AN OVERVIEW OF ZERO-KNOWLEDGE PROOFS

INTRODUCTION

A zero-knowledge proof (ZKP) is a cryptographic method that allows someone to prove a statement is true without revealing the details that make it true. It enables one party (the prover) to convince another party (the verifier) of a statement’s validity without sharing any additional information. For example, a person can prove they are over 21 without revealing their birthdate. Zero-knowledge proofs enhance privacy by allowing verification without disclosure of underlying knowledge.

Zero-Knowledge Proof Example

Imagine you have a friend who is blind and owns two balls—one red and one blue. You can see colors, but your friend cannot. They want to prove to you that the balls are different colors without revealing which ball is which.

Here’s how a zero-knowledge proof would work in this scenario:

Your friend holds both balls behind their back.

They show you both balls.

They put them behind their back again and may or may not swap them.

They show you the balls again.

You tell them whether or not they swapped the balls.

If the balls were the same color, you wouldn’t be able to tell if they were swapped. But since you can always tell, your friend becomes convinced that the balls are indeed different colors. By repeating this process multiple times, they gain confidence that you can distinguish between the balls—without ever learning which ball is which color.

At first, the idea of zero-knowledge proofs might seem paradoxical: how can I prove I know something without revealing it? However, we use zero-knowledge protocols more often than we realize.

For example, digital signatures are a form of zero-knowledge proof. When I sign a message, I prove that I know the private key corresponding to a widely known public key—without revealing the private key itself. In fact, public-key encryption relies on this concept. If digital signatures leaked information about the private key, attackers could reverse-engineer it and impersonate you.

How Do Zero-Knowledge Proofs Work

Zero-knowledge proofs (ZKPs) allow one party (the prover) to convince another party (the verifier) that a statement is true—without revealing any additional information.

At a high level, ZKPs work by having the verifier ask the prover to perform a series of actions that can only be completed correctly if the prover truly knows the underlying information. If the prover is guessing, they will eventually fail the verifier’s tests with a high probability.

ZKPs can be classified into two types:

Interactive ZKPs: The prover engages with a specific verifier, repeating the process for each verifier individually.

Non-Interactive ZKPs: The prover generates a proof that can be verified by anyone without further interaction.

ZKPs must satisfy three fundamental properties:

Completeness: If the statement is true, an honest verifier will be convinced by an honest prover.

Soundness: If the statement is false, a dishonest prover cannot trick an honest verifier into believing it is true.

Zero-Knowledge: If the statement is true, the verifier gains no additional information beyond knowing the statement is true.

Types of Zero-Knowledge Proofs

Zero-Knowledge Proofs (ZKPs) come in different types, each with trade-offs in proof size, computation time, and verification speed. The main types include:

zk-SNARKs

SNARK stands for “Succinct Non-Interactive Argument of Knowledge.” These proofs are small in size and easy to verify. They use elliptic curve cryptography, making them more gas-efficient than zk-STARKs, which rely on hashing.

zk-STARKs

STARK stands for “Scalable Transparent Argument of Knowledge.” These proofs require minimal interaction between the prover and verifier, making them faster than SNARKs. They also don’t rely on a trusted setup, increasing security.

Bulletproofs

Bulletproofs are short, non-interactive zero-knowledge proofs that do not require a trusted setup. They are mainly used in cryptocurrencies to enable private transactions while keeping proofs compact.

Comparison of the most popular zkp systems

Zero-Knowledge Proof Use Cases

• Confidential Blockchain Transactions

Blockchains like Zcash use ZKPs to enable privacy-preserving transactions, keeping the transaction amount, sender, and receiver addresses confidential.

• Trustless Data Verification

Decentralized oracle networks rely on ZKPs to verify facts about off-chain data without exposing the actual data on-chain. This enhances trust while maintaining privacy.

• Scalable and Secure Blockchain Layers

Technologies like zk-Rollups, Validiums, etc use ZKPs to create fast, scalable, and secure layer 2 networks. These solutions settle transactions on Ethereum or other layer 1 blockchains, improving efficiency for dApps and users.

Applications of Zero Knowledge proof:

Blockchain – 

• ZK Sync by Matter Labs: “A Layer 2 protocol that achieves scalability through clever compression of transactions using zero-knowledge proofs, fundamentally reimagining how we approach blockchain throughput”
• ZK SDK: “A developer toolkit that abstracts away the complexity of zero-knowledge cryptography, democratizing the ability to build privacy-preserving applications”

Non Blockchain – 

• Zero-Knowledge Machine Learning: “An intersection of privacy and AI that allows models to prove their outputs without revealing their training data, a breakthrough for sensitive applications”
• Proof of Passport: “A privacy-preserving way to prove citizenship or identity attributes without exposing the underlying document data”
• Semaphore: “Semaphore is a generic privacy layer. Leveraging zero-knowledge technology, users can prove their membership in groups and send messages off-chain or across EVM-compatible blockchains, all without revealing their personal identity.”