Zero-knowledge proof
Cryptographic proof where a prover convinces a verifier that a statement is true without revealing why it's true (e.g. "I know a password" without sending it).
Three properties: completeness (true statements always pass), soundness (false statements have negligible chance), zero-knowledge (verifier learns nothing beyond "true"). Goldwasser, Micali, Rackoff 1985 (Turing Award 2012 for Goldwasser).
Practically realised in zk-SNARKs and zk-STARKs (succinct, non-interactive). Uses: zk-rollups (Polygon, Starknet), private transactions (Zcash), anonymous credentials, password authentication without sending the password.