ZK-SNARKs are a zero-knowledge (ZK) proof technology used for succinct proofs and verifications. However, this technology comes with several limitations. ZK-STARK (T standing for "transparent") is a newer zero-knowledge proof technology that helps resolve the primary weaknesses of ZK-SNARKs.
ZK-STARKs utilize simpler cryptographic assumptions and avoid: 1. Reliance on a "trusted setup" 2. The uses of elliptic curves and pairings 3. The knowledge-of-exponent assumptions ZK-STARKs only rely on hashes and information theory. Which keeps them secure from attackers with quantum computers.
Let f(x) = y - f: public function - x: private input - y: public output A ZK proof allows one to prove that they know an x such that f(x) =y without revealing the private input.