Zero-Knowledge Proof
A zero-knowledge proof (ZKP) is a cryptographic protocol where a prover convinces a verifier that a statement is true without disclosing anything beyond the statement's validity. A user can prove they have sufficient funds for a transaction without revealing their balance or history.
Three properties define ZKPs: completeness (an honest prover always convinces the verifier), soundness (a dishonest prover cannot fool the verifier except with negligible probability), and zero-knowledge (the verifier learns nothing beyond the truth of the statement). Modern blockchain constructions add succinctness, meaning the proof is small and fast to verify regardless of computation size. These variants are called zk-SNARKs or zk-STARKs.
On Aleo, zero-knowledge proofs are the mechanism behind private-by-default execution. When a user runs a program function, SnarkVM generates a proof of correct execution given private inputs. The proof goes on-chain for validators to verify, but nobody can extract the private inputs from it. Aleo's proof system is Varuna. Beyond privacy, ZKPs also enable verifiable computation: expensive work done once off-chain, cheaply verified on-chain, reducing validator load.