Zero-knowledge proofs, explained

What is a zero-knowledge proof?

A zero-knowledge (ZK) proof is a cryptographic protocol that enables one person (the prover) to convince another (the verifier) that a particular claim is true without disclosing any details about the claim itself. 

Researchers Shafi Goldwasser, Silvio Micali and Charles Rackoff presented the idea for the first time in the early 1980s. The main goal of a ZK-proof is to persuade the verifier that a claim is true without revealing any information other than the claim’s veracity. 

A good zero-knowledge proof should fulfill the following three criteria:

• Completeness: The verifier will accept the proof with a high probability if the proposition is true, and both the prover and the verifier adhere to the protocol.
• Soundness: If the claim is untrue, no prover should be able to persuade the verifier of the opposite, save under extremely unlikely circumstances.
• Zero-knowledge: Even after engaging with the prover, the verifier only understands the truth of the statement and nothing else about the secret.

There are different types of ZK-proofs:

Interactive ZK-proofs

Interactive zero-knowledge proofs require back-and-forth communication between the prover and verifier.

Non-interactive ZK-proofs

Non-interactive zero-knowledge proofs provide a compact proof that can be verified in a single step.

Statistical ZK-proofs

Statistical zero-knowledge proofs offer computational soundness with a small probability of error. 

Proof-of-knowledge (PoK)

PoK is a subclass of ZK-proofs that shows that the prover possesses specific knowledge related to the statement.

Proofs of shuffle and range

These ZK-proofs are used in electronic voting and privacy-preserving transactions.

Sigma protocols

Sigma protocols are a class of ZK-proofs that involve three steps: commitment, challenge and response.

Bulletproofs

Bulletproofs are designed to provide efficient range proofs for large sets of values.

2.

How do zero-knowledge proofs work?

ZK-proofs allow a prover to persuade a verifier of a statement’s veracity without disclosing any information about the assertion itself. The prover and verifier interact in multiple rounds of the protocol, and in the conclusion, the verifier develops confidence in the veracity of the claim without learning any additional information about the secret.

Let’s use the “Three Color Problem,” also known as the “Graph Coloring Problem,” as an illustration of how ZK-proofs function.

The problem

Imagine that you have a map with multiple areas (vertices) connected by lines (edges), and this is the issue. The goal is to use one of three colors to color each region so that no two neighboring parts have the same color. Can you persuade someone that you are aware of the correct coloring without exposing the actual hues given to each region?

Solution using the ZK-proofs protocol

Setup

The prover and the verifier both agree on the regions and links of the graph (map).

Statement

The prover asserts to have a reliable three-coloring for the provided graph.

Round 1: Commitment

The prover chooses colors at random for each location in secret without disclosing them. Instead, the prover provides the verifier with one encrypted promise for each region. The verifier cannot see what colors are inside the commitments because they are locked like boxes.

Round 2: Challenge 

The verifier chooses a random region and requests that the prover open the commitment for that particular zone. The prover must disclose the hue of that area’s commitment.

Round 3: Response

After committing to the colors, the prover must now prove that the revealed coloring is accurate. This entails displaying the color differences between adjacent sections. The verifier examines the response to ensure that the prover correctly followed the rules.

Iteration

Rounds 2 and 3 are repeated numerous times using various regions that are chosen at random. This procedure is repeated as many times as necessary to establish a high degree of trust in the veracity of the prover’s assertion.

Conclusion

The verifier becomes confident that the prover actually has a valid three-coloring without knowing the actual colors used if the prover regularly produces valid responses for each round.

The verifier gradually increases the prover’s capacity to recognize a valid three-coloring of the graph by repeating the procedure for various regions. However, the zero-knowledge property is maintained since the verifier never discovers the real colors assigned to each region during the procedure.

The above illustration shows how ZK-proofs can be used to persuade someone that a solution exists while keeping the solution’s identity a secret, offering a potent tool for boosting privacy and security in a variety of applications.

3.

What are the applications of zero-knowledge proofs?

ZK-proofs are useful tools that have many uses in a variety of fields and address important privacy and security issues.

ZK-proofs are crucial in the world of cryptocurrencies for improving transaction privacy and scalability. They allow for anonymous transactions without disclosing the particulars of the transaction or the identity of the users, as is the case with privacy-focused cryptocurrencies, such as Zcash (ZEC).

ZK-proofs can be used in the authentication and access control fields to demonstrate an understanding of a password or a cryptographic key without revealing the password or key itself. This results in better user-friendly and secure authentication techniques.

ZK-proofs are also used in electronic voting systems, where they allow voters to demonstrate the legitimacy of their vote without disclosing the actual vote, protecting both voter privacy and the integrity of the electoral process.

ZK-proofs also have implications for secure data transfer and verification, giving one side the ability to demonstrate the accuracy of computations on private data without disclosing the data itself.

Zero-knowledge proofs can improve transaction privacy in central bank digital currencies (CBDCs) by facilitating private transactions and upholding user anonymity. By balancing privacy and transparency in CBDC transactions, ZK-proofs enable auditability without disclosing transaction specifics.

4.

Can ZK-proofs be integrated into blockchain platforms?

Yes, ZK-proofs can be integrated into blockchain platforms, and in fact, they have been successfully implemented in various blockchain networks. ZK-proofs provide a potent technique for boosting efficiency, security and privacy in blockchain systems.

When integrated into blockchain platforms, ZK-proofs can serve multiple purposes:

Privacy and confidentiality

ZK-proofs allow for private transactions, letting users perform transactions without disclosing the underlying information, such as the transaction amount and sender and receiver addresses. The improvement of user privacy on open blockchains depends on this.

Verification and auditing

Without disclosing the real data or information, ZK-proofs can be used to check the accuracy of specific computations or statements. This guarantees data integrity and makes effective auditing procedures possible.

Scalability

ZK-proofs can increase the scalability of the platform by offering concise proofs for complex computations, which can help minimize the computational and storage overhead on the blockchain.

Identity and authentication

By using ZK-proofs for safe identity verification and authentication while protecting user privacy, blockchain-based applications will be securer.

Cross-chain interoperability

ZK-proofs can help with cross-chain communication and asset transfers while protecting privacy by facilitating interoperability among various blockchain networks.

5.

What are the disadvantages of zero-knowledge proofs?

ZK-proofs provide privacy and security benefits, but they can be computationally intensive and complex to implement. 

Developing and verifying ZK-proofs can be resource- and computationally intensive, particularly for more complicated proofs. This can result in longer processing times for transactions and more computational work, which might make blockchain systems more difficult to scale.

Furthermore, ZK-proofs might add a layer of complexity that might make the protocol more difficult to audit and verify, sparking worries about potential security flaws or bugs. Furthermore, while ZK-proofs improve privacy by hiding information, they may also facilitate illegal activity in some situations, creating difficulties for regulatory compliance.

ZK-proofs might also not be appropriate for all use cases or sectors because they require particular training and experience to implement properly. This might prevent them from being widely used and adopted across many fields. 

Although ZK-proofs provide useful privacy and security features, their drawbacks necessitate careful study and evaluation of the associated trade-offs prior to their adoption into particular systems or applications