Zero-knowledge proofs

In short: A zero-knowledge proof convinces someone that a statement is true without revealing more than exactly that. For example you prove you know a password or are over 18 without disclosing it.

In more detail: The prover and the verifier exchange messages. In the end the verifier is convinced but learns nothing about the secret. Classic picture: the cave with two entrances and a secret door.

In Depth

• Properties: Completeness (true statements are accepted), soundness (false ones are rejected with high probability), zero-knowledge.
• Non-interactive: With the Fiat-Shamir technique a single message suffices (SNARKs, STARKs).
• Use: Privacy in cryptocurrencies, proofs of age or identity, authentication without sending a password, scaling blockchains (rollups).
• zk-SNARK: Short proofs, often trusted setup. zk-STARK: transparent, larger proofs.
• Limits: Computing effort when proving, complex implementation.

See also: Elliptic curves and digital signatures, Post-quantum cryptography