Zero-knowledge proofs explained: Proving you know a secret without sharing it

Learn how zero-knowledge proofs (ZKP) work at a high level and why they are important for enabling privacy and security in many different applications.

In our daily lives, we often need to prove something about ourselves without revealing private or sensitive information. For example, you may want to prove you’re over 21 to enter a bar without showing your exact birth date or other identification documents. Or prove you have a valid ticket for an event without publicly sharing the ticket number.

Zero-knowledge proofs are a breakthrough in cryptography that allows you to prove these types of statements in a secure way. With zero-knowledge proofs, you can convince someone that you know a secret or that a statement is true, without revealing the secret itself or any other information beyond the bare fact that the statement is true.

How does zero-knowledge proof (ZKP) work?

Zero-knowledge proofs are interactive protocols where one party (the prover) convinces another party (the verifier) that they know some secret information, called the witness. The key innovation is that the verifier learns nothing about this secret witness except that the prover truly knows it.

For example, say you have a secret number X. I want to prove to you that I know X, without revealing X itself. Here is how our interaction might go:

1. I randomly generate a question based on X that only someone who knows X could answer correctly.
2. I send you the question (but not X).
3. You send me back a “challenge” – another question related to X.
4. I use X to respond to your challenge correctly.
5. You verify that my response is correct, proving I have knowledge of X.
6. But you learn nothing about X itself beyond the fact that I know it.

By repeating this type of interaction multiple times, I can convince you beyond any reasonable doubt that I know X, without ever revealing X. That’s the essence of how zero-knowledge proofs work.

The key properties of zero-knowledge proofs

For a protocol to be considered zero-knowledge, it must satisfy three core properties:

1. Completeness – If the statement is true and the prover knows the witness, an honest verifier will be convinced of this fact by the proof.
2. Soundness – If the statement is false, no cheating prover can convince an honest verifier that it is true, except with some extremely small probability.
3. Zero-knowledge – The verifier learns nothing beyond the fact that the statement is true or false.

The first major zero-knowledge protocol, designed in the 1980s, required multiple rounds of interaction between the prover and verifier. But newer proofs require only a single round of communication, making them more efficient. These “non-interactive” proofs work by relying on common reference strings – public parameters that the prover and verifier agree to use.

Different types of zero-knowledge proofs have been developed over the years, including ZK-SNARKs and ZK-STARKs. The core ideas remain the same, but newer protocols have improved efficiency and removed certain assumptions required by earlier proofs.

Why zero-knowledge proofs are important

Zero-knowledge proofs enable many groundbreaking applications that would otherwise be impossible. Here are some examples:

• Anonymous blockchain transactions. Cryptocurrencies like Zcash use zero-knowledge proofs to hide sender, receiver, and transaction details while still allowing the network to validate transactions. This provides strong privacy protection to users.
• Decentralized identity. You can leverage zero-knowledge proofs to authenticate yourself online and validate claims about your identity without revealing actual private details like your social security number.
• Secure multi-party computation. Zero-knowledge proofs enable different entities to jointly compute functions using private data without any one party exposing their data to others. This allows new models of privacy-preserving data analysis.
• True electronic voting. Voting schemes can use zero-knowledge proofs to guarantee that votes were tallied correctly while keeping individual votes private. This prevents vote buying or selling.
• Verifiable outsourced computation. Blockchains can outsource certain types of computation off-chain and accept the results if they come with validity proof. This enables scalability while retaining security.

Zero-knowledge proofs applications: Zk-rollups

One emerging application of zero-knowledge proofs that is quickly growing in popularity is so-called ZK-rollups. ZK-rollups are an off-chain scalability solution similar to the more famous optimistic rollups that leverage zero-knowledge proofs instead.

There are many reasons why zero-knowledge proofs make sense in this field of application:

1. Validation without revealing data – Zero-knowledge proofs allow the validity of transactions to be proven without exposing any of the actual transaction data. This provides privacy and reduces the amount of data that needs to be posted to Ethereum.
2. Succinct proofs – zk proofs are extremely small in size compared to the transactions they represent — which is also possible because they do not have to actually contain all the data they are proving. This compression allows thousands of transactions to be bundled into a proof just a few hundred bytes large. Other encryption methods would produce much larger proof sizes.
3. Easy verification – While generating proofs is computationally expensive, the linear algebra used in zero-knowledge proofs enables their simple and efficient verification. The validity of thousands of transactions can be confirmed with minimal computational resources.
4. Trustlessness – Zero-knowledge proofs are trustless and don’t require participants to hold any secret data. This makes the system highly secure and decentralized compared to alternatives relying on trusted setups.
5. Flexibility – Zero-knowledge proofs are adaptable and can be tailored to validate any type of computation, not just simple payments. This will allow zk-rollups to scale a wide range of decentralized applications in the future.

In summary, zero-knowledge proofs are a breakthrough that allows you to prove the truth of a statement in a way that provides very strong privacy guarantees. As cryptography and software improve, we will continue seeing new applications of this deep concept take hold and empower users.