What are Zero-Knowledge Proofs?

As I embark on my journey as part of the PSE Core Program, I'm delving deeper into the fascinating world of Zero-Knowledge Proofs (ZKPs). These cryptographic innovations are transforming the landscape of privacy and security in digital transactions. Through the PSE Core Program, I'm gaining a comprehensive understanding of how ZKPs work, their practical applications, and their potential to revolutionize various aspects of technology and cybersecurity.

I am excited to start sharing my insights and discoveries about ZKPs, exploring their real-world impacts and innovations, and contributing to the ongoing discourse on privacy and security.

So what are they?

In today's digital landscape, privacy and security are paramount. Zero-Knowledge Proofs (ZKPs) are cryptographic methods that enable a Prover to demonstrate to a Verifier that a specific statement is true without revealing any information beyond the validity of the statement itself. This ensures that the Verifier learns nothing about the statement other than the fact that it is true.

Let’s say we have two people, John which will be our “Prover” and Maria which will be our “Verifier”.

John and Maria are friends, and John has a secret code that unlocks a treasure box. Maria wants to be sure that John really knows the code without John telling her what the code is.

• Maria locks the treasure box and hands the locked box to John.

• She asks John to open the box without telling her the code

• John uses the secret code to unlock the treasure box in front of Maria.

Result:

• Maria sees that John successfully opens the treasure box.

• Since John was able to open the box, Maria is convinced that John knows the correct code without John having to tell her what the code is.

Important: ZKPs must follow three properties.

Key Properties of ZKPs

• Soundness: The proof is truthful, so that when it proves it is true.

• Completeness: It must be comprenhensive so it can prove all the true statements.

• Zero-Knowledge: The verifier mustn’t know any information aside from the true statement.

Why are ZKPs Important?

Privacy: Enhance the privacy of transactions and data.

Security: Increase the security of authentication and verification processes.

Scalability: Improve the scalability of blockchain systems.

Some Practical Applications

Privacy-Preserving Transactions

• Zcash: A cryptocurrency that uses zk-SNARKs to provide privacy-preserving transactions.

Identity Verification

• zkID: Zero-Knowledge Identity verification solutions.

Now let’s follow up with some classifications for ZKPs.

Interactive Zero-Knowledge Proofs (iZKPs)

Definition: An Interactive Zero-Knowledge Proof involves a back-and-forth communication between the Prover and the Verifier. The Prover performs multiple steps, responding to challenges from the Verifier, to prove that they know a secret without revealing the secret itself.

Example:

1. Scenario: John has a secret code to unlock a treasure box, and Maria wants to verify that John knows the code without him revealing it.

2. Interaction:

   • Maria locks the treasure box and gives the locked box to John.

   • She asks John to open the box, and John successfully unlocks it using the secret code.

   • To ensure John truly knows the code, Maria repeats the process several times, each time with a different challenge (like locking the box again).

3. Result: Each time John successfully opens the box, Maria becomes more convinced that John knows the secret code without him ever revealing it.

Non-Interactive Zero-Knowledge Proofs (niZKPs)

Definition: A Non-Interactive Zero-Knowledge Proof requires no back-and-forth communication between the Prover and the Verifier. The Prover generates a single proof that can be verified by the Verifier at any time, without needing any interaction.

Example:

1. Scenario: John has a secret code to unlock a treasure box, and Maria wants to verify that John knows the code without him revealing it.

2. Interaction:

   • John writes down a detailed, sealed proof that he knows the secret code (ex. a photo of the unlocked box with a timestamp) and gives this sealed proof to Maria.

   • Maria can open the sealed proof at any time and verify its validity.

3. Result: Maria can be convinced that John knows the secret code by verifying the proof, without needing to interact with John again.

zk-SNARKs (Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge)

Definition: zk-SNARKs are a specific type of non-interactive zero-knowledge proof that is efficient in terms of proof size and verification time.

Applications: Widely used in blockchain technologies, particularly in privacy-focused cryptocurrencies like Zcash.

zk-STARKs (Zero-Knowledge Scalable Transparent Arguments of Knowledge)

Definition: zk-STARKs are another type of non-interactive zero-knowledge proof that provides greater scalability and transparency compared to zk-SNARKs, avoiding the need for a trusted setup.

Applications: Emerging in blockchain and other cryptographic applications requiring high scalability and transparency.

Conclusion

Zero-Knowledge Proofs represent a significant advancement in cryptographic methods, offering enhanced privacy, security, and scalability. From privacy-preserving transactions in cryptocurrencies to secure identity verification solutions, ZKPs are poised to play a crucial role in the future of digital interactions.

By understanding and leveraging ZKPs, we can ensure more secure and private transactions, paving the way for a safer digital world.