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
Famous quotes containing the word knowledge:
“Men look on knowledge which they learn—or might learn—from others as they do on the most beautiful structures which are not their own: in outward objects, they would rather behold their own hogsty than their neighbor’s palace; and in mental ones, would prefer one grain of knowledge gained by their own observation to all the wisdom of a thousand Solomons.”
—Sarah Fielding (1710–1768)
“The endless cycle of idea and action,
Endless invention, endless experiment,
Brings knowledge of motion, but not of stillness;
Knowledge of speech, but not of silence;
Knowledge of words, and ignorance of the Word.
All our knowledge brings us nearer to our ignorance.”
—T.S. (Thomas Stearns)