In the world of cryptography, zero-knowledge proofs (ZKPs) have emerged as a powerful tool. This article aims to provide a beginner-friendly introduction to the concept of zero-knowledge proofs, how they work, and their applications.

## Cryptography

Before we jump in, let’s briefly talk about cryptography. Cryptography is the science of securing information by transforming it into a form that only intended recipients can process and read. It has been around for years and has evolved for use in many applications, including modern blockchain technology. Cryptography puts the “crypto” in cryptocurrency.

## Understanding Zero-Knowledge Proofs

Zero-knowledge proofs are cryptographic protocols that enable one party (the prover) to convince another party (the verifier) that a particular statement is true (i.e., I am a citizen of X country) without revealing any details about the statement itself (i.e., A social security or passport number). The crucial aspect of a zero-knowledge proofs is that it doesn’t disclose any additional information apart from the statement’s validity. Generally speaking, there are two types of zero-knowledge proofs, interactive and non-interactive.

#### Interactive ZKPs

Interactive ZKPs require multiple exchanges between the prover and verifier to verify that the statement at hand is true. An excellent explanation of interactive ZKPs comes from Jean-Jacques Quisquater’s famous Ali Baba Cave story, published in his paper How to Explain Zero-Knowledge Protocols to Your Children:

In this story, Peggy (the prover) has uncovered the secret word used to open a magic door in a cave. The cave is shaped like a ring, with the entrance on one side and the magic door blocking the opposite side. Victor (the verifier) wants to know whether Peggy knows the secret word; but Peggy, being a very private person, does not want to reveal her knowledge (the secret word) to Victor or to reveal the fact of her knowledge to the world in general.
They label the left and right paths from the entrance A and B. First, Victor waits outside the cave as Peggy goes in. Peggy takes either path A or B; Victor is not allowed to see which path she takes. Then, Victor enters the cave and shouts the name of the path he wants her to use to return, either A or B, chosen at random. Providing she really does know the magic word, this is easy: she opens the door, if necessary, and returns along the desired path.
If they were to repeat this trick many times, say 20 times in a row, her chance of successfully anticipating all of Victor’s requests would be reduced to 1 in 220, or 9.56 × 10−7. Thus, if Peggy repeatedly appears at the exit Victor names, he can conclude that it is extremely probable that Peggy does, in fact, know the secret word.

#### Non-interactive ZKPs

A drawback of interactive ZKPs is that the prover and verifier must be available for multiple exchanges, and only the single verifier present can attest to the validity-proven statement. Non-interactive zero-knowledge proofs were designed to overcome this flaw. This new iteration requires a single round of communication to confirm validity, vastly increasing efficiency. The prover and verifier share a key; only the holders can participate in the process. Then, the prover passes the secret information to a special algorithm to compute a zero-knowledge proof. This proof is sent to the verifier, who checks that the prover knows the secret information using another algorithm. Another benefit is that anyone with access to the shared key and verification algorithm can verify the statement’s validity, meaning it can be revisited or reverified in the future as needed.

## Key Components of Non-Interactive Zero-Knowledge Proofs

1. Statement: A statement is the assertion the prover wants to prove to the verifier. For example, it could be knowing a password or possessing a particular piece of information.

2. Proof: The prover generates proof that attests to the truthfulness of the statement without revealing any underlying information. This proof is usually based on complex mathematical computations and cryptographic techniques.

3. Verification: The verifier examines the proof provided. Using the protocol associated with the zero-knowledge proof, the verifier can verify the proof’s correctness without gaining any knowledge beyond the statement’s validity.

## Applications of Zero-Knowledge Proofs

Zero-knowledge proofs have found applications in various domains, including:

1. Authentication and Digital Identification: Zero-knowledge proofs can authenticate users without revealing their passwords or sensitive information. For example, a user can prove to a system that they possess a valid password without disclosing the actual password or prove they are a specific person without revealing specific identifying information.

2. Privacy-Preserving Transactions: In blockchain technology, zero-knowledge proofs can be employed to ensure the validity of transactions without disclosing the transaction details or sender/receiver information. This enhances privacy while maintaining the integrity of the transaction.

3. Secure Data Sharing: Zero-knowledge proofs enable secure data sharing between parties. A party can prove possession of certain data without revealing the data itself, ensuring confidentiality.

4. Password Recovery: Zero-knowledge proofs can be used to recover a lost password or access an account without revealing the password to a third party. The prover can demonstrate knowledge of the password without disclosing the actual password.

While the underlying mathematics and cryptographic techniques can be complex, understanding the fundamental idea of zero-knowledge proofs is a great starting point for exploring some of the latest technological advancements in web3, including ways to own and verify your digital identity.

Stay tuned for next week’s article, where we will dive into Decentralized Identity!

Resources

https://www.coindesk.com/learn/what-is-cryptography/

https://ethereum.org/en/zero-knowledge-proofs/

https://pages.cs.wisc.edu/~mkowalcz/628.pdf

https://en.wikipedia.org/wiki/Zero-knowledge_proof#cite_note-6

https://medium.com/edureka/what-is-cryptography-c94dae2d5974

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