A Survey of Zero-Knowledge Proofs with Applications to Cryptography

Zero-knowledge proofs are proofs that show a statement to be true without revealing anything other than the veracity of the statement to be proven. After a formal definition of zero-knowledge proof schemes and a simple example, zero-knowledge proofs for Graph Isomorphism and Graph 3-colorability are presented, the latter being the basis for the proof that all languages in NP have zero-knowledge proofs. The paper concludes with an application of zero-knowledge proofs in cryptography, the Fiat-Shamir Indentification Protocol, which is the basis for modern zero-knowledge entity authentication schemes.