kzg-mini

A minimal implementation of the KZG commitment scheme. Built on top of the arkworks ecosystem.

🧩 Features

• Define and operate on univariate polynomials over finite fields.
• Efficient polynomial arithmetic (add, sub, mul, scale, evaluate).
• Divide polynomials by linear factors.
• Minimal implementation of KZG commitments using a trusted setup.
• Fully generic over any pairing-friendly curve (ark_ec::Pairing).
• Suitable for educational, experimental, and constrained environments.

📦 Crate Status

⚠️ Experimental: This crate is designed for educational purposes. Not intended for production use.

🛠 Installation

Add to your Cargo.toml:

[dependencies]
kzg-mini = "0.1"
ark-ff = "0.4"
ark-ec = "0.4"
ark-std = "0.4"
ark-bls12-381 = "0.4" # Or any curve from arkworks

🚀 Usage Examples

The following examples demonstrate how to create a polynomial commitment and open a KZG proof using the kzg_mini crate on the BLS12-381 curve. See examples for the full code.

1. Manually defined polynomial

This example constructs a polynomial f(x) = 3x² + 2x + 1, commits to it, and verifies a KZG proof:

fn main() {
    let mut rng = test_rng();

    let poly = Polynomial::new(vec![Fr::from(1u64), Fr::from(2u64), Fr::from(3u64)]);

    let tau = Fr::rand(&mut rng);
    let g1 = G1Projective::generator();
    let g2 = G2Projective::generator();

    let setup = KZGCeremony::<Bls12_381>::setup(2, tau, g1, g2);

    let commitment = setup.commit(&poly);
    let point = Fr::from(42u64);
    let proof = setup.open(&poly, point);

    let ok = setup.verify(commitment, &proof);
    println!("Reference Polynomial: {:#?}", poly);
    println!("Commitment: {}", commitment);
    println!("Proof: {:#?}", proof);
    println!("KZG proof verified: {}", ok);
}

2. Polynomial from string

This example shows how to generate a polynomial from a string, commit to it, and verify the corresponding proof:

fn main() {
    let mut rng = test_rng();

    let poly = Polynomial::from_str("hell0, world!")?;

    let tau = Fr::rand(&mut rng);
    let g1 = G1Projective::generator();
    let g2 = G2Projective::generator();

    let setup = KZGCeremony::<Bls12_381>::setup(poly.coeffs.len(), tau, g1, g2);

    let commitment = setup.commit(&poly);
    let point = Fr::from(42u64);
    let proof = setup.open(&poly, point);

    let ok = setup.verify(commitment, &proof);
    println!("Reference Polynomial: {:#?}", poly);
    println!("Commitment: {}", commitment);
    println!("Proof: {:#?}", proof);
    println!("KZG proof verified: {}", ok);
}

🌉 Structure

• Polynomial<F>: A simple polynomial type over any ark_ff::Field, with arithmetic operations and evaluation.
• KZGCeremony<E>: Holds the trusted setup parameters for a KZG commitment over a pairing engine E.
• KZGCommitment, KZGProof: Types representing the output of commitment and opening.

📄 License

MIT or Apache-2.0

Acknowledgments

Built using arkworks libraries.