Nullifier Circuit

A Noir circuit implementing a privacy-preserving nullifier scheme using Poseidon hashing.

Overview

This circuit generates deterministic nullifiers from a private secret, allowing anonymous authentication without revealing the underlying secret.

Input	Visibility	Purpose
secret_base	Private	User's secret, never revealed
app_id	Public	Application identifier
scope	Public	Context/action scope
Output	Public	Deterministic nullifier

Prerequisites

Install Nargo (Noir's package manager):

curl -L https://raw.githubusercontent.com/noir-lang/noirup/main/install | bash
noirup

Usage

Check circuit compiles correctly

nargo check

Compile to ACIR

nargo compile

Execute with witness generation

nargo execute

This will output the nullifier value and save the witness to target/nullifier_circuit.gz.

Generate and verify proofs

Noir 1.0 uses external backends for proof generation. Install Barretenberg:

curl -L https://raw.githubusercontent.com/AztecProtocol/aztec-packages/master/barretenberg/cpp/installation/install | bash
source ~/.zshrc  # or restart terminal

# Download v3.0.3 manually (bbup may have issues with newer versions)
curl -L "https://github.com/AztecProtocol/aztec-packages/releases/download/v3.0.3/barretenberg-arm64-darwin.tar.gz" -o /tmp/bb.tar.gz
tar -xzf /tmp/bb.tar.gz -C ~/.bb/

Then generate and verify proofs:

# Generate proof (with --write_vk to also output verification key)
bb prove -b ./target/nullifier_circuit.json -w ./target/nullifier_circuit.gz -o ./target/proof --write_vk

# Verify proof
bb verify -k ./target/proof/vk -p ./target/proof/proof -i ./target/proof/public_inputs

Run tests

nargo test

How It Works

1. Identity Secret Derivation: Combines secret_base and app_id using Poseidon hash

   identity_secret = poseidon_hash(secret_base, app_id)
   

2. Nullifier Derivation: Combines identity_secret and scope using Poseidon hash

   nullifier = poseidon_hash(identity_secret, scope)
   

The nullifier is deterministic (same inputs produce the same output) but reveals nothing about the secret_base, making it useful for:

• Anonymous authentication
• Voting systems (prevent double-voting)
• Token systems (prevent double-spending)

Test Inputs

The Prover.toml file contains example inputs for testing:

secret_base = "12345"
app_id = "1"
scope = "100"

Modify these values to test different scenarios.