Zero-Knowledge Proofs

This chapter presents some of the most influential notions and results concerning zero-knowledge (ZK) proofs, discussing both theoretical and practical achievements. ZK proofs are extremely powerful. They can be used to enforce honest computations and therefore they simplify the task of designing cryptographic protocols. The protection of the confidentiality of the input in a proof system can be defined in several ways. The chapter overviews some notions that are easier to achieve compared to ZK. One of the most popular privacy-preserving proof systems is known as ∑-protocol. It consists of three messages, is public coin and guarantees some special soundness and special honest-verifier ZK properties. The chapter discusses more demanding notions of ZK proof systems that offer additional features/security. The classical definition of a ZK proof system assumes that honest players are stateful and when playing the next message they know exactly the history of the conversation.