Zero Knowledge
Not only can interactive proof systems solve problems not believed to be in NP, but under assumptions about the existence of one-way functions, a prover can convince the verifier of the solution without ever giving the verifier information about the solution. This is important when the verifier cannot be trusted with the full solution. At first it seems impossible that the verifier could be convinced that there is a solution when the verifier has not seen a certificate, but such proofs, known as zero-knowledge proofs are in fact believed to exist for all problems in NP and are valuable in cryptography. Zero-knowledge proofs were first mentioned in the original 1985 paper on IP by Goldwasser, Micali and Rackoff, but the extent of their power was shown by Oded Goldreich, Silvio Micali and Avi Wigderson.
Read more about this topic: Interactive Proof System
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