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What Is a Zero-Knowledge Proof?

Succinct

Succinct

— 2 min read

Zero-knowledge proofs (ZKPs) are one of the most important breakthroughs in modern cryptography. They’re changing how blockchains scale, how users protect their privacy, and how applications verify compute. But the concept can feel abstract or complicated if you’re seeing it for the first time.

✅ TL;DR

A zero-knowledge proof (ZKP) lets someone prove a statement is true without revealing any of the underlying information used to prove it.

It’s:

  • a cryptographic proof,
  • small and verifiable,
  • and requires no trust.
Example: Prove you’re over 21 without showing your birthday.

Here's a magician's guide to zero-knowledge proof from a16z to explain.

1. What Problem Do Zero-Knowledge Proofs Solve?

Today, proving something usually requires revealing private information.

  • To prove your age → you show your ID.
  • To prove your bank balance → you share statements.
  • To prove a computation happened correctly → you share the inputs and outputs.

This creates friction, privacy leaks, and trust assumptions.

Zero-knowledge proofs remove the need to reveal any sensitive data at all.

They allow a prover to convince a verifier:

"I know this is true - and you don’t need to see how."

2. What Exactly Is a Zero-Knowledge Proof?

Formally, a ZKP has two roles:

  • Prover computes and creates a proof.
  • Verifier checks the proof.

A ZKP must satisfy three core properties:

✅ Completeness

If the statement is true, the proof will verify.

✅ Soundness

If the statement is false, the prover cannot cheat.

✅ Zero-Knowledge

The verifier learns nothing about the underlying data.

These properties allow ZKPs to be used for privacy, security, and computation verification.

3. How Does a Zero-Knowledge Proof Work?

Here’s the simplest way to think about it:

A prover transforms:

  • their private information
  • plus a claim

into a mathematical proof.

This proof is a small cryptographic object - often just a few hundred bytes - that a verifier can check extremely quickly.

The verifier doesn’t learn:

  • the private data
  • how the computation was done
  • intermediate values
  • anything beyond the truth of the statement

This is why ZKPs are so powerful.

4. Types of Zero-Knowledge Proofs

There are multiple ZKP constructions: each optimized for different use cases.

✅ SNARKs (Succinct Non-Interactive Arguments of Knowledge)

  • Very small proofs
  • Fast verification
  • Require a trusted setup (sometimes)
  • Used by many zkVMs, rollups, and L1s

✅ STARKs (Scalable Transparent Arguments of Knowledge)

  • No trusted setup
  • Post-quantum secure
  • Larger proofs
  • Very scalable

✅ Bulletproofs

  • Used in privacy-preserving cryptocurrencies
  • No trusted setup
  • Slower to verify

✅ zkVM-based proofs (e.g., SP1)

  • General-purpose proving
  • Verify arbitrary programs
  • Fast-growing segment of the ZK ecosystem

Succinct’s zkVM SP1 uses a combination of modern ZK techniques to generate proofs efficiently across many applications.

5. Where Are Zero-Knowledge Proofs Used?

ZKPs enable real systems used today across blockchain, identity, and compute.

✅ Scaling blockchains (ZK rollups)

ZK rollups prove all execution off-chain and submit a succinct proof on-chain. This is what makes rollups fast, cheap, and secure.

✅ Privacy-preserving applications

Examples:

  • Prove your age without sharing your birthday
  • Hide account balances
  • Private on-chain transactions

✅ Verifiable compute

Prove a computation was done correctly without revealing inputs. This is the foundation for:

  • decentralized prover networks
  • off-chain compute markets
  • transparent machine learning verification

✅ Identity & authentication

Zero-knowledge credentials are becoming a major alternative to Web2-style data sharing.

✅ Conclusion

Zero-knowledge proofs let us prove the correctness of data, computations, and statements without revealing any private information. They’re the foundation for scalable, privacy-preserving, verifiable systems — and they’re core to what we’re building at Succinct.

As ZKPs power more rollups, identity protocols, prover networks, and general-purpose zkVMs, they’re quickly becoming one of the most important tools in modern cryptography.

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