Zero-Knowledge Proofs

Zero-knowledge proofs are one of the more counterintuitive ideas in applied cryptography: it is possible to convince someone that a statement is true without revealing anything about why it is true. This chapter works through how that holds up mathematically and where it matters in practice—from the zk-SNARKs powering Zcash’s private transactions to the zk-STARKs behind StarkNet’s rollup architecture, along with Bulletproofs, commitment schemes, ring signatures, and verifiable random functions. By the end, you will have covered: