A zero-knowledge proof (ZKP) is a method of proving the possession of certain information, such as the solution to a mathematical problem, without revealing any information about the solution itself. The idea is to prove that the prover knows the information without revealing what the information is.
The most common form of zero-knowledge proof is the interactive proof, where a prover and a verifier engage in a conversation. The prover attempts to convince the verifier that they know the information in question, and the verifier checks the proof to ensure that it is valid.
A zero-knowledge proof typically consists of three parts: the statement to be proven (for example, “I know the solution to this mathematical problem”), a set of rules for the prover to follow (for example, a set of mathematical operations that the prover must perform), and a set of checks that the verifier can perform to ensure that the proof is valid.
The most common example of ZKP is the “ZK-SNARK” (zero-knowledge succinct non-interactive argument of knowledge), that enables a prover to prove possession of certain information, e.g. the solution to a computational problem, to a verifier, without revealing that information, and without any interaction between the prover and verifier after the proof construction.
It is widely used in blockchain and crypto-currency, such as Zcash, to enhance privacy and security.