Zero-Knowledge Proofs: What Are zk-STARKs and How Do They Work?

What Are zk-STARKs?

zk-STARKs (Zero-Knowledge Scalable Transparent Arguments of Knowledge) are cryptographic proof systems leveraging STARK theory—a sophisticated mathematical framework. Developed with contributions from Ethereum's Vitalik Buterin ("V神"), this technology ensures computational integrity and privacy on blockchain networks. Below, we break down its operational principles without complex math.

How zk-STARKs Work

Step 1: Constraint Setup

To verify a platform’s asset reserves, three core assertions are validated:

1. Balance Accuracy: The sum of all user assets (per crypto and total net value) is correct.
2. Non-Negativity: No "ghost users" with negative balances artificially reduce total reserves.
3. Inclusivity: Every user’s assets are included in the platform’s aggregate holdings.

Constraints Applied:

• Balance Sum: Validate arithmetic correctness via user_trace_size and total_balance.
• Non-Negativity: Ensure no negative balances using finite-field checks.
• Inclusivity: Confirm all users are accounted for.

Example: A 32×5 table logs user IDs and balances. Each 8-row segment aggregates values, with divisibility checks to enforce non-negativity.

Step 2: Low-Degree Polynomial Extension

The constraints generate a polynomial p(x), expanded for security using an extension_factor (default: 16). Sampling checks reduce fraud probability to ≤2⁻⁸⁰.

Key Insight: Valid and fraudulent polynomials diverge beyond D shared points.

Step 3: Polynomial Commitment

A Merkle tree root commits to polynomial values, hashing user balances, IDs, and constraint outputs.

Step 4: Sampling Proofs

Using the Merkle root as a randomness seed, data is sampled (avoiding k*extension_factor indices). Merkle paths prove sample authenticity without exposing raw data.

Step 5: Low-Degree Testing

Linear combinations of constraint polynomials (l(x) = k0*p0(x) + k1*p1(x) + p2(x)) are tested. Passing confirms all p(x) are ≤D degree.

Step 6: Balance Verification

Validate:

1. Low-degree proofs.
2. Sample consistency with commitments.
3. Constraint satisfaction.

Step 7: Inclusivity Proofs

Users receive:

• Their balance, ID, and a random nonce.
• A Merkle path to verify leaf-node inclusion in the root.

Example JSON:

{
  "batch_inclusion_proof": {
    "batch_mtree_root": "34d4e17...",
    "user_id": "47db1d2...",
    "total_value": 138312291,
    "BTC": 2152907,
    "merkle_path": ["5e3dd0a...", ...]
  }
}

Step 8: User Verification

Users hash their data (hash("20" + "15" + "id_k" + "nonce")), then validate the leaf via the Merkle path using open-source tools.

How to Self-Verify Reserve Proofs

2.1 Verify Inclusivity

1. Log in to your exchange account and download the audit JSON.

2. Save the JSON and run the validator tool:

   zk-STARKValidator --inclusion proof.json

3. Output:

   • ✅ Inclusion constraint validation passed
   • ❌ Validation failed (if discrepancies exist).

2.2 Verify Total Balances & Non-Negativity

1. Download the platform’s sum_proof_data folder.

2. Execute:

   zk-STARKValidator --sum-proof sum_proof_data/

3. Output:

   • ✅ Total sum and non-negative constraint validation passed
   • ❌ Validation failed.

FAQs

Q1: Why use zk-STARKs over other ZK proofs?

👉 zk-STARKs offer transparency and scalability without trusted setups, unlike zk-SNARKs.

Q2: How secure is the 80-bit threshold?

With 16 checks at extension_factor=16, fraud probability drops below 1 in a trillion.

Q3: Can I verify without technical skills?

Yes! Use the exchange’s guided tools—no coding required.

Q4: What if my verification fails?

Contact support with your proof data for investigation.

👉 Explore advanced cryptographic techniques to deepen your understanding of blockchain security.