Application of Zero-Knowledge Proofs in Financial Transaction Privacy Protection

Topic Description
Zero-Knowledge Proof (ZKP) is a cryptographic protocol that allows a prover to convince a verifier of the truth of a statement without revealing any additional information. In the field of financial technology, ZKP can be used to protect transaction privacy, achieve regulatory compliance, and enable data verification. For example, banks can use ZKP to prove a client's sufficient assets without disclosing the specific amount, or in blockchain, to hide transaction details while verifying legitimacy. This topic requires an in-depth understanding of the basic principles of ZKP, typical implementations (such as zk-SNARKs), and the specific application logic in financial scenarios.

Background Knowledge

1. Core Properties of Zero-Knowledge Proofs:

   • Completeness: If the statement is true, an honest verifier will be convinced.
   • Soundness: If the statement is false, the prover cannot deceive the verifier.
   • Zero-Knowledge: The verifier learns only the truthfulness of the statement and cannot obtain any other information.

2. Financial Scenario Requirements:

   • Transaction privacy (e.g., hiding transfer amounts, account balances).
   • Compliance verification (e.g., proving transaction legality in anti-money laundering checks without leaking user data).

Problem-Solving Process and Principle Analysis

Step 1: Understanding Interactive Zero-Knowledge Proofs (Using the "Ali Baba's Cave" Example)

• Scenario Setup: The prover P claims to know the secret password to the cave's back door (two caves A and B are connected, but only P knows the secret passage switch). The verifier V waits at the cave entrance and asks P to randomly enter from either A or B.
• Process:
  1. V turns his back to the cave, and P randomly chooses an entrance to enter.
  2. V turns around and asks P to exit from a specified exit (e.g., cave A).
  3. If P truly knows the password, he can always exit from the requested exit; if not, he only has a 50% chance of success.
  4. After repeating this multiple times, if P succeeds each time, V believes P knows the password, but V does not learn the password itself.
• Financial Analogy: A bank can prove to a regulatory agency that "client assets > threshold" through multiple random challenge verifications without revealing the specific asset value.

Step 2: Non-Interactive Zero-Knowledge Proofs (e.g., zk-SNARKs)

• Problem: Interactive proofs require real-time participation from both parties, which is inefficient. Financial systems require asynchronous verification (e.g., blockchain transactions).
• zk-SNARK Solution:
  1. Arithmetic Circuit Transformation: Convert the statement to be proven (e.g., "transaction amount ≥ 0") into a mathematical circuit.
     • Example: Proving that a transfer amount x satisfies 0 ≤ x ≤ balance. The circuit includes logic gates such as comparators and adders.
  2. Polynomial Conversion: Transform the circuit into polynomials, using "polynomial blind verification" to hide data.
     • Key technique: If a polynomial evaluates to zero at a random point, it proves that the circuit constraints are satisfied.
  3. Trusted Setup: Generate a proving key (PK) and a verification key (VK), requiring an initial trusted ceremony (e.g., multi-party computation to avoid single-point cheating).
  4. Proof Generation: The prover uses PK and private data (e.g., amount x) to generate a concise proof π.
  5. Verification: The verifier uses VK and π to quickly verify the proof without recalculating.

Step 3: Financial Application Example — Privacy-Preserving Transfers (Using Zcash as an Example)

• Goal: Hide the addresses and amounts of transacting parties while proving transaction legality (e.g., no overspending).
• Process:
  1. Commitment Scheme: The sender encrypts the amount v into a commitment C = v*G + r*H (where G and H are elliptic curve points, r is a random number), hiding v but allowing public verification.
  2. Range Proof: Use zk-SNARK to prove v ≥ 0 and v ≤ upper limit, preventing negative amount attacks.
  3. Balance Verification: Prove that the total input amount ≥ total output amount, and the difference is the transaction fee (without revealing specific values).
     • Key equation: C_in1 + C_in2 - C_out1 - C_out2 = fee*G, verified via zero-knowledge proof.
  4. Regulatory Interface: Authorized parties can decrypt transaction data using a special key to meet compliance requirements.

Step 4: Challenges and Optimizations

• Computational Overhead: zk-SNARK proof generation is slow (requires specialized hardware), but verification is fast (suitable for batch processing).
• Trusted Setup Risks: Newer solutions (e.g., zk-STARKs) eliminate the need for a trusted setup but produce larger proofs.
• Regulatory Balance: Selective disclosure mechanisms (e.g., in central bank digital currencies, users reveal specific data only to regulators).

Summary
Zero-Knowledge Proofs balance privacy and verification needs through mathematical protocols, facilitating scenarios such as private transfers, compliance audits, and credit verification in financial technology. Mastering the technical evolution from interactive to non-interactive proofs, as well as the circuit construction and verification logic of specific algorithms (e.g., zk-SNARKs), is key to understanding their financial applications.