prove_threshold_policy

This Noir project implements a zero-knowledge circuit that proves whether a secret input x (called secret_share) satisfies a fixed policy:

recovery_score = 2 * secret_share + public_offset == 17

The circuit ensures that a prover can demonstrate compliance with the threshold without revealing the private value secret_share.

📦 Circuit Logic

fn main(secret_share: Field, public_offset: pub Field) {
    let recovery_score = secret_share * 2 + public_offset;
    let recovery_threshold = 17;
    assert(recovery_score == recovery_threshold);

This Noir circuit checks whether the prover satisfies a publicly verifiable threshold policy without revealing their secret value:

 recovery_score = 2 * secret_share + public_offset == 17

It allows the prover to demonstrate compliance with a predefined access or eligibility policy while keeping their secret (secret_share) private.

This is not just a proof of knowledge of a secret—it is a threshold policy compliance proof: The prover must demonstrate that their secret, combined with a public offset, satisfies a specific linear constraint without revealing the secret itself.

Such constructions are essential for enabling:

• 🔐 Social recovery in wallets
• 🎓 Anonymous eligibility checks
• 🛡️ Zero-knowledge access control
• ✅ Proving policy compliance without exposing sensitive data

Project Structure

An example repo to verify Noir circuits (with bb backend) using a Solidity verifier.

• /circuits - contains the Noir circuits.
• /contract - Foundry project with a Solidity verifier and a Test contract that reads proof from a file and verifies it.
• /js - JS code to generate proof and save as a file.

Tested with Noir 1.0.0-beta.6 and bb 0.84.0

Circuit Logic

The Noir circuit checks if x * 2 + y == expected, where:

• x is a private input
• y and expected are public inputs

Installation / Setup

# Foundry
git submodule update

# Build circuits, generate verifier contract
(cd circuits && ./build.sh)

# Install JS dependencies
(cd js && yarn)

zk Proof generation in JS

# Use bb.js to generate proof and save to a file
(cd js && yarn generate-proof)

# Run foundry test to read generated proof and verify
(cd contract && forge test --optimize --optimizer-runs 5000 --gas-report -vvv)

zkProof generation with bb cli

cd circuits

# Generate witness
nargo execute

# Generate proof
bb prove -b ./target/prove_threshold_policy.json -w target/prove_threshold_policy.gz -o ./target --oracle_hash keccak

# Run foundry test to read generated proof and verify
cd ..
(cd contract && forge test --optimize --optimizer-runs 5000 --gas-report -vvv)

🔁 Dual Workflow Support (CLI and JS)

The project supports two approaches for generating proofs:

• JavaScript-based workflow using bb.js
• CLI-based workflow using nargo and bb directly

🛠 Building the Solidity Verifier

Use the build.sh script to compile the circuit and generate the Solidity verifier:

./build.sh

This will:

• Compile the Noir circuit
• Generate the verification key (vk)
• Export the Solidity verifier to contract/Verifier.sol