Greco

A Rust workspace for generating and validating zero-knowledge proofs of correct ciphertext encryption under BFV public key homomorphic encryption.

This project is based on the research and implementation by the Privacy & Scaling Explorations (PSE) team. We extend our gratitude for their groundbreaking work on zero-knowledge proofs for BFV encryption correctness, detailed in their research paper.

Crates

e3-greco-polynomial

Core polynomial arithmetic library supporting:

• Basic operations (add, sub, mul, div) with arbitrary precision
• Modular reduction and centered coefficients
• Cyclotomic polynomial operations
• Range checking for cryptographic bounds

use e3_greco_polynomial::{Polynomial, BigInt};

let poly = Polynomial::new(vec![BigInt::from(2), BigInt::from(3), BigInt::from(1)]); // 2x² + 3x + 1
let reduced = poly.reduce_and_center(&modulus); // Center coefficients in [-q/2, q/2]

e3-greco-generator

Generator for cryptographic parameters and constants:

• BFV parameter generation and validation
• Input validation vector computation
• Prover TOML file generation

use e3_greco_generator::{BfvConfig, GeneratorConfig, generate_all_outputs};

let config = BfvConfig {
    degree: 2048,
    plaintext_modulus: 1032193,
    moduli: vec![18014398492704769],
};

let results = generate_all_outputs(config, GeneratorConfig::default())?;

Quick Start

1. Install dependencies:

cargo build --workspace

2. Generate parameters:

cargo run --bin generator

This will create:

• Prover.toml: Input validation vectors

Mathematical Background

The workspace implements polynomial arithmetic in rings of the form Z_q[X]/(X^N + 1), where:

• Z_q is the ring of integers modulo a prime q
• X^N + 1 is a cyclotomic polynomial
• Coefficients are centered in [-(q-1)/2, (q-1)/2]

These structures are fundamental to the BFV homomorphic encryption scheme and its zero-knowledge proofs.

License

This project is licensed under the MIT License - see the LICENSE file for details.