zk-SNARKs: Succinct Non-Interactive Arguments

A zk-SNARK (Zero-Knowledge Succinct Non-interactive ARgument of Knowledge) is a proof that: (1) is zero-knowledge, (2) is succinct (tiny proof, fast verification regardless of computation size), (3) is non-interactive (single proof string).

Sigma protocols work for simple statements (discrete log knowledge). For complex computations — "I ran this function correctly on private inputs" — we need a general-purpose proof system. SNARKs prove arbitrary computations in O(1) verification time.