ZK Age Verifier: Conditionals in Finite Fields

Goal: Prove I am older than 18 without revealing my actual age.

This repository documents my progression from simple Arithmetic Circuits to Logic Circuits. While my previous project (Multiplier) handled basic math, this project tackles the challenge of Comparisons (>, <) inside a Zero-Knowledge Proof.

🧠 The Core Problem: "The Clock"

In Python, writing if age >= 18 is trivial. In ZK-SNARKs, it is surprisingly difficult because we work over Finite Fields.

Think of a Finite Field like a clock:

• On a standard number line, 20 is clearly greater than 18.
• On a 12-hour clock, if you add 3 hours to 11, you get 2.
• The Ambiguity: Is 2 "greater" than 11? Or did it just wrap around?

Because of this wrap-around property, a direct algebraic comparison is dangerous. A hacker could input a massive number that wraps around to a small one, tricking the circuit.

The Solution: Binary Comparators

To compare numbers safely in ZK, we cannot treat them as abstract field elements. We must:

1. Convert the number into Binary Bits (0s and 1s).
2. Compare the bits explicitly.
3. Limit the number of bits (e.g., 8 bits) to ensure the number never gets big enough to wrap around.

🛠️ Implementation Details

1. Using CircomLib

Instead of writing the bit-wise logic from scratch, I used CircomLib, the standard library for Circom.

• Template: GreaterEqThan(n)
• Bit Limit (n): I selected 8 bits. This supports numbers up to 255, which is plenty for an age check and safe from overflow.

2. Public vs. Private Inputs

This circuit introduces the distinction between public and private data availability:

• Private Input (age): The user's secret (e.g., 25). This is never revealed.
• Public Input (limit): The threshold (e.g., 18). This is revealed in public.json so the Verifier knows what rule was checked.

Code Snippet:

// We explicitly tag 'limit' as public. 'age' remains private by default.
component main {public [limit]} = AgeVerifier();

📂 Project Structure

• age.circom: The circuit logic.
• input.json: The inputs used for the demo. (Note: In a real production app, this would be git-ignored).
• build/: Contains the compiled machine code (.wasm) and cryptographic keys (.zkey).
• outputs/: Contains the proof artifacts generated during execution (proof.json, witness.wtns).

🚀 Quick Start

1. Install Dependencies

npm install

2. Generate the Proof

I have pre-compiled the circuit and keys in the build/ folder. You can run the proof generation immediately.

# 1. Calculate Witness (Inputs -> Calculation)
node build/age_js/generate_witness.js build/age_js/age.wasm input.json outputs/witness.wtns

# 2. Generate Proof (Witness + Key -> Proof)
snarkjs groth16 prove build/age_final.zkey outputs/witness.wtns outputs/proof.json outputs/public.json

# 3. Verify (Proof + Public Limit -> Result)
snarkjs groth16 verify build/verification_key.json outputs/public.json outputs/proof.json

3. Check the Output

Open outputs/public.json.

["1", "18"]

• 1 = True (The age is >= limit).
• 18 = The limit used.
• Note: The actual age (25) is nowhere to be found. Privacy preserved.

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Built with Circom & SnarkJS