Zero-Knowledge Proofs

Zero-knowledge proofs (ZKPs) allow one party (prover) to convince another (verifier) of a statement’s truth without revealing any information beyond that truth. They’re a privacy breakthrough in cryptography. This article explains their mechanics, an example, types, and uses.

How They Work

ZKPs have three properties:

• Completeness: Honest prover convinces verifier if true.
• Soundness: Dishonest prover rarely succeeds.
• Zero-Knowledge: Verifier learns nothing else.

Interactive protocols or non-interactive proofs (e.g., zk-SNARKs) achieve this.

Simple Example

“I know a 3-coloring of a graph” (without showing it):

• Prover commits to colors, scrambles them.
• Verifier picks an edge; prover reveals colors (valid if different).
• Repeated rounds convince without revealing the full coloring.

Probability of cheating drops exponentially.

Types (zk-SNARKs, zk-STARKs)

• zk-SNARKs: Succinct, non-interactive, used in Zcash; require trusted setup.
• zk-STARKs: Scalable, transparent, no trusted setup, more computationally intensive.

Both rely on complex math (e.g., elliptic curves).

Applications

ZKPs enable:

• Privacy Coins: Zcash hides transaction details.
• Authentication: Prove identity without revealing it.
• Blockchain: Scalable, private smart contracts (Ethereum).

They’re key to future privacy tech.