BN254 Accumulator

This Rust crate provides a simple cryptographic accumulator based on the BN254 pairing-friendly elliptic curve, using the arkworks ecosystem. The accumulator supports membership proofs, which can be verified on-chain using Ethereum's pairing precompile.

✨ Features

• Deterministic hashing of arbitrary data to Fr scalars using keccak256
• Accumulation of elements using exponentiation in G1
• Generation of membership witnesses
• Verification of membership via bilinear pairing
• On-chain verifiability with Ethereum precompiles

🔍 Background

The accumulator stores a product of hashed inputs as a G1 group element:

A = g1^{x1 * x2 * ... * xn}

To prove membership of xi, a witness is computed:

witness = g1^{product of all xj where j ≠ i}

Verification is done via:

e(witness^xi, g2) == e(A, g2)

🚀 Usage

let mut acc = Bn254Accumulator::new();

let member = b"hello world";
let x = acc.add_member(member);

let witness = acc.membership_witness(x).unwrap();
let is_valid = acc.verify_membership(x, witness);
println!("Proof valid: {}", is_valid);

🧪 Tests

Two basic tests are included:

• test_membership_proof: Ensures all added members generate valid proofs
• test_non_member_should_fail: Ensures a non-member fails proof generation

🔐 On-chain Integration

Use Ethereum's pairing precompile at address 0x08 to verify proofs. Convert the accumulator value (G1Projective) to affine coordinates and pass the x, y components to Solidity as uint256[2].

Example Solidity representation:

struct G1Point {
    uint256 x;
    uint256 y;
}

📦 Dependencies

• arkworks ecosystem: ark-ec, ark-ff, ark-bn254
• tiny-keccak: For keccak256 hashing

📁 File Structure

• Bn254Accumulator: Core logic for accumulation, witness generation, and verification
• main(): Simple usage example
• #[cfg(test)]: Test suite for validation

⚠️ Security Note

This accumulator relies on a trusted setup of group generators. For production use, ensure generators are either fixed from a secure source (e.g., Ethereum alt-BN254 spec) or auditable.

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Made with ❤️ using zk-friendly curves.