building block in modern zero-knowledge proof systems such as SNARKs.

A good reference for the theory is Justin Thaler's book Proofs, Arguments, and Zero-Knowledge.

What This Code Does

• Defines Prover and Verifier structs that exchange messages in n rounds
• Implements the boolean hypercube enumeration
• Implements partial evaluation of multivariate polynomials
• Performs all arithmetic in the finite field F₁₀₁ (integers mod 101), instantiated via ark-ff
• Runs a concrete example with a 4-variable polynomial and prints the full protocol transcript

Project Structure

src/
├── main.rs       # Entry point; defines the example polynomial and runs the protocol
├── protocol.rs   # Core logic: Prover, Verifier, hypercube, polynomial evaluation
└── tests.rs      # Unit tests for helper functions

Dependencies

Crate	Purpose
ark-ff	Finite field arithmetic
ark-poly	Sparse multivariate and univariate polynomials
rand / rand_chacha	Randomness for verifier challenges

Getting Started

Prerequisites: Rust (edition 2021)

git clone https://github.com/msmirnov18/mysumcheck
cd mysumcheck
cargo run

Run the tests:

cargo test