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A proof system can be used by a prover to demonstrate to one or more verifiers that a statement is true. Proof systems can be interactive where the prover and verifier exchange many messages, or non-interactive where the prover sends a single convincing proof to the verifier. Proof systems are widely used in cryptographic protocols to verify that a party is following a protocol correctly and is not cheating.

A particular type of proof systems are zero-knowledge proof systems, where the prover convinces the verifier that the statement is true but does not leak any other information. Zero-knowledge proofs are useful when the prover has private data that should not be leaked but needs to demonstrate a certain fact about this data. The prover may for instance want to show it is following a protocol correctly but not want to reveal its own input.

In these lecture notes we give an overview of some central …